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Veterinary epidemiology Third edition

Veterinary epidemiology THIRD EDITION

Michael Thrusfield Veterinary Clinical Studies Royal (Dick) School of Veterinary Studies University of Edinburgh

Blackwell Science

First edition © 1986 by Butterworth & Co. (Publishers) Ltd Second edition © 1995 by Blackwell Science Ltd Third edition © 2005,2007 by Blackwell Science Ltd,a Blackwell Publishing company Editorial offices: Blackwell Science Ltd,9600 Garsington Road,Oxford OX4 2DQ,UK Tel: +44 (0) 1865 776868 Blackwell Publishing Professional,2121 State Avenue,Ames,Iowa 50014-8300,USA Tel: +1 515292 0140 Blackwell Science Asia Pty,550 Swanston Street,Carlton,Victoria 3053,Australia Tel: +61 (0)3 8359 1011 The right of the Author to be identified as the Author of this Work has been asserted in accordance with the Copyright,Designs and Patents Act 1988. All rights reserved. N o part of this publication may be reproduced,stored in a retrieval system,or transmitted,in any form or by any means, electronic,mechanical,photocopying,recording or otherwise, except as permitted by the UK Copyright,Designs and Patents Act 1988,without the prior permission of the publisher. Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names,service marks,trademarks or registered trademarks of their respective owners. The Publisher is not associated with any product or vendor mentioned in this book. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold on the understanding that the Publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional should be sought. First published 1986 by Butterworth & Co. (Publishers) Ltd Second edition published 1995 by Blackwell Science Ltd Reissued in paperback with updates 1997 Reprinted 1999,2000,2001,2003 (twice) Third edition published 2005 Reissued in paperback with updates 2007 2

2008

ISBN: 978-1-405-15627-1 Library of Congress Cataloging-in-Publication Data (from the hardback third edition) Thrusfield,M.V. Veterinary epidemiology / Michael Thrusfield. - 3rd ed. p.

cm.

Includes bibliographical references and index. ISBN-13: 978-0-632-06397-0 (hardback: alk. paper) ISBN-1O: 0-632-06397-1 (hardback: alk. paper) 1. Veterinary epidemiology. SF780.9.T48

I. Title.

2005

636.089'44 -dc22

2005 004 105

A catalogue record for this title is available from the British Library Set in 10/12pt Palatino by Graphicraft Ltd,Hong Kong Printed and bound in Great Britain by TJ International Ltd,Padstow,Cornwall The publisher's policy is to use permanent paper from mills that operate a sustainable forestry policy,and which has been manufactured from pulp processed using acid-free and elementary chlorine-free practices. Furthermore,the publisher ensures that the text paper and cover board used have met acceptable environmental accreditation standards. For further information on Blackwell Publishing, visit our website: www.blackwellpublishing.com

To Marjory and Harriet, and in memory of David

Contents

From the preface to the first edition From the preface to the second edition Preface to the third edition The development of veterinary medicine Historical perspective

Evans' rules

37

xiii

Variables

38

XIV

Types of association

38

Confounding

40

Causal models

40

Formulating a causal hypothesis

42

Methods of deriving a hypothesis Principles for establishing cause: Hill's criteria

44

xii

1 1

43

Domestication of animals and early methods of healing Changing concepts of the cause of disease Impetus for change Quantification in medicine

10 11

Some basic terms Basic concepts of disease quantification

46

Contemporary veterinary medicine

Current perspectives The fifth period Recent trends

11

The structure of animal populations

50

16

Contiguous populations Separated populations

50

Measures of disease occurrence

53

1 2 4

16

2 The scope of epidemiology

22

Definition of epidemiology

22

The uses of epidemiology

23

Types of epidemiological investigation

25

Epidemiological subdisciplines

26

Components of epidemiology

28

Qualitative investigations Quantitative investigations

28

Epidemiology's locale

32

The interplay between epidemiology and other sciences The relationship between epidemiology and other

32

diagnostic disciplines Epidemiology within the veterinary profession 3 Causality

28

32 33 34

4 Describing disease occurrence

Prevalence Incidence The relationship between prevalence and incidence rate Application of prevalence and incidence values Mortality Survival Example of calculation of prevalence, incidence, mortality, case fatality and survival Ratios, proportions and rates Displaying morbidity and mortality values and demographic data

46

49

52 53 53 56 57 57 58 60 61 65

Mapping

65

Geographic base maps Geographical information systems

67

5 Determinants of disease

69 75

Philosophical background

34

Classification of determinants

75

Causal inference

35

Host determinants

78

Methods of acceptance of hypotheses

36

Genotype Age

78

Koch's postulates

37

79

i

Contents

Sex Species and breed Other host determinants

79

Trends in the temporal distribution of disease

80

87

Short-term trends Cyclical trends Long-term (secular) trends True and false changes in morbidity and mortality Detecting temporal trends: time series analysis

Environmental determinants

88

Trends in the spatial and temporal

Location Climate Husbandry Stress

88

Interaction

92

Biological interaction Statistical interaction The cause of cancer

93

81

Agent determinants

82

Virulence and pathogenicity Gradient of infection Outcome of infection Microbial colonization of hosts

82 85 86

88 90

distribution of disease

Spatial trends in disease occurrence Space-time clustering

144 144 144 145 146 146 150 150 151

91 9 The nature of data

152

Classification of data

152

Scales (levels) of measurement Composite measurement scales

153

Data elements

156 156

103

Nomenclature and classification of disease Diagnostic criteria Sensitivity and specificity Accuracy, refinement, precision, reliability and validity Bias

94 95

6 The transmission and maintenance of

155

infection

98

Horizontal transmission

98

Types of host and vector Factors associated with the spread of infection Routes of infection Methods of transmission Long-distance transmission of infection

98

105

Representation of data: coding

161

106

162

Vertical transmission

110

Types and methods of vertical transmission Immunological status and vertical transmission Transovarial and trans-stadial transmission in arthropods

110

Maintenance of infection

111

Code structure Numeric codes Alpha codes Alphanumeric codes Symbols Choosing a code Error detection

Hazards to infectious agents Maintenance strategies

111

7 The ecology of disease

100

110 110

112

10 Surveillance

158 159 160

162 163 164 165 165 166 168

Some basic definitions and principles

168 168

120

Definition of surveillance Goals of surveillance Types of surveillance Some general considerations

123

Sources of data

173

124

Mechanisms of surveillance

179

Surveillance networks

179

116

Basic ecological concepts

116

The distribution of populations Regulation of population size The niche Some examples of niches relating to disease The relationships between different types of animals and plants Ecosystems Biotope Types of ecosystem

116

Landscape epidemiology

132

Nidality Objectives of landscape epidemiology

132

126 130 130 130

169 169 171

Surveillance in developing countries: participatory epidemiology

Techniques of data collection Strengths and weaknesses of participatory epidemiology Some examples of participatory epidemiology

179 184 186 186

133 11 Data collection and management

8 Patterns of disease

157

137

188

Data collection

188 188

140

Questionnaires Quality control of data

142

Data storage

196

Epidemic curves

137

The Reed-Frost model Kendall's waves

195

Contents

196

249

Database models Non-computerized recording techniques Computerized recording techniques

197

Data management

201

Changing approaches to computing The Internet

201

Parametric and non-parametric techniques Hypothesis testing versus estimation Sample size determination Statistical versus clinical (biological) significance

203

Interval and ratio data: comparing means

252

Veterinary recording schemes

204

252

Scales of recording Veterinary information systems Some examples of veterinary databases and information systems

204

Hypothesis testing Calculation of confidence intervals What sample size should be selected? Ordinal data: comparing medians

254

Hypothesis testing Calculation of confidence intervals What sample size should be selected?

254 258

Nominal data: comparing proportions

258

198

205 207

1 2 Presenting numerical data

214

Some basic definitions

214

Some descriptive statistics

215

Measures of position Measures of spread

216 216

Statistical distributions

217

The Normal distribution The binomial distribution The Poisson distribution Other distributions Transformations Normal approximations to the binomial and Poisson distributions

217

218

Estimation of confidence intervals

220

The mean The median A proportion The Poisson distribution Some epidemiological parameters Other parameters Bootstrap estimates

218 218 219

Hypothesis testing Calculation of confidence intervals What sample size should be selected? X2 test for trend

249 250 250

252 253

257

258 261 261 262

Correlation

263

Multivariate analysis

264

Statistical packages

265

1 5 Observational studies

266

Types of observational study

266 266

220

Cohort, case-control and cross-sectional studies Ecological studies

221

Measures of association

269

221

269

223

Relative risk Odds ratio Attributable risk Attributable proportion

223

Interaction

274 275

219

221 222

269

270 272 273

Displaying numerical data

224

The additive model

Monitoring performance: control charts

224

Bias

276

Controlling bias

278

What sample size should be selected?

281

Calculating the power of a study

282

13 Surveys

228

Sampling: some basic concepts

228

Types of sampling

229

Non-probability sampling methods Probability sampling methods

230 230

What sample size should be selected?

232

Estimation of disease prevalence Detecting the presence of disease The cost of surveys

232

Calculation of confidence intervals

242

14 Demonstrating association

238 242

247

Some basic principles

247

The principle of a significance test The null hypothesis Errors of inference One- and two-tailed tests Independent and related samples

247 248 248 248 249

Calculating upper confidence limits

283

Multivariate techniques

284

The logistic model

284

16 Clinical trials

Definition of a clinical trial

289 289

Design, conduct and analysis

291

The trial protocol The primary hypothesis The experimental unit The experimental popUlation Admission and exclusion criteria Blinding Randomization Trial designs What sample size should be selected? Losses to 'follow-up'

291 291 293 294 294 294 295 296 297 298

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Fig.1. 3

League table of causes of human mortality in the UK:

(a) 1 860, (b) 1 900, (c) 1 9 70. (Data from Thrusfield, 2001 . )

'J

!

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The development of veterinary medicine

Qua ntification in m edicine

The evolution of understanding of the cause of disease purely qualitatively was accompanied by increased interest in disease in quantitative terms. This began primarily as a descriptive exercise. The ancient Japanese reported outbreaks of animal diseases. John Graunt (1662) published quantitative observations on London parish registers and 'Bills of Mortality'. An outbreak of rinderpest in France in the late 18th cen­ tury was responsible for the establishment of a com­ mission on epidemics, headed by Felix Vicq d'Azyr, Marie Antoinette's personal physician. This evolved into the Royal Society of Medicine, which pioneered the collection of statistical data on animal and human epidemics and the weather (Matthews, 1995). Post-Renaissance thinking and 'The Enlightenment'

The scientific revolution that began during the 1 6th century posited that the physical universe was orderly and could be explained mathematically (Dampier, 1948). This argument was extended to the biological world, where it was considered that 'laws of mortality' must exist. Graunt's mortality studies included attempts to formulate such laws by constructing life tables (see Chapter 4), Edmund Halley (1656-1742) constructed life tables for Breslau (Benjamin, 1959), and Daniel Bernoulli (1700-1 782) applied life-table methods to smallpox data, thereby demonstrating that inoculation was efficacious in conferring lifelong immunity (Speiser, 1982). A hundred years later, William Farr (Halliday, 2000) produced a simple mathematical model of the 1 865 rinderpest epidemic in the UK (see Chapter 19). Quantitative analysis of biological (including med­ ical) phenomena evolved in the 1 8th century, when the Age of Enlightenment saw a growth in literature dealing with the relationship between probability and the need for objectivity in science and society (the 'Prob­ abilistic Revolution'). The mathematical foundation of probability was laid by Jakob Bernoulli in his Ars Conjectandi, which was published posthumously in 1713. He developed a theory of 'inverse probability', which stated that the frequency of an event would approach its probability of occurrence if the number of observations was large enough. This theory was mathematically refined by Simeon-Denis Poisson, who proposed a 'law of large numbers', which stated that, if an event was observed a large number of times, one could assume that the probability of its future occur­ rence would correspond to its observed frequency. The logical consequence of this conclusion is that, if there are sufficient observations, sound predictions can be made. Thus, in relation to therapy, Pierre-Simon Laplace (1814) suggested that a preferred method of treatment 'will manifest itself more and more in the measure that the number (of observations) is increased'.

A pivotal move towards comparative statistical techniques occurred when Pierre-Charles-Alexander Louis developed his 'numerical method', requiring systematic record keeping and rigorous analysis of multiple cases (Bonett, 1973). He documented typhoid in Paris, showing that the disease occurred predomin­ antly in young adults, and that the average age of fatal cases was higher than that of survivors, suggest­ ing that the younger patients had the best prognosis (Louis, 1 836). He subsequently demonstrated that blood-letting was of no benefit to typhoid cases, and his calculation of average values was adopted by other early protagonists of clinical trials (e.g., Joseph Lister; see Chapter 1 6). Average values were also applied to provide a quantitative definition of a 'normal' indi­ vidual; Adolphe Quetelet (1835), for example, recorded the range of the human cardiac and respiratory rates. Application of probability theory to medicine was cautiously and tendentiously accepted by British and French medical statisticians, who were largely con­ cerned with the descriptive statistics of the major public health issues (e.g., Figure 1.3), rather than with statistical inference. Nevertheless, during the 19th century, strong links were forged between epidemio­ logists, mathematicians and statisticians through the common influence of Louis (Lilienfeld, 1978) 13, and, by the 20th century, rigorous methods of statistical infer­ ence were developing (Stigler, 1 986) and were being applied in medicine and agriculture. These methods necessitate observation of events in populations, rather than in the individual, and are thus central to the development of quantitative epidemiology (see Chapter 2). The formulation of physical and biological events, however, now, as then, needs to be very carefully assessed, and may convey an illusion of certainty and security that is not warranted (Gupta, 2001). Moreover, it is not always considered to be socially beneficial14, and is not a substitute for rigorous, albeit sometimes onerous, analysis of field data (The Eco­ nomist, 2002). Additionally, there may be a tendency to use whatever numerical data are available, regardless of their relevance and quality (Gill, 1993)15.

13 An interesting 'family tree', showing the links between 1 8th-20th century statisticians, public-health physicians and epidemiologists, is depicted by Lilienfeld and Lilienfeld ( 1 980).

14 See, for example, Gregory (2002) for a brief theological discussion. 15 Chambers (1997) amalgamates Gupta's and Gill's points, with sights set particularly on economists: 'Quantification alld statistics call mis­ lead, distract, be wasteful, simply not make sCllse or conflict with COlnlllOIi values . .. Yet professionals, especially economists and consultants tight for time, have a strong felt need for statistics. At worst they grub aroulld alld grab what lIum­ bers they can, feed them into their computers and prillt out not just numbers, but more and more elegant graphs, bar charts, pie charts allli three-dimensional wonders ... Numbers can also reassure by appCllrilig to extmd control, precision and knowledge beyond their real limits ... wrong numbers, one might add, are worst of all because al/numbers pose as true.' Porter (1 995) provides a philo­

sophical discussion of quantification in general.

Contemporary veterinary medicine

Table 1.4

Current trends in the distribution of some in fectious d iseases of an imals. ( Extracted main l y from Mulhern

Bl aha, 1 989; West, 1 99 5 ; and Radostits et al., 1 999.)

et al.,

I I

1 9 62; Knight, 1972;

Disease

Host

Trends

Anthrax

All animals, particu larl y

World -wide ran ge, now contracting to main l y tropics

devastati ng in cattle

and sub-tropics

Aujeszky's disease

Pigs

Spread in g, recently entered Japan

Bluetongue

Sheep

Spread ing for past 100 years

Bovine bruce l l osis

Cattle

Eradicated from many developed countries in recent decades

Contagious bovine

Cattle

Eradicated from much of Europe

pleuropneumonia Glanders

Horses

Mostly eradicated from developed countries

Johne's disease

Cattle, sheep, goats

World -wide distribution with increasing prevalence in some countries, and spread ing in Europe

Lumpy skin d isease

Cattle

Rabies

Al l mammals, some birds

Extending from Africa to the Middle East Eradication is problematic. Geographically isol ated areas (includ ing some island masses) are generally free, al though most countries experience rabies to some extent

Rift Valley fever

Cattle, sheep, goats, man

Rinderpest

Artiodactyls

Extendin g from Africa to the Middle East Only a few pockets of in fection remain ing. Global mass vaccination now ended

Sheep pox

Sheep

Eradicated from Europe in 1 9 5 1 . Presen t in AfricJ, Middle

Pigs

Decreased significance since 1982

East and India Swine vesicular disease Tuberculosis

Many species, especially

Eradication has proved problematic but some success has

serious in cattle

been achieved. No country is totally free of tubercul osis

Contemporary veterinary medicine Current perspectives Infectious diseases

Although there have been notable successes in the con­ trol of the infectious diseases, some still pose problems in both developed and developing countries (Table 1.4), and some continue to recur; for example, foot-and­ mouth disease (Table 1.5), which erupted most recently in western Europe with devastating consequences (notably in the UK) in 2001 (Table 1.1) . Some have emerged as major problems this century, although there is circumstantial evidence that the infectious agents have existed for some time (Table 1.6). Others are apparently novel (Table 1.7)16. Military conflict con­ tinues to be responsible for spreading these diseases 1h

(Table 1.2); for example, at the end of the Second World War, retreating Japanese soldiers brought rinderpest from Myanmar (Burma) to north-eastern Thailand. The infectious diseases are particularly disruptive in the developing countries, where more than half of the world's livestock are located (Table 1.8), accounting for over 80% of power and traction (Pritchard, 1986) and, in pastoral communities, at least 50% of food and income (Swift, 1988) (with milk, alone, accounting for up to 75% of human daily energy requirements: Field and Simkin, 1985). There have been some successes, for example, the JP1 5 campaign against rinderpest in Africa (Lepissier and MacFarlane, 1966), although the benefits of this campaign were subsequently negated by civil strife and complacency (Roeder and Taylor, 2002) and the disease has only recently been effectively tackled again (FAO, 1996), with the goal of global erad­ ication by 2010. Several vector-transmitted diseases

Emergent and novel infectious diseases may be classified together

that both ecological and genetic evolutionary changes can contribute to

as 'emerging diseases' : ' ... illfectiolls that have newly appeared in a popula­

the emergence of infectious diseases, but that ecological change is prob­

tion or have existed but are rapidly iI/creasing in il/cidence or geographic range'

ably the more general explanation for new epidemics (probably because

(Morse, 1995). Infectious diseases may emerge either as a result of genetic

ecological changes are less constrained than evolutionary changes in

changes in infectious agents or their hosts (see Chapter 5) or following

hosts and pathogens).

ecological changes (see Chapter 7). Schrag and Wiener ( 1 995) conclude

I}

The development of veterinary medicine

Table 1.5

Number of outbreaks of foot-and-mouth disease in the United Kingdom, 1 892-2001 .

Year

Outbreaks

Year

Outbreaks

1 89 2

95

1912

83

1 932

1 89 3

2

1913

2

1 933

25

1 95 2

495

87

1 95 3

1 89 4

3

1914

27

1934

40

79

1 954

1 895

1915

56

12

1 935

56

195 5

1 89 6

1916

9

1

1 936

67

1 95 6

1 62

1 89 7

1 898

1 91 7

1937

187

1 95 7

1 84

1918

3

1 938

1 90

1 9 58

116

1 899

1 9 00

21

1919

75

1 939

99

1959

45

1 920

13

1 940

1 9 60

298

1 921

44

1941

100 264

1901

12

1 9 02

1

1 9 61

1 03

1 9 22

1 1 40

1 942

670

1962

1 903

1 9 23

5

1 929

1 943

27

1 9 63

1904

1 9 24

1 905

1 925

260

1 906

1 9 26

204

1907

1 927

1 43

Year

Year

Outbreaks

Outbreaks

1944

181

1 9 64

1 945

1 29

1 9 65

1 946

64

1966

34

1 947

104

1 9 67

2210 1 87

1 9 08

3

1 928

1 38

1 948

15

1 9 68

1 9 09

1 9 29

38

1 949

15

1969 -2000

1910

2

1 9 30

8

1 95 0

20

2001

19

1 931

97

1 95 1

116

191 1

It 2030

t An isolated ou tbreak occurrin g on the Isle of Wight in 1 98 1 .

Table 1.6

Some emergent infectious diseases and p l agues of animals in the 20th Century.

Year

Country

Infection

1907

Kenya

African swine fever

Montgomery (1921)

1910

Kenya

Nairobi sheep disease

Montgomery (1 9 1 7) Shope (1 931 )

Source

1918

US

Swine influenza

1929

South Africa

Lumpy skin disease

Thomas and Mare (1 9 45 )

1 9 29

US

Swine pox

McNutt et al. (1 929) Kissling et al. (1 954)

1 930

US

Eastern equine encephalomyelitis

1 930

US

Western equine encephalomyelitis

Kissling (1 958)

1 932

US

Vesicu l ar exanthema of pigs

Traum (1 936) Sigu rdsson (19 5 4)

1 933

Iceland

Maedi-visna

1 9 39

Colombia

Venezuelan equine encephal omyelitis

Kubes and Rios (1 939)

1 946

Canada

Mink enteritis

Schofield (1949)

1 947

US

Transmissible mink encephalopathy

Hartsough and Burger (1965)

1 95 3

US

Bovine mucosal disease

Ramsey and Chivers (1 95 3)

1 95 5

US

Infectious bovine rhinotracheitis

Miller (1 9 5 5 )

1 95 6

Czechoslovakia

Equ ine influenza A (H7N7)

Bryans ( 1 9 64)

1 9 62

France

West Nile equ ine encephalomyel itis

Panthier (1968)

1 9 63

US

Equine influenza A (H3N8)

Bryans (1 9 64) Martin et al. (1 966)

1966

UK

Bovine u lcerative mammillitis

1 9 72

Iran

Camel pox

Baxby (1 972)

1 9 72

US

Lyme disease

Steere et al. (1 977)

1 9 74

Kenya

Horsepox

Kaminjolo et al. (1 974)

1 9 75

South Africa

Haemorrhagic Rift Valley fever

Van Velden et al. (1 977)

1 9 77

Worl dwide

Canine parvovirus

Eugster et al. ( 1 9 78)

1 9 77

USSR

Cat pox

Marenn ikova et al. (1 977) McFerran et al. (1980)

1 98 0

UK

Infectious bu rsitis-2

1 98 1

Zimbabwe

Mokola virus infection

Foggin (1 983)

1 983

US

Fulminating avian influenza (H5N2)

Buisch et al. (1 984)

1 985

Denmark

Danish bat rabies (Duvenhage)

Grauballe et al. (1 987)

1 98 6

UK

Bovine spongiform encephalopathy

Wells et al. (1 987)

1 98 6

US

Cache Valley teratogenesis

Chu ng et al. (1 991 )

Contemporary veterinary medicine

Table 1.7

Some novel in fectious d iseases and pl agues of animals in the 20th Century.

Year

Country

Infection

Source

1 907

Hungary Kenya

Marek's d isease

19 1 2

Marek ( 1907) Daubney etal. ( 1 931 )

1923

The Netherlands

Duck p l ague

Baudet ( 1 9 23)

1925 1 926

US java France

Avian l aryngotracheitis Newcastle d isease Fel ine panleukopenia

May and Tittsler ( 1 9 25 ) Doyle ( 1 9 27) Verge and Cristoforoni ( 1 928)

US

Avian encephalomyelitis

jones ( 1 9 32)

Avian infectious bronchitis Equine virus abortion Turkey haemorrhagic enteritis

Schal k and Hawn (1931 ) Dimock and Edwards ( 1932) Pomeroy and Fenstermacher (1937)

1942

US US US Ivory Coast

Goat plague (peste des petits ruminants)

Gargadennec and Lalanne ( 1942)

1945

US

Duck virus hepatitis-1

Levine and Fabricant (1950)

1945 1 946

US US

Transmissible gastroenteritis of pigs Bovine virus d iarrhoea

Doyle and Hutchings ( 1 9 46) Ol afson et al. ( 1 9 46) Hartsough and Gorham ( 1 9 5 6) Rubarth ( 1 9 47)

1 928 1 930 1 930 1 932 1 937

Rift Valley fever

1946

US

Aleutian d isease of mink

1 947

Sweden

In fectious can ine hepatitis

1 95 0 1 95 1

US US US

1953 195 4

Avian aden ovirus-1 Turkey bluecomb d isease Feline infectious anaemia Akabane d isease

Olson ( 1 9 5 0) Peterson and Hymas ( 1 9 5 1) Flint and Moss (1953) Miura et al. ( 1 974)

195 4

japan Canada

Avian reovirus

Fahey and Crawley (1954)

1 956

China

Goose pl ague

1 95 7

Fel ine cal icivirus

1 95 8

US US

Fang and Wang (198 1 ) Fastier ( 1 9 5 7)

Fel ine viral rhinotracheitis

Crandell and Maurer ( 1 9 5 8 )

1959

Canada

Turkey viral hepatitis

Mongeau et al. ( 1959)

1959

japan

Ibaraki disease

Omori et al. (1969)

1960

Israel

Turkey meningoencephalitis

1 9 62

US

Bovine aden ovirus-1 ,2

Komarov and Kalmar ( 1 960) Klein ( 1 962)

1 9 62

US

1 964 1 9 64

UK UK

Avian in fectious bursitis-1 Fel ine leukaemia

Cosgrove ( 1 962) jarrett et al. ( 1 9 64)

1965 1965

UK US

1 9 65

US Italy

1966 1 967 1 9 67

UK UK

Porcine adenovirus

Haig et al. ( 1 9 64)

Duck virus hepatitis-2 Canine herpes

Asplin ( 1 9 65 ) Carmichael et al. ( 1 965)

Porcine enteroviruses

Dunne et al. (1965)

Swine vesicular d isease Porcine parvovirus

Nardelli etal. ( 1 968) Cartwright and Huck ( 1 9 67)

Border d isease in sheep

Dickinson and Barlow ( 1 967)

1 9 67

US

Chronic wasting d isease of deer

Will iams and Young ( 1 980)

1968 1 9 69

Canada US UK

Bovine adenovirus-3 Duck virus hepatitis-3 Lymphoproliferative d isease of turkeys

Darbyshire ( 1 968) Toth (1969)

US

Equine adenovirus

McChesney et al. ( 1 9 73)

US US japan

Feline herpes urol ithiasis

1974 1 9 74

Caprine arthritis-encephalitis Kunitachi v irus

Fabricant and Gillespie (1974) Cork et al. ( 1 974)

1 9 76

The Netherlands

Egg-drop syndrome

Van Eck et al. (1976)

1 976

japan

Avian infectious nephritis

Yamaguchi et al. ( 1 979)

1 977 1977 1978

US Ireland Iraq

Chicken parvovirus Contagious equine metritis Pigeon paramyxovirus-1

1 9 79

japan

1 98 1

US China

Chick anaemia age n t Canine cal icivirus

Parker et al. (1977) O'Driscoll et al. ( 1 9 77) Kaleta et al. ( 1 9 8 5 ) Yuasa e tal. ( 1 979)

1 9 72 1 973 1 974

1984

Rabbit haemorrhagic d isease

Biggs et al. ( 1 9 74)

Yoshid a et al. ( 1 9 77)

Evermann et al. ( 1 981) Liu et al. ( 1 984) Rikihisa and Perry ( 1 9 8 5 )

US

Potomac horse fever

1 985

UK japan

Chuzon d isease of cattle

Anon. ( 19 8 5 ) Miura et al. ( 1 990)

1985 1 985

Rhinotracheitis of turkeys

1 98 7

USSR

Phocid d istemper-2 (Baikal)

Grachev et al. ( 1 989)

1987 198 7

US

Keffaber (1989)

US

Porcine reproductive and respiratory syndrome Morbi l l ivirus of dol phins

1 988

The Netherl ands

Phocid d istemper-1 ( North Sea)

Lipscomb et al. ( 1 994) Osterhaus and Vedder ( 1 988)

1 990

The Netherl ands Australia

Bovine birnavirus Hendra virus ( formerl y equine morbil l ivirus)

Vanopdenbosch and Wel lemans (1990)

1994 1 995

New Zealand

Wobbly possum disease virus

Anon. (1997)

1996

US

Porcine wasting d isease synd rome

Daft et al. ( 1 996)

Murray et al. ( 1 9 9 5 )

I j

,

The development of veterinary medicine

"

Table 1.8

World l ivestock popul ations, 2001 ( 1OOOs of animals). (From FAO, 2002.)

Cattle

Sheep

Goats

Pigs

Horses

Buffaloes

Chickens

110 223

7 8 05

1 380

71 738

5 68 5

5 0 453

7 5 22

12 308

25 707

8 45 3

716 000

5

South America

308 5 69

75 312

22 148

5 5 399

15 651

1 765 000

1 151

US and Canada Central America

Camels

1 988 000

Europe

143 8 5 8

144 812

17 904

194 15 3

7 010

1 746 000

230

12

Africa

230 047

25 0 147

218 625

18 467

4 8 79

1 276 000

3 430

15 124

Asia

470 920

406 5 8 4

406 5 8 4

5 5 2 372

16 302

7 25 0 000

160 892

4 198

37 722

164 001

684

5 09 4

376

119 000

1 35 1 792

1 05 6 184

738 246

922 929

5 8 244

14 859 000

165 724

19 334

Oceania All parts of the world

Table 1.9

The livestock population of Great Britain, 1866-19 9 7 (1OOOs of animals). (From HMSO, 1968, 1982, 1991, 1998.)

Year

Cattle

Sheep

Horses

Pigs

Fowls

Turkeys

(agricultural use)

1866

4 78 6

22 048

2 478

1900

6 805

26 592

2 382

1 078

1925

7 368

23 094

2 799

910

39 036

730

1950

9 630

19 714

2 463

347

71 176

855

21

1965

10 826

28 837

6 731

101 9 5 6

4 323

1980

11 919

30 385

7 124

115 895

6 335

1989

10 5 10

38 869

7 39 1

121 279

1997

9 9 02

39 943

7 375

111 566*

- Data not available. * 1995 figure. (A new approach to collecting poultry in formation began in 1997, preventing direct comparisons with previous years.)

with complex life-cycles, including haemoprotozoan infections such as trypanosomiasis, have not been controlled satisfactorily17. The techniques of the micro­ bial revolution have enabled these diseases to be identified. However, accurate means of assessing the extent and distribution of the diseases also are neces­ sary in order to plan control programmes (e.g., the Pan-African Rinderpest Campaign: IAEA, 1 991). Some infectious diseases, for example brucellosis and tuberculosis, persist at low levels in developed countries, despite the application of traditional control methods. This problem can result from inadequate survey techniques and insensitive diagnostic tests (Martin, 1977). In some cases, an infectious agent may have a more complex natural history than initially sus­ pected. For example, continued outbreaks of bovine

tuberculosis in problem herds in England (Wilesmith et al., 1982) have been shown to be associated with pockets of infection in wild badgers (Little et al., 1982;

Krebs, 1997), which has resulted in a somewhat con­ tentious control strategy of badger culling (Donnelly et al. , 2003; DEFRA, 2004). The effective control of the major infectious dis­ eases has allowed an increase in both animal numbers (Table 1.9) and productivity (Table 1.10) in the devel­ oped countries (mechanization making draft horses the exception)18. There has been an increase in the size of herds and flocks, notably in dairy, pig (Table 1.11) and poultry enterprises. Intensification of animal industries is accompanied by changes in animal health problems. Complex infectious diseases

17

The reasons for lack of progress in the control of animal diseases in

developing countries are complex, including more than lack of technical

The animal plagues are caused by 'simple' agents, that is, their predominant causes can be identified as single

feaSibility. Insufficient applied research to solve field problems, poor information, and neglect of farmers' needs and the requirement for farmer participation in disease control, all contribute to the problem (Huhn and Baumann, 1 996; Bourn and Blench, 1999). With the demand

1R

Some earlier improvements in productivity had occurred as a

for livestock products in developing countries estimated to double by

consequence of improved nutrition. For example, in England in the 18th

2020 (Delgado et aI., 1999), the supply of livestock services, including vet­

century, more land was planted with high-yielding roots (e.g., turnips)

erinary services, is likely to increase in importance, and issues such as

and new types of grass, enabling animals to be fed adequately through­

privatisation (Holden

et

al., 1 996) and delivery to the poor (Ahuja and

Redmond, 2004) will require close scrutiny.

out the year. The average weight of an ox at London's Smithfield Market increased from 370 lb in 1 710 to 800 lb in 1 795 (Paston-Williams, 1993).

Contemporary veterinary medicine

Table 1.10

World cattle productivity, 2001. (From FAO, 2002.)

Number of animals slaughtered (1ODDs ofanimals)

Carcass weight (kg/anima/)

Milk yield (kg/animal)

Milk production (1 ODDs metric tonnes)

US

36 690

327

8 226

75 025

South America

55 369

2 13

1 580

47 055

Asia

78 380

143

1 232

96 674

Africa

27 255

149

486

18 645

Europe

53 447

219

4 149

2 10 193

12 408

2 14

4 232

24 623

277 353

204

2 206

493 828

Oceania All parts of the world

Table 1.11

I)

Pig herd structure in England and Wales (June). (Data supplied by the Meat and Livestock Commission.)

1965 Number of farms with pigs Total sows (1 OOOs) Average herd size (sows)

94 639

1971 56 900

1975 32 29 1

1980 22 973

1991 13 738

1999 10 460

756.3

791.0

686.0

70 1. 1

672.4

580.5

10.4

18.5

27.6

4 1.4

70.4

86.3

Number of herds by herd size (sows): 1-49

56 560 (75.4%)

39 000 (90.9%)

20 873 (84.0%)

12 900 (76.3°;'»)

6 47 1 (67.8'Yo)

4 7 14 (70.1%)

50-99

10 445 ( 13.9%)

2 700 (6.3%)

2 40 1 (9.7%)

2 000 ( 1 1 .8%)

1 050 ( 1 1 .0%)

522 (7.8%)

100-199

8 034 ( 10.7%)

1 000 (2.3%)

1 14 1 (4.6%)

1 300 (7.7%)

1 1 15 (1 1.7%)

581 (8.6%,)

200 (0.5%)

426 ( 1.7%)

700 (4.1%)

200 and over

Total number of herds with sows

75 039

42 900

infectious agents. Diseases caused by single agents still constitute problems in developed countries. Examples include salmonellosis, leptospirosis, babesiosis and coccidiosis. However, diseases have been identified that are produced by simultaneous infection with more than one agent (mixed infections), and by inter­ action between infectious agents and non-infectious factors. These are common in intensive production enterprises. Diseases of the internal body surfaces - enteric and respiratory diseases - are particular problems. Single agents alone cannot account for the pathogenesis of these complex diseases. Subclinical diseases

Some diseases do not produce overt clinical signs although often affect production. These are called subclinical diseases. Helminthiasis and marginal min­ eral deficiencies, for example, decrease rates of live­ weight gain. Porcine adenomatosis decreases growth in piglets, although there may be no clinical signs (Roberts et ai., 1979). Infection of pregnant sows with porcine parvovirus in early pregnancy destroys fetuses, the only sign being small numbers of piglets in litters. These diseases are major causes of production loss; their identification often requires laboratory investigations.

24 84 1

16 900

9 14 (9.5%) 9 550

9 1 1 ( 13.5%) 6 728

Non-infectious diseases

Non-infectious diseases have increased in importance following control of the major infectious ones. They can be predominantly genetic (e.g., canine hip dys­ plasia), metabolic (e.g., bovine ketosis) and neoplastic (e.g., canine mammary cancer). Their cause may be associated with several factors; for example, feline urolithiasis is associated with breed, sex, age and diet (Willeberg, 1977). Some conditions, such as ketosis, are particularly related to increased levels of production; ketosis is more likely in cows with high milk yields than in those with low yields. Intensive production systems may also be directly responsible for some conditions, for example foot lesions in individually caged broilers (Pearson, 1983). Diseases of unknown cause

The cause of some diseases has not been fully elucid­ ated, despite intensive experimental and field investigations over many years. Examples include the related diseases, feline dysautonomia (Edney et ai., 1987; Nunn et ai., 2004) and equine grass sickness (Hunter et al., 1999; McCarthy et ai., 2001; Wlaschitz, 2004).

Ib

The development of

medicine

In some situations, infectious agents have been isolated from cases of a disease but cannot be unequi­ vocally associated with the disease. An example is Mannheimia haemolytica (previously named Pasteurella haemolytica) in relation to 'shipping fever' (Martin et al., 1982). This syndrome occurs in cattle soon after their arrival at feedlots. Post-mortem examination of fatal cases has revealed that fibrinous pneumonia is a common cause of death. Although M. haemolytica is frequently isolated from lungs, it is not invariably pre­ sent. Attempts to reproduce the disease experiment­ ally are fraught with problems, not the least of which is the difficulty of establishing colonization of the nasal tract with the bacterium (Whiteley et al., 1992). Other factors also seem to be involved (Radostits et al., 1999). These include mixing animals and then penning them in large groups, the feeding of corn silage, dehorning, and, paradoxically, vaccination against agents that cause pneumonia, including M. haemolytica - factors associated with adrenal stress (see Figure 3.5b and ChapterS). Management and environment also appear to play significant, although often not clearly defined, roles in other diseases. Examples include enzootic pneumonia and enteritis in calves (Roy, 1980), enteric disease in suckling pigs, porcine pneumonia, bovine mastitis associated with Escherichia coli and Streptococcus u beris (Blowey and Edmondson, 2000b) and mastitis in intensively housed sows (Muirhead, 1976). In some instances, the infectious agents that are isolated are ubiquitous and also can be isolated from healthy animals, for example, enteric organisms (Isaacson et al., 1978). These are 'opportunistic' patho­ gens, which cause disease only when other detrimen­ tal factors are also present. In all of these cases, attempts to identify a causal agent fulfilling Koch's postulates frequently fail, unless unnatural techniques, such as abnormal routes of infection and the use of gnotobiotic animals, are applied. The fifth period

The animal-health problems and anomalies that emerged in the 20th century stimulated a change, which began in the 1960s, in attitude towards disease causality and control. Causality

The inappropriateness of Koch's postulates as criteria for defining the cause of some syndromes suggested that more than one factor may sometimes operate in producing disease. A multifactorial theory of disease has developed, equally applicable to non-infectious

and infectious diseases. Interest in human diseases of complex and poorly understood cause grew in the early years of the 20th century (Lane-Claypon, 1926) and was responsible for the development of new methods for analysing risk factors, for example smok­ ing in relation to lung cancer (Doll, 1959), and these epidemiological techniques are now firmly established in veterinary medicine, too (e.g., in the investigation of risk factors for respiratory disease in pigs: Shirk, 2000). There is also now an awareness that the causes of disease include social, geographical, economic and political factors, as well as biological and physical ones (Hueston, 2001). For instance, although bovine spongi­ form encephalopathy subsequently spread to main­ land Europe, its initial emergence in the UK (Table 1.6) was the result of recycling infective meat and bone meal to cattle, and this practice was extensive because meat and bone meal was an inexpensive source of high-quality protein in cattle rations in a country that had heavily intensified and in which plant proteins were limited. Likewise, bovine tuberculosis is a mani­ fest and expanding problem in white-tailed deer in north-eastern Michigan in the US because the deer populations have increased as a result of feeding pro­ grammes established to serve the hunting industry that has replaced cattle farming in this economically deprived area. New control strategies

Two major strategies have been added to the earlier techniques (Schwabe, 1980a,b): 1. 2.

the structured recording of information on disease; the analysis of disease in populations.

These methods involve two complementary ap­ proaches: the continuous collection of data on disease - termed surveillance and monitoring and the intensive investigation of particular diseases. A fur­ ther technique, used at the individual farm level, is the recording of information on both the health and productivity of each animal in a herd, as a means of improving production by improving herd health. -

Recent trends

Several recent trends have occurred in relation to the services that the veterinarian supplies to his clients, and to national and international disease reporting. Veterinary services

Veterinarians practising in the livestock sector con­ tinue to control and treat disease in individual

Contemporary veterinary medicine

1

/

20 _1980 15 Fig.1.4

Areas of empl oyment of

veterinarians in the US, 1980 and 1990. LAE: exclusivel y large animal;

LAP: predominantly l arge animal; MIX: mixed practice; SAP: predominantly small animal; SAE: excl usivel y smal l animal; EQ: equine; OPP: other private practice;

., � c ., os"C

0': a � ., .- :::J !� �t::.

�1990

10

5

UNI: university; FC: federal government; SLC: state or l ocal government; US: uniformed services; IND: industry; OPC: other public and corporate. (From Wise and Yang, 1992.)

animals. Developments in molecular biology are improving diagnostic procedures (Goldspink and Gerlach, 1990), and offer new opportunities for vaccine production (Report, 1 990). Additionally, in intensive production systems, the multifactorial nature of many diseases necessitates modification of the environment of the animal and management practices, rather than concentrating exclusively on infectious agents. Diseases of food animals are also being considered directly in relation to their effect on production. Reduced levels of production can be used as 'diag­ nostic indicators', for example small litter size as an indicator of infection with porcine parvovirus. More significantly, veterinary emphasis has shifted from disease as a clinical entity in the individual animal to disease assessed in terms of suboptimal health, manifested by decreased herd performance: disease is being defined as the unacceptable performance of groups of animals. There is thus a need to identify all factors that contribute to the occurrence of disease, to select suitable 'performance indicators' (e.g., 'calving to conception interval'), and to define targets for these indicators in herds under a particular system of hus­ bandry. It is then possible to identify those herds that miss the targets. This is called performance-related diagnosis (Morris, 1982), and includes not only the measurement of overt indicators, such as liveweight gain, but also estimation of covert biochemical values, such as metabolite levels in serum. Thus, clinical disease, subclinical disease and production need to be monitored in the context of anticipated ('normal') levels for a particular production system (Dohoo, 1 993). The veterinarian therefore has become more involved in husbandry, management and nutrition than previously, and less involved in traditional 'fire brigade' treatment of clinically sick animals. However, the livestock owner frequently still regards the veter­ inarian solely as a dispenser of treatment (Goodger

LAE LAP MIX SAP SAE EQ OPP UNI

FG

SlG US

INO ope

Primary employment

and Ruppanner, 1982), relying on feed representatives, dairy experts and nutritionists for advice on breeding, nutrition and management. The extent of this problem varies from one country to another, but indicates that the veterinarian's evolving role in animal production requires a change not only in veterinary attitudes but also sometimes in those of animal owners. Government veterinary services, too, are becoming increasingly concerned with investigations of specific animal health problems of complex cause, such as mastitis, thereby extending their role beyond the tradi­ tional control of mass infectious diseases. As the mass infectious diseases are controlled, and animal production becomes more intensive, other diseases become relatively more important. They are currently major problems in developed countries, and in some developing countries that have intensive enter­ prises, such as poultry and pig units in Malaysia, the Philippines and Taiwan. These diseases will become increasingly significant in the developing countries when the mass infectious diseases are controlled. Attention is being focussed on the health of compan­ ion animals, particularly in the developed countries (e.g., Heath, 1998) 19. This is reflected in the employ­ ment trends in the veterinary profession (Figure 1.4). Many health problems of companion animals are complex too, and a full understanding of their cause and control is possible only when the contribution of genetic and environmental factors is appreciated. Examples include urinary tract infections in bitches, in which concurrent disease and recent chemother­ apy are important factors (Freshman et ai., 1989), and equine colic, which is related to age and breed (Morris et ai., 1989; Reeves et ai., 1989). Problems of veterinary 19 In many developing countries, private veterinary practice remains a minority employer of veterinarians, with companion animals of little significance (e.g., Turkson, 2003).

18

The development of veterinary medicine ------

Fig.l.5

A Victorian satire: Microcosm dedicated to the London Water Companies' Monster soup commonly called Thames Water' by George

Cruikshank (1792-1878). British Museum, London UK/Bridgeman Art Library.

interest now extend beyond clinical conditions to wider social issues, such as the biting of children by dogs (Gershman et al., 1994), and animal welfare (see below). Additionally, veterinary services have an enlarging responsibility for human health, including preventing and controlling emerging zoonotic diseases, and addressing antibiotic resistance (an area of endeavour that has been traditionally labelled veterinary public health), and protecting the environment and ecosys­ tems (Chomel, 1998; Marabelli, 2003; Pappaioanou, 2004). Food quality

A particular area of concern in veterinary public health is food quality. The public's concern about what it con­ sumes is not new (Figure 1.5). However, during the last two decades of the 20th century, concern increased because of major outbreaks of foodborne infections of animal origin (Cohen, 2000). Examples include an out­ break of salmonellosis affecting over 200 000 people in the US in 1994, and Escherichia coli 0157:H7 infection

affecting over 6000 schoolchildren in Japan in 1996 (WHO, 1996). Other emerging foodborne pathogens include Cryptasparidium and Campylabacter spp. (Reilly, 1996) and Listeria manacytagenes (WHO, 1996). Additionally, the emergence of bovine spongiform encephalopathy, with its putative role as the cause of the fatal human disease, variant Creutzfeldt-Jakob disease (Will, 1997), has served to heighten public concern over food safety. In several western countries, this has led to the establishment of Food Standards Agencies whose remit is to oversee food quality. The veterinarian's role is now extended beyond guaranteeing wholesomeness of food at the abattoir, and addresses all levels of the production chain, from the farm to the table ('from paddock to plate') (Smulders and Collins, 2002, 2004). This necessitates the establishment of quality assurance programmes on the farm, using techniques such as HACCP (Hazard Analysis Critical Control Points) (Noordhuizen, 2000), thus marking a shift in focus from herd health, alone, to quality control of food throughout the production chain (Figure 1.6). This approach is strengthened by quantitative evaluation of the risk of transmission

Contemporary veterinary medicine

High

I

(j

Focus on the food

Standardization and certification of herd health, food safety and food quality

Consumer concerns with food safety and food quality Increasing herd health and productivity

Focus on the

Treating diseases

Low

1950

1900 Fig.l.6

1990

2000

The changing focus of veterinary medicine practised in livestock, in relation to consumer concerns with food quality. (Reprinted

from Preventive Veterinary Medicine, 39, Blaha, Th., Epidemiology and quality assurance application to food safety, Copyright © (1999), with permission from Elsevier Science.)

of infection throughout the chain (see Chapter 2: 'Microbial risk assessment'). Animal welfare

The attitude of the public to animals (notably in devel­ oped countries) is reflected in contemporary concern for animal welfare, both among the scientific com­ munity (Moss, 1994; Appleby and Hughes, 1 997) and the general public (Bennett, 1996) 2°. This encompasses health and 'well-being' (Ewbank, 1986; Webster, 2001) 21. The latter term is difficult to define, and is also included in the Worl d Health Organization's definition of human health (Old English: hal whole) as 'a state of complete physical, mental and social well-being and not merely the absence of disease or infirmity' (WHO, 2003). Although this definition was not designed to be =

20

Concern for the welfare of animals is not just recent, though. In 1 790,

for example, there was public outrage over the wastage of horses in the British Army, which was losing more animals from disease and lack of care than from enemy action. This resulted, in 1 795, in the Army directing that a veterinarian should be attached to each regiment. (The first to enlist as an Officer was John Shipps in 1796.) The shortage of trained veterin­ arians was so acute that London's Royal Veterinary College temporarily reduced its period of training from three years to three months. 21

Animal welfare is therefore assessed primarily biologically, and is

distinct from 'animal rights', which is an ethical and philosophical issue (Singer, 2000).

a framework for formulating goals of health policy (Noack, 1987), it illustrates that health is more than just absence of disease. Obvious aspects of animal welfare are deliberate physical abuse (non-accidental injury) and neglect; contentious topics are surgical mutilation, such as tail docking of dogs (Morton, 1 992), horses (Cregier, 1990) and pigs (Day and Webster, 1998), and velvet antler removal from deer (Pollard et al., 1 992). Companion animals are known to suffer a wide range of types of physical abuse (Munro and Thrusfield, 2001a,b,c) and sexual abuse (Munro and Thrusfield, 2001d) which are remarkably similar to those found in child abuse, and the link between abuse of animals and abuse of children is becoming recognized (Ascione and Arkow, 1999). Other animal-welfare issues may be more subtle; for example, the relationship between bovine mastitis and use of bovine somatotropin to increase milk production (Willeberg, 1993, 1997). Welfare in livestock production systems is often evaluated in the context of the 'five freedoms' (Spedding, 2000): 1. 2. 3. 4. 5.

freedom from hunger and thirst; freedom from discomfort; freedom from pain, injury and disease; freedom to express normal behaviours; freedom from fear and distress.

)

The development of veterinary medicine

Behavioural problems may be associated with intensive husbandry systems; for example, cannibal­ ism in laying hens (Gunnarsson et al., 1998), but there may be less tangible issues (Ewbank, 1986) such as behavioural deprivation in sows tethered in stalls. The move towards organic farming in some western countries is justified, in part, by improved animal welfare (Sundrum, 2001), and the veterinarian there­ fore is concerned with disease, productivity and well­ being, all of which can be interrelated, in all types of production system (Ewbank, 1 988) . National and international disease reporting

There is a requirement for improved disease report­ ing systems at the national and international level to identify problems, define research and control prior­ ities and assist in the prevention of spread of infectious agents from one country to another. Additionally, residues need to be identified and eliminated (WHO, 1993). These include contamination of meat by pesti­ cides (Corrigan and Seneviratna, 1989) and hormones (McCaughey, 1992), as well as the more long-standing issue of antibiotic residues, with the attendant prob­ lem of antibiotic resistance (Hugoson and Wallen, 2000; Teal, 2002). The move towards a free internal market in the European Union (Anon., 1992), and global goals to lib­ eralize international trade through the World Trade Organization (WTO), are highlighting the requirement for comprehensive disease reporting, and govern­ mental veterinary services are responding to this need (DEFRA, 2002c). If liberalization is achieved, it will have advantageous effects on world trade, including that in livestock commodities (Page et al., 1 991). An important component of free trade therefore is assess­ ment of the risk of disease and related events (e.g., carcass contamination) associated with the importa­ tion of animals and animal products (Morley, 1993). Established organizations, such as the Office Inter­ national des Epizooties (OlE), are modifying their goals and reporting techniques, taking account of these new requirements (Blajan and Chillaud, 1991; Thiermann, 2005). The advent of low-cost computing following the microelectronic revolution offers powerful means of storing, analysing and d istributing data. Information can be transported rapidly using modern communica­ tions systems. These developments increase the scope for efficient disease reporting and analysis of the many factors that contribute to clinical disease and sub­ optimal production, both of which require increased statistical acumen among veterinarians. Epidemiology has developed to supply these contemporary veterin­ ary requirements.

Further reading Ainsworth, G.C (1986) Introduction to the History of Medical and Veterinary Mycology. Cambridge University Press, Cambridge Blancou, J. (2002) History of the control of foot and mouth disease. Comparative Immunology, Microbiology and Infectious Diseases, 25, 283-296 Blancou, J. (2003) History of the Surveillance and Control of Transmissible Animal Diseases. Office International des Epizooties, Paris. (Includes a global bibliography of veterinary writings from ancient times to the 15th century) British Veterinary Association Trust Project (1982) Future of Animal Health Control - The Control of Infectious Diseases in Farm Animals. Report of a symposium, University of Read­ ing, 14-16 December 1982. British Veterinary Association, London Brown, C and Bolin, CA. (2000) Emerging Diseases ofAnimals. ASM Press, Washington Burroughs, T., Knobler, S. and Lederberg, J. (Eds) (2002) The Emergence of Zoonotic Diseases: Understanding the Impact on Animal and Human Health. National Academy Press, Washington Cohen, M.L. (2000) Changing patterns of infectious disease. Nature, 406, 762-767 Cornelius, S.T. (2003) Emerging African animal diseases. Commonwealth Veterinary Association News, 19 (2), 44-50 Dorn, CR (1992) Veterinary epidemiology and its economic importance in A.D. 2000. Preventive Veterinary Medicine, 13, 129-136 Dunlop, RH. (2004) Bourgelat's vision for veterinary educa­ tion and the remarkable spread of the 'meme'. Journal of Veterinary Medical Education, 31, 310-322. (A brief history of veterinary education) Dunlop, RH. and Williams, DJ (1995) Veterinary Medicine: an Illustrated History. Mosby Year-Book, St Louis Faber, K. (1930) Nosography: The Evolution of Clinical Medicine in Modern Times, 2nd edn. Paul B. Hoeber, New York. Reprinted by AMS Press Inc., New York, 1978. (A history of concepts of pathogenesis) Fleming, G. (1871) Animal Plagues: Their History, Nature and Prevention. Chapman and Hall, London Fleming, G. (1882) Animal Plagues: Their History, Nature and Prevention, Vol. 2 (from AD 1 800 to 1 844). Bailliere, Tindall and Cox, London International Atomic Energy Agency (1998) Towards Livestock Disease Diagnosis and Control in the 21st Century. Proceed­ ings of an international symposium on the diagnosis and control of livestock diseases using nuclear and related techniques jointly organized by the International Atomic Energy Agency and the Food and Agriculture Organiza­ tion of the United Nations and held in Vienna, 7-1 1 April, 1997. International Atomic Energy Agency, Vienna

Jackson, R (2002) Veterinary epidemiology in New Zealand: a 50-year perspective. New Zealand Veterinary Journal, 50 (3) (Supplement), 13-16 Karasszon, D. (1988) A Concise History of Veterinary Medicine. Akademiai Kiad6, Budapest MacIntyre, D.K. and Breitschwerdt, E.B. (Eds) (2003) Emerg­ ing and re-emerging infectious diseases. The Veterinary Clinics of North America, Small Animal Practice, 33, 677-943

Contemporary veterinary medicine

,

j l

Matthews, J.R (1995) Quantification and the Quest for Medical Certainty. Princeton University Press, Princeton. (A history of the application of s tatistical methods in medicine)

ing of Measurement in the Natural and Social Sciences. Ed. Woolfe, H., pp. 85-107. The Bobbs-Merrill Company,

Melby, E.C (1 985) The veterinary profession: changes and challenges. Cornell Veterinarian, 75, 16-26 Michell, AR (Ed.) ( 1993) The Advancement of Veterinary

Smith, F. (1976) The Early History of Veterinary Literature. 4 vols. J.A Allen & Co, London Smithcors, J.P. (1957) Evolution of the Veterinary Art. Veter­

Indianapolis

Science. The Bicentenary Symposium Series. Volume 1 : Veterin­

inary Medicine Publishing Company, Kansas City. (A

ary Medicine beyond 2000. CAB International, Wallingford

general history of veterinary medicine to the 1 950s)

Michell, AR (Ed.) (1993) The Advancement of Veterinary Science. The Bicentenary Symposium Series. Volume 3: History of the Healing Professions, Parallels between Veterinary and Medical History. CAB International, Wallingford Ministry of Agriculture, Fisheries and Food (1965) Animal Health: A Centenary 1 865-1965. Her Majesty's Stationery Office, London. (A history of the government veterinary ser­ vice in the UK) OlE (1994) Early methods of animal disease control. Revue Scientifique et Technique, Office International des Epizooties, 13, 332-614 Pattison, I. (1984) The British Veterinary Profession 1 791-1948. J.A Allen, London Phalen, D. (Ed.) (2004) Emerging diseases. Seminars in Avian and Exotic Pet Medicine, 13, 49-107. (Describes some emerging diseases in birds, exotic pets and wild animals) Prescott, L.M., Harley, J.P. and Klein, D.A (2002) Micro­ biology, 5th edn. McGraw Hill, Boston. (Includes a concise description of the development of microbiology) Pritchard, W.R (1986) Veterinary education for the 21st cen­ tury. Journal of the American Veterinary Medical Association, 189, 172-177. (A general review of con temporary veterinary requirements in developed coun tries) Pugh, L.P. (1962) From Farriery to Veterinary Medicine, 1 785-1 795. W. Heffer, Cambridge Saunders, L.Z. (1996) A Biographical History of Veterinary Pathology. Allen Press Inc., Lawrence. (An international history of veterinary pathology, including microbiology and parasitology, described through the lives of individuals) Schwabe, C.W. (1978) Cattle, Priests, and Progress in Medicine. The Wesley W. Spink lectures on comparative medicine, Vol. 4. University of Minnesota Press, Minneapolis. (A comparative history of veterinary and human medicine) Schwabe, CW. (1993) The current epidemiological revolu­ tion in veterinary medicine. Part II. Preventive Veterinary Medicine, 18, 3-1 6 Sherman, D.M. (2002) Tending Animals in the Global Village. Lippincott Williams & Wilkins, Baltimore. (Includes a discussion of recen t global trends in veterinary medicine) Shryock, RH. (1961) Quantification. The history of quant­ ification in medical science. In: A History of the Mean-

Spinage, CA (2003) Cattle Plague: A History. Kluwer Aca­ demic/Plenum Publishers, New York (An encyclopaedic history of rinderpest) Stalheim, o.V.H. (1994) The Winning of Animal Health: 1 00 Years of Veterinary Medicine. Iowa State University Press, Ames. (A history of veterinary medicine in the US) Suilleabhain, B. O . (1994) The evolution of the State Veter­ inary Services. Irish Veterinary Journal, 47, 21-27 Swabe, J. (1999) Animals, Disease and Human Society. Human-Animal Relations and the R ise of Veterinary Medicine. Routledge, London and New York Thrusfield, M. (1988) The application of epidemiological techniques to contemporary veterinary problems. British Veterinary Journal, 144, 455-469 Thrusfield, M. (1990) Trends in epidemiology. Society for General Microbiology Quarterly, 17, 82-84 US Department of Health and Human Resources (1998) Preventing Emerging Infectious Diseases. A Strategy for the 21st Century. US Department of Health and Human Resources, Centres for Disease Control and Prevention, Atlanta. (A comprehensive discussion of the control of emerg­ ing human infections in the US, but also including some general principles and details of zoonotic and foodborne infections) Waltner-Toews, D. and Lang, T. (2000) A new conceptual basis for food and agriculture policy: the emerging model of links between agriculture, food, health, environment and society. Global Change & Human Health, 1, 1 16-130. (A debate of the future offood and farming) Waterson, AP. and Wilkinson, L. (1978) An Introduction to the History of Virology. Cambridge University Press, Cambridge Wilkinson, L. (1992) Animals and Disease: an Introduction to the History of Comparative Medicine. Cambridge University Press, Cambridge Winslow, CE.A (1944) The Conquest of Epidemic Disease. Princeton University Press, Princeton. (A historical account of the control of infectious diseases) Worboys, M. (1991) Germ theories of disease and British veterinary medicine, 1860-1890. Medical History, 35, 308-327

The scope of epidem iology

Many contemporary disease problems can be solved by an investigation of animal populations rather than the individual. The natural history of infectious dis­ eases can be understood by studying their distribution in different populations. The measurement of the amount of infectious and non-infectious diseases in a population assists in determining their importance and the efficacy of control campaigns. Complex and unknown causes of diseases can be elucidated by studying the diseases in various groups of animals. The effects of diseases on production can be realistic­ ally estimated only in relation to decreased produc­ tion in the herd or flock, rather than in a single animal. The economic impact of disease and of attempts to con­ trol it similarly are evaluated best in groups of animals, ranging from the individual farm to the national level. The investigation of disease in populations is the basis of epidemiology.

Greek swo- (zoo-) animal, to the studies of animal (excluding human) populations (e.g., Karstad, 1962). Outbreaks of disease in human populations were called 'epidemics', in animal populations were called 'epizootics', and in avian populations were called 'epornitics', from the Greek opvz8- (ornith-) bird (e.g., Montgomery et al., 1 979). Other derivatives, such as 'epidemein' ('to visit a community'), give hints of the early association between epidemiology and infections that periodically entered a community, in contrast to other diseases that were usually present in the population. The various derivatives can be used in different contexts. A study of a disease that is present only in an animal population, such as Brucella ovis infection of sheep, would not involve a simultaneous study of dis­ ease in humans; the term 'epizootiology' might then be =

=

1 Two adjectives, 'epidemiologic' and 'epidemiological' are in use, the

Definition of epidemiology

former being more common in North American publications, whereas the latter is usual in British literature. The shorter version has probably

Epidemiology is the study of disease in populations and of factors that determine its occurrence; the key word being populations. Veterinary epidemiology additionally includes investigation and assessment of other health-related events, notably productiv­ ity. All of these investigations involve observing animal populations and making inferences from the observations. A literal translation of the word 'epidemiology', based on its Greek roots EJrl- (epi-) upon, bTff10(demo-) people, and AOyO- (logo-) discoursing, is 'the study of that which is upon the people' or, in modern parlance, 'the study of disease in popuiations'l. Traditionally, 'epidemiology' related to studies of human populations, and 'epizootiology', from the =

=

=

arisen because of the general human tendency to go for simpler forms wherever possible. In the case of '-ic' and '-ical' this tendency is helped by the fact that they are virtually interchangeable. '-ic-' (pedantically, '-ik-') is one of the commonest Greek suffixes used to turn a noun into an adjective, whereas -al- performs the same function in Latin. Very many adjectives of these types were borrowed into English, and native speakers became so familiar with both suffixes that they used them with­ out any conscious reference to their linguistic origin (e.g., 'anecdote' is a Greek borrowing, and should really have 'anecdotic' as its adjective, instead of the hybrid 'anecdotal'). Moreover, it is a feature of both Latin and Greek to use adjectives syntactically as nouns, and this has been carried over when words have been borrowed into English, resulting in 'logic' (properly an adjective) being used as a noun. This was then converted to the common adjective, 'logical', using the Latin suffix. However, since many of the '-ic' forms also remained as adjectives (e.g., 'comic', 'classic'), doublets such as 'comic(al)' and 'classic(al)' arose. The existence of these doublets explains why 'epidemiologic' and 'epidemio­ logical' are essentially identical, one not being 'more correct' than the other.

The use of epidemiology

used by some to indicate that the study was confined to animals other than man. Many diseases, called zoonoses, may be shared by man and lower animals. Thus, when studying diseases such as bovine brucel­ losis and leptospirosis, both of which are zoonoses, mechanisms of transfer of disease between human and non-human populations have to be considered. An important factor that determines the occurrence of such occupationally acquired zoonoses (in veterinar­ ians, abattoir workers and farmers in these examples) is the amount of disease in domestic animals. The 'epidemiology' of brucellosis and leptospirosis in dairy farmers is therefore closely associated with the 'epi­ zootiology' of these diseases in cattle. The semantic differentiation between studies involving human dis­ eases and those concerned with animal diseases there­ fore is considered neither warranted nor logical (Oohoo et al., 1994). Throughout this book, the word 'epidemi­ ological' is used to describe any investigation relating to disease in a population, whether or not the popula­ tion consists of humans, domestic animals, or wildlife.

The uses of epidemiology There are five objectives of epidemiology: 1.

determination o f the origin o f a disease whose cause is known; 2. investigation and control of a disease whose cause is either unknown or poorly understood; 3. acquisition of information on the ecology and natural history of a disease; 4. planning, monitoring and assessment of disease control programmes; 5. assessment of the economic effects of a disease, and analysis of the costs and economic benefits of alternative control programmes. Determination of the origin of a disease whose cause is known

Many diseases with a known cause can be diagnosed precisely by the signs exhibited by the affected animals, by appropriate laboratory tests and by other clinical procedures such as diagnostic imaging. For instance, the diagnosis of foot-and-mouth disease is relatively straightforward: the infection produces distinct clinical signs in most species (sheep can be an exception), and can be readily diagnosed in the laboratory. However, determining why an outbreak occurred is important in limiting its spread and eradic­ ating the disease. For example, the first reported case of the UK epidemic in 2001 was in an abattoir in south-east England. However, epidemiological invest­ igations revealed that the disease had originated on a

pig farm several hundred miles north (Gibbens et al., 2001b), and it was only by careful tracing of move­ ments of animals that had been exposed to infection at this source that the widespread dissemination of the virus through sheep marketing was identified, and appropriate national control measures therefore instituted (Mansley et al., 2003). There are many examples of the investigation of dis­ eases with known causes that involve answering the questions 'Why has an outbreak occurred?' or 'Why has the number of cases increased?'. For instance, an increased number of actinobacillosis cases in a group of cattle might be associated with grazing a particular pasture of 'burnt-off' stubble. Such an occurrence could be associated with an increase in abrasions of the buccal mucosae, caused by abrasive ash, which could increase the animals' susceptibility to infection with Actinobacillus lignieresi (Rados tits et al., 1999). Similarly, consumption of prickly pears (Opuntia spp.) may be associated with an increased frequency of the disease in sheep, for a similar reason. An increased number of cases of bone defects in puppies might be due to local publicitybeing given to the use of vitamin supplements, resulting in their administration to animals that were already fed a balanced diet, with consequent hypervitaminosis 0, inducing osteosclerosis and bone rarefaction (Jubb et al., 1 993). An increase in the number of lamb carcasses with high ultimate pH values could be associated with excessive washing of the animals prior to slaughter (Petersen, 1983). These possible explanations can be verified only by epidemio­ logical investigations. Investigation and control of a disease whose cause is either unknown or poorly understood

There are many instances of disease control based on epidemiological observations before a cause was identified. Contagious bovine pleuropneumonia was eradicated from the US by an appreciation of the infectious nature of the disease before the causal agent, Mycoplasma mycoides, was isolated (Schwabe, 1984). Lancisi's slaughter policy to control rinderpest, mentioned in Chapter I, was based on the assump­ tion that the disease was infectious, even though the causal agent had not been discovered. Edward Jenner's classical observations on the protective effects of cowpox virus against human smallpox infection in the 1 8th century (Fisk, 1959), before viruses were isolated, laid the foundations for the global eradication of smallpox. More recently, epidemiological studies in the UK suggested that cattle developed bovine spongiform encephalopathy following consumption of feedstuffs containing meat and bone meal contaminated with a scrapie-like agent (Wilesmith et al., 1 988). This was

The scope of epidemiology

sufficient to introduce legislation prohibiting the feed­ ing of ruminant-derived protein, although the causal agent had not been identified at the time. Although the exact cause of 'blood splashing' (ecchymoses in muscle) in carcasses is still not known, observations have shown that there is a correlation between this defect and electrical stunning by a 'head only' method (Blackmore, 1983); and the occurrence of this condition can be reduced by adopting a short 'stun-to-stick' interval, stunning animals with a cap­ tive bolt, or using a method of electrical stunning that causes concurrent cardiac dysfunction (Gracey et al., 1999). Similarly, there is a strong correlation between grass sickness and grazing, and the disease can be almost totally prevented by stabling horses continu­ ously during spring and summer, although the cause of the disease is unknown (Gilmour, 1989). The cause of squamous cell carcinoma of the eye in Hereford cattle ('cancer eye') is not known. Epidemio­ logical studies have shown that animals with unpig­ mented eyelids are much more likely to develop the condition than those with pigment (Anderson et al., 1957). This information can be utilized by cattle breeders to select animals with a low susceptibility to this neoplasm. Epidemiological studies are also used to identify causes of disease (many of which are multifactorial and initially poorly understood) so that the most appropriate disease control techniques can be applied. Thus, the identification of low levels of water intake as an important component of the cause of feline urolithiasis (Willeberg, 1981) facilitated control of this syndrome by dietary modification. Investigations can also be used to identify characteristics of animals that increase the risk of disease. For example, entire, nulli­ parous bitches with a history of oestrus irregularity, pseudopregnancy, and use of oestrus-suppression drugs are particularly at risk of developing pyometra (Fidler et al., 1966; Niskanen and Thrusfield, 1998); this information is of diagnostic value to the clinician, and is of assistance when advising owners on breeding policy. Acquisition of information on the ecology and natural / history of a disease

An animal that can become infected with an infectious agent is a host of that agent. Hosts and agents exist in communities that include other organisms, all of which live in particular environments. The aggregate of all facts relating to animals and plants is their natural history. Related communities and their environments are termed ecosystems. The study of ecosystems is ecology. A comprehensive understanding of the natural history of infectious agents is possible only when they

are studied in the context of their hosts' ecosystems. Similarly, an improved knowledge of non-infectious diseases can be obtained by studying the ecosystems and the associated physical features with which affected animals are related. The geological structure of an ecosystem, for example, can affect the mineral content of plants and therefore can be an important factor in the occurrence of mineral deficiencies and excesses in animals. The environment of an ecosystem affects the sur­ vival rate of infectious agents and of their hosts. Thus, infection with the helminth Fasciola hepatica is a serious problem only in poorly drained areas, because the parasite spends part of its life-cycle in a snail that requires moist surroundings. Each of the 200 antigenic types (serovars) of Leptospira interrogans is maintained in one or more species of hosts. Serovar copenhageni, for instance, is maintained primarily in rats (Babudieri, 1958). Thus, if this serovar is associated with leptospirosis in either man or domestic stock, then part of a disease control programme must involve an ecological study of rat populations and control of infected rats. Similarly, in Africa, a herpesvirus that produces infections with­ out signs in wildebeest is responsible for malignant catarrhal fever of cattle (Plowright et al., 1960). Wilde­ beest populations, therefore, must be investigated when attempting to control the disease in cattle. An ecosystem's climate also is important because it limits the geographical distribution of infectious agents that are transmitted by arthropods by limit­ ing the distribution of the arthropods. For example, the tsetse fly, which transmits trypanosomiasis, is restricted to the humid parts of Sub-Saharan Africa (Ford, 1971). Infectious agents may extend beyond the eco­ systems of their traditional hosts. This has occurred in bovine tuberculosis in the UK, where the badger population is an alternative host for Mycobacterium tuberculosis (Little et al., 1982; Wilesmith et al., 1982) in which the disease has been refractory (Report, 2000). Similarly, in certain areas of New Zealand, wild opossums are infected with this bacterium and can therefore be a source of infection to cattle (Thorns and Morris, 1983). Purposeful routine observation of such infections provides valuable information on changes in the amount of disease and relevant ecological factors and may therefore indicate necessary changes in control strategies. Infectious diseases that are transmitted by insects, ticks and other arthropods, and which may be main­ tained in wildlife, present complex ecological relation­ ships and even more complex problems relating to their control. Comprehensive epidemiological studies of these diseases help to unravel their life-cycles, and can indicate suitable methods of control.

Types of epidemiological investigation

Planning, monitoring and assessment of disease control programmes

The institution of a programme to either control or eradicate a disease in an animal population must be based on a knowledge of the amount of the disease in that population, the factors associated with its occur­ rence, the facilities required to control the disease, and the costs and benefits involved. This information is equally important for a mastitis control programme on a single dairy farm and for a national brucellosis eradication scheme involving all the herds in a country. The epidemiological techniques that are employed include the routine collection of data on disease in populations (monitoring and surveillance) to decide if the various strategies are being successful. Surveillance is also required to determine whether the occurrence of a disease is being affected by new factors. For example, during the eradication scheme for bovine tuberculosis in New Zealand, opossums became infected in certain areas. New strategies had to be introduced to control this problem (Julian, 1981). During the foot-and-mouth disease epidemic in the UK in 1967 and 1968, surveillance programmes indic­ ated the importance of wind-borne virus particles in the transmission of the disease (Smith and Hugh­ Jones, 1969). This additional knowledge was relevant to the establishment of areas within which there was a restriction of animal movement, thus facilitating eradication of the disease. Assessing the economic effects of a disease and of its control

The cost of the control of disease in the livestock industry must be balanced against the economic loss attributable to the disease. Economic analysis there­ fore is required. This is an essential part of most modern planned animal health programmes. Although it may be economic to reduce a high level of disease in a herd or flock, it may be uneconomic to reduce even further the level of a disease that is present at only a very low level. If 15% of the cows in a herd were affected by mastitis, productivity would be severely affected and a control programme would be likely to reap financial benefit. On the other hand, if less than 1 % of the herd were affected, the cost of further reduction of the disease might not result in a suffi­ cient increase in productivity to pay for the control programme. This introduction to the uses of epidemiology indicates that the subject is relevant to many areas of veterinary science. The general agricultural practi­ tioner is now primarily concerned with herd health. The companion animal practitioner is faced with chronic refractory diseases, such as the idiopathic

l )

dermatoses, which may be understood better by an investigation of the factors that are common to all cases. The state veterinarian cannot perform his rou­ tine duties without reference to disease in the national animal population. The diagnostic pathologist invest­ igates the associations between causes and effects (i.e., lesions); this approach is epidemiological when inferences are made from groups of animals. The veterinarian in abattoirs and meat-processing plants attempts to reduce the occurrence of defects and con­ tamination by understanding and eliminating their causes. Similarly, industrial veterinarians, concerned with the design of clinical trials, compare disease rates and response to treatment in groups of animals to which different prophylactic and therapeutic com­ pounds are administered.

Types of epidemiological investigation There are four approaches to epidemiological invest­ igation that traditionally have been called 'types' of epidemiology. These types are descriptive, analytical, experimental and theoretical epidemiology. Descriptive epidemiology

Descriptive epidemiology involves observing and recording diseases and possible causal factors. It is usually the first part of an investigation. The observa­ tions are sometimes partially subjective, but, in com­ mon with observations in other scientific disciplines, may generate hypotheses that can be tested more rigorously later. Darwin's theory of evolution, for example, was derived mainly from subjective observa­ tions, but with slight modification it has withstood rigorous testing by plant and animal scientists. Analytical epidemiology

Analytical epidemiology is the analysis of observations using suitable diagnostic and statistical procedures. Experimental epidemiology

Experimental epidemiologists observe and analyse data from groups of animals from which they can select, and in which they can alter, the factors associated with the groups. An important component of the experimental approach is the control of the groups. Experimental epidemiology developed in the 1920s and 1930s, and utilized laboratory animals whose short lifespans enabled events to be observed more rapidly than in humans (see Chapter 18). A notable example is the work of Topley (1942) who infected

colonies of mice with ectromelia virus and Pasteurella spp. The effects of varying the rate of exposure of mice maintained in groups of various sizes provided insights into the behaviour of human epidemic dis­ eases such as measles, scarlet fever, whooping cough and diphtheria, which followed similar patterns to the experimental infections (MRC, 1938). This work demonstrated the importance of the proportion of susceptible individuals in the population in deter­ mining the progress of epidemics (see Chapter 8); hitherto, changes in the virulence of a microorganism were thought to be the most important factor affecting epidemic patterns; for example, the decline in the occurrence of rinderpest in the UK in the 1 8th century was ascribed to its passing into a mild form of the disease (Spinage, 2003). Rarely, a 'natural' experiment can be conducted when the naturally occurring disease or other fortuitous cir­ cumstance approximates closely to the ideally designed experiment. For instance, when bovine spongiform encephalopathy occurred in the UK, outbreaks of the disease on the Channel Islands (Jersey and Guernsey), which maintain isolated populations of cattle, pro­ vided an ideal situation in which to study the disease, uncomplicated by the possibility of transmission by contact with infected animals (Wilesmith, 1993). This added credence to the hypothesis that the disease was transmitted in contaminated feedstuffs. Theoretical epidemiology

Theoretical epidemiology consists of the representation of disease using mathematical 'models' that attempt to simulate natural patterns of disease occurrence. Epidemiol ogica l subdiscipli n es

Various epidemiological subdisciplines2 are now recognized. These generally reflect different areas of interest, rather than fundamentally different tech­ niques. They all apply the four types of epidemiology described above, and can overlap, but their separate identities are considered by some to be justifiable3.

2

The term 'subdiscipline' implies that epidemiology is a discipline.

That it is, is generally accepted (Howe and Christiansen, 2004), following the criterion of Hirst (1965); namely, that a discipline involves certain central concepts that are peculiar in character and form. The central con­ cept of epidemiology is measuring, and drawing inferences from, disease in populations. J

The author's preference is not to compartmentalize epidemiology,

which implies an insular, specialists' modus operandi rather than a broad approach to problems. However, listing of subdisciplines is vindicated on the grounds that they are still widely cited.

Clinical epidemiology

Clinical epidemiology is the use of epidemiological principles, methods and findings in the care of indi­ viduals, with particular reference to diagnosis and prognosis (Last, 2001), and therefore brings a numer­ ate approach to traditional clinical medicine, which has tended to be anecdotal and subjective (Grufferman and Kimm, 1984). It is concerned with the frequency and cause of disease, the factors that affect prognosis, the validity of diagnostic tests, and the effectiveness of therapeutic and preventive techniques (Fletcher et al., 1988; Sackett et al., 1991 ), and therefore is an important component of evidence-based medicine (Polzin et al., 2000; Sackett et al., 2000; Cockroft and Holmes, 2003; Marr et al., 2003), which is concerned with patient care based on evidence from the best available studies. Computational epidemiology

Computational epidemiology involves the applica­ tion of computer science to epidemiological studies (Habtemariam et al., 1988). This includes the repre­ sentation of disease by mathematical models (see 'Quantitative investigations', below) and the use of expert systems. These systems are commonly applied to disease diagnosis where they incorporate a set of rules for solving problems, details of clinical signs, lesions, laboratory results, and the opinions of experts; examples are identification of the cause of coughing in dogs (Roudebush, 1984), and the diagnosis of bovine mastitis (Hogeveen et al., 1993). Expert systems are also employed in formulating disease control strat­ egies (e.g., for East Coast fever: Gettinby and Byrom, 1989), predicting animal productivity (e.g., reproduc­ tive performance in dairy herds: McKay et al., 1988), and supporting management decisions (e.g., decisions on replacing sows: Huirne et al., 1991). Genetic epidemiology

Genetic epidemiology is the study of the cause, distribu­ tion and control of disease in related individuals, and of inherited defects in populations (Morton, 1982; Roberts, 1985; Khoury et al., 1993). It indicates that the disciplinary boundary between genetics and epidemio­ logy is blurred. Many diseases involve both genetic and non-genetic factors (see Chapter 5), and genes are increasingly incriminated in diseases of all organ systems (Figure 2.1). Thus, the geneticist and epidemio­ logist are both concerned with interactions between genetic and non-genetic factors - only the frequently indistinct time of interaction may be used to classify an investigation as genetic or epidemiological.

Types of epidemiological investigation

jOints

Fig. 2. 1

The discovery of the role of genes

in the pathogenesis of disease. An analogy

' Reefs' of

is made using the sea and reefs. The sea represents environmental factors (infectious

genetic disease

ir auma

and non-infectious); the reefs represent genetic factors. Only the reefs above the water level are known . As time passes, the water level falls, and more genetic factors are identified. (From Thrusfield, 1 99 3 ; after Patterson, 1 99 3 . )

Field epidemiology

Field epidemiology is the practice of epidemiology in response to problems of a magnitude significant enough to require a rapid or immediate action (Good­ man and Buehler, 2002). For example, when outbreaks of foot-and-mouth disease occur, field epidemiologists promptly trace potential sources of infection in an attempt to limit spread of the disease (see Chapters 1 0 and 22). Field epidemiology is a timely, judgemental process based on description, analysis, common sense and the need to design practical control policies. It is sometimes termed 'shoe-leather epidemiology' be­ cause the investigator is often required to visit the field to study disease4. Participatory epidemiology

Awareness, in the 1980s, of the rudimentary develop­ ment of veterinary services in some parts of the devel­ oping world, where animals were economically and socially important, prompted the use of local know­ ledge to gain information, with the main goal of improving animal health (Catley et al., 2002a). The techniques that are employed evolved in the social sciences, and consist of simple visual methods and interviews to generate qualitative data. This approach became known as 'participatory appraisal' and its application in veterinary medicine is now termed 'participatory epidemiology'. It is a tool for the field epidemiologist, which is increasingly used in develop­ ing countries. This area of interest is closely related to 'ethnoveter­ inary medicine' (McCorkle et al., 1996; Martin et al., 2001; Fielding, 2004), which is concerned with local

4

This contrasts with 'armchair epidemiology' : a term (sometimes

used cynically) referring to the analysis of data within the confines of one's office.

metabolic

knowledge of, and practices relating to, the health of animals. A brief introduction to participatory epidemiology is given in Chapter 10. Molecular epidemiology

New biochemical techniques now enable microbio­ logists and molecular biologists to study small genetic and antigenic differences between viruses and other microorganisms at a higher level of discrimination than has been possible using conventional serological techniques. The methods include peptide mapping, nucleic acid 'fingerprinting' and hybridization (Keller and Manak, 1989; Kricka, 1 992), restriction enzyme analysis, monoclonal antibodies (Oxford, 1985; Goldspink and Gerlach, 1990; Goldspink, 1993) and the polymerase chain reaction (Belak and Ballagi­ Pordany, 1993). For example, nucleotide sequencing of European foot-and-mouth disease virus has indicated that some outbreaks of the disease involved vaccinal strains, suggesting that improper inactivation or escape of virus from vaccine production plants may have been responsible for the outbreaks (Beck and Strohmaier, 1987). Sequencing has also indicated that unrestricted animal movement is a major factor in dissemination of the disease in West Africa (Sangare et al., 2004). Additionally, infections that hitherto have been difficult to identify are now readily distinguished using these new molecular techniques; examples are infection with Mycobacterium paratuberculosis (the cause of Johne's disease) (Murray et al., 1989) and latent infection with Aujeszky's disease virus (Belak et al., 1 989). The application of these new diagnostic techniques constitutes molecular epidemiology. A general description of the methods is given by Persing et al. (1993). Molecular epidemiology is part of the wider use of biological markers (Hulka et al., 1 990). These are

!;l

The scope o f epidemiology

cellular, biochemical or molecular alterations that are measurable in biological media such as tissues, cells or fluids. They may indicate susceptibility to a causal factor, or a biological response, suggesting a sequence of events from exposure to disease (Perera and Weinstein, 1982). Some have been used by veterinari­ ans for many years, for instance serum magnesium levels as indicators of susceptibility to clinical hypo­ calcaemia (Whitaker and Kelly, 1982; van de Braak et al., 1987), serum transaminase levels as markers for liver disease, and antibodies as indicators of exposure to infectious agents (see Chapter 17).

Qua litative investigations The natural history of disease

The ecology of diseases, including the distribution, mode of transmission and maintenance of infectious diseases, is investigated by field observation. Eco­ logical principles are outlined in Chapter 7. Methods of transmission and maintenance are described in Chapter 6, and patterns of disease occurrence are described in Chapter 8. Field observations also may reveal information about factors that may directly or indirectly cause disease. The various factors that act to produce disease are described in Chapter 5.

Other subdisciplines

Several other epidemiological subdisciplines have also been defined. Chronic disease epidemiology is involved with diseases of long duration (e.g., cancers), many of which are non-infectious. Environmental epi­ demiology is concerned with the relationship between disease and environmental factors such as industrial pollution and, in human medicine, occupational hazards. Domestic animals can act as monitors of envir­ onmental hazards and can provide early warning of disease in man (see Chapter 18). Micro-epidemiology is the study of disease in a small group of individuals with respect to factors that influence its occurrence in larger segments of the population. For example, stud­ ies of feline acquired immunodeficiency syndrome (FAIOS) in groups of kittens have provided insights into the widespread human disease, AIDS (Torres­ Anjel and Tshikuka, 1988; Bendinelli et al., 1993). Micro-epidemiology, which frequently uses animal biological models of disease, therefore is closely related to comparative epidemiology (see Chapter 18). In contrast, macro-epidemiology is the study of national patterns of disease, and the social, economic and political factors that influence them (Hueston and Walker, 1993; Hueston, 2001). Other subdisciplines, such as nutritional epidemiology (Willett, 1990; Slater 1996b), subclinical epidemiology (Evans, 1987), and, specifically in human medicine, social epidemiology (Kasl and Jones, 2002) and psychosocial epidemio­ logy (Martikainen et al., 2002) can also be identified to reflect particular areas of interest.

Causal hypothesis testing

If field observations suggest that certain factors may be causally associated with a disease, then the association must be assessed by formulating a causal hypothesis. Causality (the relating of causes to effects) and hypo­ thesis formulation are described in Chapter 3. Qualitative investigations were the mainstay of epidemiologists before the Second World War. These epidemiologists were concerned largely with the identification of unknown causes of infectious disease and sources of infection. Some interesting examples of the epidemiologist acting as a medical 'detective' are described by Roueche (1991) and Ashton (1994). Quantitative investigations

Quantitative investigations involve measurement (e.g., the number of cases of disease), and therefore expres­ sion and analysis of numerical values. Basic methods of expressing these values are outlined in Chapters 4 and 12. The types of measurement that are encoun­ tered in veterinary medicine are described in Chap­ ter 9. Quantitative investigations include surveys, monitoring and surveillance, studies, modelling, and the biological and economic evaluation of disease control. Some of these may be confined with­ in the walls of the research organization 'armchair -

epidemiology' . Surveys

Components of epidemiology The components of epidemiology are summarized in Figure 2.2. The first stage in any investigation is the collection of relevant data. The main sources of information are outlined in Chapter 10. Investigations can be either qualitative or quantitative or a combina­ tion of these two approaches.

A survey is an examination of an aggregate of units (Kendall and Buckland, 1982). A group of animals is an example of an aggregate. The examination usually involves counting members of the aggregate and char­ acteristics of the members. In epidemiological surveys, characteristics might include the presence of particular diseases, or production parameters such as milk yield. Surveys can be undertaken on a sample of the popula­ tion. Less commonly, a census, which examines the

Components of epidemiology

}'!

Sources of veterinary data

Qualitative evaluation

The natural history of disease Causal factors Host, agent and environment

Ecology Transmission and mai ntenance

Quan titative evaluation

\

Studies and surveys

/\

Experimental studies

Observational studies

Cli nical trials; intervention studies

Cross-sectional studies Case-control studies

Surveys

L ongitudinal studies

�t

Cohort studies

Causal hypothesis testing

Economic evaluation

Disease control Fig. 2. 2

Components of veterinary epidemiology. (Based on Thrusfield, 1 985a.)

total animal population, can be undertaken (e.g., tuberculin testing). A cross-sectional survey records events occurring at a particular point in time. A longi­ tudinal survey records events over a period of time. These latter events may be recorded prospectively from the present into the future; or may be a retro­ spective record of past events. A particular type of diagnostic survey is screening. This is the identification of undiagnosed cases of dis­ ease using rapid tests or examinations. The aim is to separate apparently healthy individuals that probably

have a disease from those that probably do not. Screen­ ing tests are not intended to be diagnostic; individuals with positive test results (i.e., that are classified as dis­ eased by the screening test) usually require further investigation for definite diagnosis. They therefore differ from diagnostic tests, which are applied to animals showing suspicion of disease. Screening frequently involves investigation of the total population (mass screening); for example, the screening of cattle populations for tuberculosis. It may also be targeted at animals only in areas where there

,I i

The scope of epidemiology

have been cases of disease (strategic screening); for example, the serological sampling of sheep within a 3-km radius of premises on which foot-and-mouth disease has been diagnosed (Donaldson, 2000). Pre­ scriptive screening aims at early identification of dis­ eases that can be controlled better if they are detected early in their pathogenesis (e.g., mammography to detect breast cancer in women). Screening also may be applied more generally to include the measurement of any characteristic or health problem which may not be apparent in a popu­ lation (e.g., measurement of heavy metal levels in wild and domesticated animals) (Toma et a/. , 1999). Diagnostic tests and screening are considered in Chapter 1 7. The design of surveys in general is described in Chapter 13. Monitoring and surveillance

Monitoring is the making of routine observations on health, productivity and environmental factors and the recording and transmission of these observations. Thus, the regular recording of milk yields is mon­ itoring, as is the routine recording of meat inspection findings at abattoirs. The identity of individual dis­ eased animals usually is not recorded. Surveillance is a more intensive form of data re­ cording than monitoring. Originally, surveillance was used to describe the tracing and observation of people who were in contact with cases of infectious disease. It is now used in a much wider sense (Langmuir, 1965) to include all types of disease - infectious and non­ infectious - and involves the collation and interpreta­ tion of data collected during monitoring programmes, usually with the recording of the identity of diseased individuals, with a view to detecting changes in a population's health. It is normally part of control programmes for specific diseases. The recording of tuberculosis lesions at an abattoir, followed by tracing of infected animals from the abattoir back to their farms of origin, is an example of surveillance. The terms 'monitoring' and 'surveillance' have previously been used synonymously, but the distinction between them is now generally accepted. Surveillance is discussed in detail in Chapter 10. Studies

'Study' is a general term, which refers to any type of investigation. However, in epidemiology, a study usually involves comparison of groups of animals; for example, a comparison of the weights of animals that are fed different diets. Thus, although a survey generally could be classified as a study, it is excluded from epidemiological studies because it involves only description rather than comparison and the analysis

that the comparison requires. There are four main types of epidemiological study: 1.

2. 3. 4.

experimental studies; cross-sectional studies; case-control studies; cohort studies.

In an experimental study the investigator has the ability to allocate animals to various groups, according to factors that the investigator can randomly assign to animals (e.g., treatment regimen, preventive tech­ nique); such studies are therefore part of experimental epidemiology. An important example is the clinical trial. In a clinical trial, the investigator assigns animals either to a group to which a prophylactic or thera­ peutic procedure is applied, or to a control group. It is then possible to evaluate the efficacy of the procedure by comparing the two groups. Clinical trials are dis­ cussed in Chapter 16. The other types of study - cross-sectional, case­ control and cohort - are observational. An observa­ tional study is similar to an experimental study: animals are allocated to groups with respect to certain characteristics that they possess (trait, disease or other health-related factors). However, observational studies are conducted on naturally occurring cases of disease in the field, and so it is not possible to assign animals to groups randomly because the investigator has little control over the factors that are being studied. For instance, a study of the relationship between bovine mastitis, type of housing and management practices would involve investigation of cases of the disease on farms under different systems of husbandry. A cross-sectional study investigates relationships between disease and hypothesized causal factors in a specified population. Animals are categorized according to presence and absence of disease and hypothesized causal factors; inferences then can be made about associations between disease and the hypothesized causal factors, for example, between heart valve incompetence (the disease) and breed (the hypothesized causal factor). A case-control study compares a group of diseased animals with a group of healthy animals with respect to exposure to hypothesized causal factors. For ex­ ample, a group of cats with urolithiasis (the disease) can be compared with a group of cats without urolithiasis with respect to consumption of dry cat food (the factor) to determine whether that type of food has an effect on the pathogenesis of the disease. In a cohort study, a group exposed to factors is compared with a group not exposed to the factors with respect to the development of a disease. It is then pos­ sible to calculate a level of risk of developing the disease in relation to exposure to the hypothesized causal fac­ tors. For instance, a group of young neutered bitches can

Components of epidemiology

be compared with a group of young entire bitches with respect to the development of urinary incontinence, to ascertain if neutering is a risk factor for the condition. Case-control and cohort studies often have been applied in human medicine in which experimental investigations of cause are usually unethical. For example, it would not be possible to investigate the suspected toxicity of a drug by intentionally adminis­ tering the drug to a group of people in order to study possible side-effects. However, if symptoms of toxicity have occurred, then a case-control study could be used to evaluate the association between the symptoms and the drug suspected of causing the toxicity. Some argue that there are fewer ethical restraints on experimental investigation in veterinary medicine than in human medicine and so experimental investigation of serious conditions is more tenable. However, observational studies have a role in veterinary epidemiology, for example when investigating diseases in farm and companion-animal populations. Moreover, the increas­ ing concern for animal welfare (see Chapter 1) is making these techniques even more attractive and useful than previously. Basic methods of assessing association between dis­ ease and hypothesized causal factors in observational studies are described in Chapters 14 and 15. Observational studies form the majority of epi­ demiological studies. Observational and experimental science have their own strengths and weaknesses, which are discussed in detail by Trotter (1930). A major advantage of an observational investigation is that it studies the natural occurrence of disease. Experi­ mentation may separate factors associated with disease from other factors that may have important inter­ actions with them in natural outbreaks. Modelling

Disease dynamics and the effects of different control strategies can be represented using mathematical equations. This representation is 'modelling'. Many modern methods rely heavily on computers. Another type of modelling is biological simulation using experimental animals (frequently laboratory animals) to simulate the pathogenesis of diseases that occur naturally in animals and man. Additionally, the spontaneous occurrence of disease in animals can be studied in the field (e.g., using observational studies) to increase understanding of human diseases. Math­ ematical modelling is outlined in Chapter 19, and spon­ taneous disease models are described in Chapter 1 8. Risk assessment

There is increasing and widespread interest in evalua­ tion of the risk of the occurrence of adverse events,

- , ) )

such as accidents and disasters (Report, 1983, 1992). The analysis, perception and management of risk therefore have been the focus for the development of formal methods of qualitative and quantitative risk assessment (Stewart, 1992; Vose, 2000). In veterinary medicine, disease is an adverse event, and observational studies provide a framework for identifying risk factors for disease occurrence. How­ ever, veterinary risk assessment has a much broader remit than identifying risks to the individual animal. For example, although diseases may occur at low levels and be adequately controlled, there may be a risk of importing them from other countries. Such a risk can only be removed completely if importation is totally prohibited. However, current political pressures in the world favour movement towards free trade, and the unquantified risk of introduction of a disease can now no longer be presented as a trade barrier. There is therefore a need to assess objectively the risks associated with the importation of livestock and their products. Examples include the risk of disease trans­ mission by bovine embryo transfer (Sutmoller and Wrathall, 1995) and the risk of introduction of bovine spongiform encephalopathy (Wahlstrom et al., 2002). Similarly, the risk of disease transmission between animals (e.g., transmission of Mycobacterium tubercu­ losis from badgers to cattle: Gallagher et al., 2003) can be assessed. Microbiological risk assessment (Kelly et al., 2003) commonly is concerned with food safety risks, and involves estimation of the magnitude of microbial exposure at various stages in the production chain (rearing on the farm; transport and processing; retail and storage; preparation), so that the risk of foodborne infection can be estimated. It has been applied notably to Campylobacter spp. (e.g., Rosenquist et al., 2003) and Salmonella spp. (e.g., Oscar, 1998) infections. The approach has also been used to assess the contribu­ tion of animal growth promoters to the transfer of antibiotic resistance to pathogens in humans (Kelly et al. , 2003). Some aspects of import risk assessment are pre­ sented in Chapter 1 7. Disease control

The goal of epidemiology is to improve the veterin­ arian's knowledge so that diseases can be controlled effectively, and productivity thereby optimized. This can be fulfilled by treatment, prevention or eradication. The economic evaluation of disease and its control is discussed in Chapter 20. Herd health schemes are described in Chapter 2 1 . Finally, the principles of disease control are outlined in Chapter 22. The different components of epidemiology apply the four epidemiological approaches to varying degrees.

)

The scope of epidemiology

Surveys and studies, for example, consist of a descriptive and an analytical part. Modelling addi­ tionally may include a theoretical approach.

Epidemiology's locale The interplay between epidemiology a n d other scien ces

During the first half of the 20th century most epi­ demiologists were trained initially as bacteriologists, reflecting epidemiologists' early involvement in the qualitative investigation of outbreaks of infectious dis­ ease. As the century proceeded, epidemiology became established in the context of the ecology of infectious diseases, and was addressed as such in the standard veterinary and infectious-disease textbooks (e.g., Blood and Henderson, 1960; Andrewes and Pereira, 1964). The epidemiological approach, however, is now prac­ tised by veterinarians from many disciplines: the geneticist concerned with an hereditary defect in a population, the nutritionist investigating a deficiency or toxicity, and the clinician concerned with risk fac­ tors for non-infectious diseases such as cancer. Today, members of a variety of other sciences also take part in epidemiological studies: statisticians analysing data from groups of animals, mathem­ aticians modelling diseases, economists assessing the economic impact of disease, and ecologists studying the natural history of disease. Each of these sciences is concerned with different facets of epidemiology, rang­ ing from the purely descriptive, qualitative approach to the quantitative analytical approach. There have been many definitions of epidemiology (Lilienfield, 1978), which reflect these facets. These definitions vary from the ecological, relating only to infectious diseases ('the study of the ecology of infectious diseases': Cockburn, 1963), to the mathematical, referring only to human populations ('the study of the distribution and dynamics of diseases in human populations': Sartwell, 1973). However, they all have the study of populations in common, and so are encompassed by the broad definition that was given at the beginning of this chapter. Moreover, the most profitable approach to epidemiology lies in balance between these qualitative and quantitative facets, with neither dominating the otherS, and in an appreciation that the validity of 5

The need for balance between different disciplines with a common

qualitative and quantitative research may be judged differently (Park, 1989; Maxwell, 1992). The rel ationship between epidemiology and other diagnostic discipl ines

The biological sciences form a hierarchy, ranging from the study of non-replicating molecules to nucleic acids, organelles, cells, tissues, organs, systems, individuals, groups and, finally, whole communities and ecosys­ tems (Wright, 1959). The various disciplines in veter­ inary medicine operate at different levels in this hierarchy. Histologists and physiologists study the structure and dynamics of the individual. Clinicians and pathologists are concerned with disease processes in the individual: clinicians diagnose disease using signs displayed by the patient; pathologists inter­ pret lesions to produce a diagnosis. Epidemiologists investigate populations, using the frequency and dis­ tribution of disease to produce a diagnosis. These three diagnostic disciplines, operating at different levels in the hierarchy, are complementary (Schwabe et al., 1977). Epidemiologists, dealing with the higher levels, must have a knowledge of those disciplines 'lower' in the hierarchy - they must be able to see both the 'wood' and 'trees'6. This means that they must adopt a broad rather than a specialist approach, avoiding the dangers of the specialist; dangers that have been described (somewhat cynically) by Konrad Lorenz (1977) in his book on the natural history of human knowledge: The specialist comes to know more and more about less and less, until finally he knows everything about a mere nothing. There is a serious danger that the specialist, forced to compete with his colleagues in acquiring more and more specialised knowledge, will become more and more ignorant about other branches of knowledge, until he is utterly incapable of forming any judgement on the role and import­ ance of his own sphere within the context of human knowledge as a whole.' Moreover, the specialist may be inclined to a 'posit­ ivist' approach (see Chapter 3), which requires strict separation of the object of inquiry from the investigat­ ing subject (and therefore, sometimes, the investigator) and thus may be somewhat divorced from the con­ sequences of the knowledge that he generates, which may have profound social and economic effects. Thus, the major attributes required to become a competent veterinary epidemiologist are a natural

interest is acknowledged in several areas of endeavour. For example, a healthy relationship between philosophy and theology is beneficial, with the philosopher providing the theologian with useful methods of argu­

6

Although the epidemiologist - operating at the higher levels - has

ment; this contrasts with periods when the relationship between these

always been concerned with the characteristics and effects of disease

disciplines has been marked by acute controversy, with little benefit

in populations and ecosystems, this interest has been freshly labelled

accruing (Macquarrie, 1998).

'conservation medicine' and 'ecological health' (Aguirre et al., 2002).

Epidemiology's locale

curiosity, a logical approach, a general interest in, and knowledge of, veterinary medicine, and experience of the realities of animal disease. In spite of the preceding remarks on specialists, a special interest and expertise in a particular sphere of veterinary science may, how­ ever, be useful in some investigations, for example, a knowledge of economics when undertaking an evaluation of the economic effects of disease. Epidemiology within the veterinary professi on

Brandeis (1971) proposed three 'peculiar characteristics' of a profession, as distinguished from other occupations: 'First. A profession is an occupation for which the necessary training is intellectual in character, involving knowledge and to some extent learning, as distinguished from mere skill. Second. It is an occupation which is pursued largely for others and not merely for one's self. Third. It is an occupation in which the amount of financial return is not the accepted measure of success.' The practice of clinical veterinary medicine is entirely congruous with these characteristics, and there is a similar consistency in the five objectives of veterinary epidemiology, outlined earlier in this chapter, which all focus on the control of animal disease, to the benefit of animals, their owners, and society in general. Further reading

\ \

Ferris, D.H. (1967) Epizootiology. Advances in Veterinary Science, 11, 261-320. (An early description of veterinary epidemiology)

Hungerford, L.L. and Austin, c.c. (1994) Epidemiological investigation of disease and health in feline populations. In: Consultations in Feline Internal Medicine 2, Ed. August, J.R., pp. 593-606. W.B. Saunders, Philadelphia James, A (2005) The state of veterinary epidemiology and economics. Preventive Veterinary Medicine, 67, 91-99 Martin, S.W. (1998) Art, science and mathematics revisited: the role of epidemiology in promoting animal health. In: Society for Veterinary Epidemiology and Preventive Medicine, Proceedings, Ennis, 25-28 March 1998, Eds Thrusfield, M.Y. and Goodall, EA, pp. xi-xxii Morabia, A (Ed.) (2004) A History of Epidemiologic Methods and Concepts. Birkhauser Verlag, Basel Nutter, F.W. (1999) Understanding the interrelationships between botanical, human, and veterinary epidemiology: the Ys and Rs of it all. Ecosystem Health, S, 1 31-140 Rapport, D.J. (1999) Epidemiology and ecosystem health: natural bridges. Ecosystem Health, S, 1 74-180 Riemann, H. (1982) Launching the new international journal 'Preventive Veterinary Medicine'. Preventive Veterinary Medicine, 1, 1-4 Scarlett, J.M. (1995) Companion animal epidemiology. Preventive Veterinary Medicine, 25, 151-159 Smith, G.D. and Ebrahim, S. (2001) Epidemiology - is it time to call it a day? International Journal of Epidemiology, 30, 1-11 Thrusfield, M. (1992) Quantitative approaches to veterinary epidemiology. In: The Royal Veterinary College Bicentenary Symposium Series: The Advancement of Veterinary Science, London 1 99 1 . Volume 1 : Veterinary Medicine beyond 2000. Ed.

Ashton, J. (Ed.) (1994) The Epidemiological Imagination: a Reader. Open University Press, Buckingham

Michell, AR., pp. 121-142. Commonwealth Agricultural Bureaux, Farnham Royal Thrusfield, M. (2001) Changing perspectives in veterin­ ary epidemiology. Polish Journal of Veterinary Sciences, 4,

Davies, G. (1983) Development of veterinary epidemiology. Veterinary Record, 112, 51-53 Davies, G. (1985) Art, science and mathematics: new approaches to animal health problems in the agricultural industry. Veterinary Record, 117, 263-267

19-25 Wilson, G. (1974) The use of epidemiology in animal disease. British Veterinary Journal, 130, 207-213 Wing, S. ( 1994) Limits of epidemiology. Medicine and Global Survival, 1, 74-86

Causal ity

Chapter 1 included a brief historical description of changing concepts of the cause of disease. This chapter initially discusses the cause of events more generally, as a necessary background to the investigation of the cause of disease, which follows.

Philosophical background Causality (causation) deals with the relationship between cause and effect, and is addressed in both science and philosophy. The scientist is primarily concerned with identification of causes to explain nat­ ural phenomena, whereas the philosopher attempts to understand the nature of causality, including its role in human actions (Vollmer, 1999). The philosopher provides an insight into the theory of the grounds of knowledge (formally termed 'epistemology'); and so a basic knowledge of the philosophy of causality con­ tributes to the scientist's ability to assess the validity and limitations of his inferences in the broader context of human knowledge as a whole. Concepts of causality have progressed historically, as new areas of interest emerge (e.g., the recent interest in causality in relation to artificial intelligence: Shafer, 1996).

maker of a thing (and by which the formal cause is therefore explained); and (4) the final cause which is the purpose of the thing (and therefore, in the case of natural things, usually synonymous with the formal cause). The notion of the 'universe of natural law' as a cause of disease (see Chapter 1 ) was consistent with this philosophy. Aristotle's emphasis lay on purpose as the only satisfactory explanation of why a thing is; and his doctrine failed to account for certain natural phe­ nomena (e.g., why bodies accelerate while falling). -

The Scholastics

The Christian medi<Eval philosophers (termed the 'Scholastics') generally endorsed Aristotle's ideas I, but focussed on God as the efficient cause of all things (a view posited by 5t Thomas Aquinas in his Summa Theologica)2. The notion that disease was induced by divine wrath (see Chapter 1) was consistent with this philosophy. The extent to which individuals were sec­ ondary efficient causes of things, with God as the prim­ ary cause, was a subject of debate during this period. The 'Modern' period

Debate on causality expanded substantially during the so-called 'Modern' period of philosophy. Beginning

The Classical period

In Classical times, Aristotle defined a doctrine of four causes (Barnes, 1984). These four 'causes' are really four different explanations or reasons for how and why a thing is as it is: (1) the material cause what 'stuff' (matter) a thing comprises (some combination of the four elements: earth, air, fire and water: Figure 1.2); (2) the formal cause the 'form and pattern' of a thing, or those properties without which a thing would not exist as it does; (3) the efficient cause which is the -

-

-

1 The origins of Scholasticism can be traced back to the sixth-century Roman philosopher, Boethius (Rand, 1928) and Aristotle's influence was pre-eminent in medi2eval universities, only being tempered by a broader philosophical curriculum in the late 1 4th century, possibly as a result of the teachings of the Byzantine scholar, Manuel Chrysoloras, who was brought to Florence in 1397 by the Chancellor of the city, Coluccio Salutati. 2

This idea had a wide influence, for example, on the concept that right

and wrong are absolute - a notion that was tempered by one that they are determined by circumstances (termed 'casuistry': Dewar, 1968).

Causal inference

with the French Philosopher, Rene Descartes (15961650), the debate (which was an integral part of 'The Enlightenment': see Chapter 1) was complex, but essentially aimed to simplify and secularize the Classical and Scholastic concepts of causality (Clatter­ baugh, 1 999). In science, the erosion of the Classical and Scholastic view had begun with Galileo. In his book, Discorsi e Dimostrazioni Matematiche (published in 1638), he emphasised the need to explain events mathematically in terms of 'how' (description), and 'why' (explana­ tion). This was prompted, in part, by increasing mechanization and the consequent need for engineers to predict the effects of different designs (e.g., of ships, as navigation extended throughout the world). Increasingly, in science, a physical and mathematical explanation for natural phenomena was sought, and the techniques of causal inference were debated.

Causal inference Scientific conclusions are derived by two methods of reasoning: deduction, and induction3. Deduction is arguing from the general to the particular; that is, a general case is established, from which all dependent events are argued to be true. For example, in Euclidean geometry, axioms are established, from which spe­ cific theorems (e.g., Pythagoras' Theorem) are then reasoned. Thus, if one posits the truth of the general proposition 'all dogs are mammals', it follows by deduction that any particular example of a dog will be a mammal. If the premisses of a deductively valid argument are true, it follows that the conclusion must also be true. Induction, in contrast, is arguing from the particular to the general. For instance, a dog may be vaccinated against distemper virus, and shown to be immune to challenge with the agent, from which the conclusion is drawn that the vaccine prevents distemper in all dogs. It is important to note that, unlike the deductive example, the premiss in this example could be true and yet the conclusion false. Induction has generally driven modern scientific investigation, requiring detached observation of events, and is frequently associated with 'positivism', a philosophical term describing scientific study based on the objective analysis of data, which excludes unverifiable speculation (Britannica, 1992)4. The

English theologian and philosopher, Thomas Bayes (1702-61) was the first to apply statistical probability inductively (Bayes, 1 763). His method, eponymously named 'Bayesian inference', involves calculating, from the frequency with which an event had occurred previ­ ously (the 'prior probability'), the probability that it will occur in the future (the 'posterior probability'). The Bayesian view of probability is a way of register­ ing degrees of belief, which may be strengthened or weakened by numerical data. A notable example of the Bayesian method is calculation of the probability of disease in an individual, depending on results of diagnostic tests (see Chapter 17). Induction was later addressed in some detail by the 19th century English philosopher, John Stuart Mill (1868), whose 'canons' of inductive reasoning are still widely used in epidemiology, and are outlined and exemplified later in this chapter. However, the validity of induction as a demonstration of proof had already been challenged by the scepticism of the 1 8th century Scottish philosopher David Hume (1739-40), whose ideas are still the subject of debate (Strawson, 1 989). Hume argued that the mere observation that one event preceded another (e.g., that a vaccine against canine distemper is observed to confer immunity to distem­ per virus when administered to a dog) was not proof that the former was the cause of the latter; because, first, even if the observation were repeated many times, coincidence could not be excluded, and, sec­ ondly, previous patterns cannot be guaranteed to con­ tinue in the future. Logically, then, inductive proof of a hypothesis5 is impossible. It is, however, possible to refute a hypothesis by observing events that conflict with it on a single occasion6. This led the philosopher,

'full picture'. For example, during the 2001 epidemic of foot-and-mouth disease in the UK, field investigations revealed uncorroborated suspicion of transmission of the disease by undisclosed movements of livestock, thereby providing a fuller explanation of the disease's spread (Gibbens et a/., 200lb) - an approach with which positivists would be unsympathetic. In the social sciences, the need to locate oneself 'within' the area of research now is accepted as fundamental to the analytical procedure, and is formally termed 'experiential analysis' (Reinharz, 1 983). This is similar to the acquisition of 'interactive knowledge', which is obtained by direct involvement with, and experience of, society (Habermas, 1972). More­ over, positivism excludes moral and ethical judgements (for example, on the social and psychological effects of a particular disease control campaign: Mepham, 2001), which are made possible only by reflection ­ so-called 'critical knowledge' (Habermas, 1972).

5 A hypothesis is a theory that is not well tested. This contrasts with laws and facts. (See Chapter 19 for a fuller discussion.) 6

Probably the commonest example quoted in the literature is of the

cockerel and the sunrise. The crowing of the cockerel always precedes J

the rising of the sun. However, the hypothesis that the cockerel causes the This is a simplification, which is inevitable in a brief introduction.

A short, but scholarly, discussion is provided by Medawar (1969). 4

This approach, which generates 'instrumental knowledge', has

become synonymous with contemporary scientific method, but repres­

sun to rise can be refuted by strangling it before dawn. The 20th century philosopher, Bertrand Russell, gives another poultry example: an 'induct­ ivist turkey' who reasons to the effect that, since every day in the past he has been fed at nine o'clock by the farmer, he will today again be fed as

ents only one way of acquiring knowledge (Feyeraband, 1 975; Giddens,

the farmer approaches at nine 0' clock, as usual - but today it is Christmas

1987; Uphoff, 1 992; Liamputton and Ezzy, 2005), and may not present the

Eve!

Causality

Karl Popper (1959), to conclude that science advances

cannot lead to unanimity or stability of belief because

only by elimination of hypotheses7.

there may be a variety of conflicting sources9.

In epidemiology, studies are generally undertaken

Secondly, appeal may be made to the opinions of

to identify causes of disease so that preventive mea­

experts, whose authority is generally acknowledged.

sures can be developed and implemented, and their

This is a reasonable and widely used approach.

subsequent effectiveness identified (Wynder, 1985).

However, experts' opinions may vary, and such

Such investigations of cause are usually based on

authority is only relatively final because opinions may

inductive reasoning, which, despite its philosophical

be modified in the light of new knowledge or more

deficiencies, still forms the pragmatic basis on which

convincing arguments.

most conclusions need to be drawn in epidemiology and other sciences, and on which a workable definition of 'proof' is based 8.

Intuition Some propositions may be considered to be self­ evident, without being sustained by evidence. Thus,

Methods of acceptance of hypotheses One may accept (or reject) a causal hypothesis by four methods (Cohen and Nagel, 1934):

many veterinarians judged speed of slaughter of animals on infected premises to be crucial in the con­ trol of foot-and-mouth disease before firm evidence in support of this proposition was presented (Honhold

et al., 2004; Thrusfield et al., 2005b). Intuition may be

1.

tenacity;

moulded by training, experience and fashion. How­

2.

authority;

ever, intuitive notions (e.g., that the Earth is flat)

3. 4.

intuition;

may subsequently be shown to be false. Therefore,

scientific inquiry.

intuitions need to be tested. Tenacity, authority and intuition may all contribute,

Tenacity Habit makes it easy to continue to believe a proposi­

to varying degrees, to an individual's belief in the veracity of a hypothesis, and such belief can be insidious, colouring scientific investigation - a danger

tion and to offer a closed mind either to the opinions of

highlighted by Sir Peter Medawar, former Director of

others or to evidence that contradicts the proposition.

the National Institute for Medical Research, London

Thus, some people continued to believe that smoking

(1979):

was beneficial because it 'cleared the chest', even after Doll (1959) provided evidence that it induced lung cancer. The method of tenacity is unsatisfactory

'. . . the intensity of the conviction that a hypothesis is true has no bearing on whether it is true or not.'

because it disregards the opinions of others, and, if they are considered, provides no framework for choosing between them.

Scientific inquiry Clarity, order and consistency in fixing beliefs, inde­ pendent of the idiosyncrasies of a few individuals,

Authority Sometimes, appeal is made to a highly respected source to substantiate views. First, this may involve an appeal to an allegedly infallible source. This is, for instance, the basis of religious beliefs. However, this

are required. This is the basis of scientific inquiry, which involves making objective observations that can be repeated by many investigators. Scientific method encourages doubt (and the scientist's prudent distrust of himself: Baker, 1973) and, as either new evidence or new doubts arise, they are incorporated in the accumu­ lating body of knowledge. Thus, science is progressive and is never too certain about its resultslO. It therefore

7 Popper's philosophy contrasts with Kuhn's concept of paradigm

shifts in science (see Chapter 1). Between the rare crises that stimulate the latter, conservatism and conformity do not favour serious criticism of

differs radically from tenacity, authority and intuition, which generally exclude the possibility of errors and have no provision for correcting them.

prevailing scientific assumptions; whereas Popper urges constant chal­ lenging of current scientific beliefs (Fuller, 2003). For a critical treatment of Popper's writings, see Notturno (1999).

H Philosophers, too, have been aware of the utility of induction.

9 These may not only vary between faiths, but also within faiths, lead­

Thus, although Mill and Hulme are both sceptical about induction,

ing, for example, to shifting definitions of orthodoxy and heresy (George,

because induction itself cannot be established empirically (i.e., as

1995).

being reliable merely by observation), they both appear to conclude that induction - though philosophically unjustifiable - is, none the less, indispensable.

10

The 19th century biologist, T.H. Huxley, concisely summarized a

'The great tragedy of Science­ the slaying of a beautiful hypothesis by an ugly fact'. necessary consequence of scientific inquiry:

Evans' rules

The remainder of this chapter now focuses on causality specifically in the context of disease.

Koch's postulates Chapter 1 indicated that there has been a transition from the idea that disease has a predominantly single cause to one of multiple causesl l . The former idea is epitomized by the postulates, formulated by Robert Koch in the late 1 9th century, to determine the cause of infectious disease (Koch, 1 892) . These postulates12, which are based on inductive reasoning, state that an organism is causal if: it is present in all cases of the disease; it does not occur in another disease as a fortuitous and non-pathogenic parasite; it is isolated in pure culture from an animal, is repeatedly passaged, and induces the same dis­ ease in other animals.

• •

Koch's postulates brought a necessary degree of order and discipline to the study of infectious disease. Few would argue that an organism fulfilling the above criteria does not cause the disease in question; but is it the sole and complete cause? Koch provided a rigid framework for testing the causal importance of a microorganism but ignored the influence of environ­ mental factors, which were relatively unimportant in relation to the lesions that were being studied. Microbiologists found it difficult enough to satisfy the postulates without concerning themselves with interactions between complex environmental factors. Therefore the microorganisms were assumed to be the sole causes of the diseases that the microbiologists were investigating. Dissatisfaction became evident in two groups (Stewart, 1 968). Some microbiologists thought that the postulates were too difficult to satisfy because there can be obstacles to fulfilling Koch's postulates with some infectious agents that are causes of disease (e.g., some pathogens can be isolated in pure culture from cases, but do not readily induce disease in other animals; see, for example, Chapter 5: 'Diseases caused by mixed agents'). Others thought that the postulates

were insufficient because they did not specify the envi­ ronmental conditions that turned vague associations into specific causes of disease. Furthermore, the postu­ lates were not applicable to non-infectious diseases. A more cosmopolitan theory of cause was needed.

Evans' rules Alfred Evans (I 976) has produced a set of rules that are consistent with modern concepts of causality: the proportion of individuals with the disease should be significantly higher in those exposed to the supposed cause than in those who are not; exposure to the supposed cause should be present more commonly in those with than those without the disease, when all other risk factors are held constant; the number of new cases of disease should be significantly higher in those exposed to the sup­ posed cause than in those not so exposed, as shown in prospective studies; temporally, the disease should follow exposure to the supposed cause with a distribution of incuba­ tion periods on a bell-shaped curve;1 3

a spectrum of host responses, from mild to severe, should follow exposure to the supposed cause along a logical biological gradient; a measurable host response (e.g., antibody, cancer cells) should appear regularly following exposure to the supposed cause in those lacking this response before exposure, or should increase in magnitude if present before exposure; this pattern should not occur in individuals not so exposed; experimental reproduction of the disease should occur with greater frequency in animals or man appropriately exposed to the supposed cause than in those not so exposed; this exposure may be deliberate in volunteers, experimentally induced in the laboratory, or demonstrated in a controlled regulation of natural exposure; elimination (e.g., removal of a specific infectious agent) or modification (e.g., alteration of a deficient diet) of the supposed cause should decrease the frequency of occurrence of the disease; prevention or modification of the host's response (e.g., by immunization or use of specific lym­ phocyte transfer factor in cancer) should decrease

11

Complexity, however, should not be sought when it is not justified.

This guideline is encapsulated in the 'principle of parsimony' (Hamilton, 1852), whose frequent and thorough use by the media2val English philosopher, William of Occam, gained it the name of 'Occam's razor': 'Pluralitas non est ponenda sine necessitate': 'multiplicity ought not to be

posited without necessity'. More generally, one should choose the simplest hypothesis that will fit the facts (Edwards, 1967). 12

The postulates are more fully termed the Henle-Koch postulates.

13

The bell shape is often obtained only when the horizontal 'time' axis

is mathematically transformed (Sartwell, 1950, 1966; Armenian and Lilienfeld, 1974; Armenian, 1987); if a linear time scale is used, then the curve is usually positively skewed, that is, there are few long incubation

Koch empirically validated postulates deductively reasoned 40 years

periods relative to the number of short incubation periods. Mathematical

earlier by his teacher, Jacob Henle (Rosen, 1938).

transformation is described in Chapter 12.

Ii

Causality

or eliminate the disease that normally occurs on exposure to the supposed cause; all relationships and associations should be bio­ logically and epidemiologically credible.

An important characteristic of Evans' rules, which unified principles of establishing causality for both infectious and non-infectious diseases14, is that some require the association between a hypothesized causal factor and the disease in question to be statistic­ ally significant. This involves comparing groups of animals, rather than investigating associations in the individual. Demonstration of a statistically significant associ­ ation, however, does not prove that a factor is causal15. The logical reduction of proof requires that the mech­ anism of induction of a disease by a cause needs to be explained by describing the chain of events, from cause to effect, at the molecular level, corresponding to a 'deeper' level of understanding than that offered by statistical association (Lower, 1 983). However, in the absence of experimental evidence, epidemiological identification of an association can be of considerable preventive value because it can indicate factors, the reduction or removal of which is empirically shown to reduce the occurrence of disease, although a specific cause has not been identified (see Chapter 2). Some of the statistical techniques of demonstrating association are described in Chapters 14 and 15.

Variables The object of detailed statistical analysis is to identify those factors that cause disease. Disease and causal factors are examples of variables. Variable

A variable is any observable event that can vary. Examples of variables are the weight and age of an animal and the number of cases of disease. Study variable

A study variable is any variable that is being considered in an investigation. 14

In so doing, Evans built on the Henle-Koch postulates, the criteria

for causality for non-infectious diseases established by Yerushalmy and Palmer (1959) and Huebner's (1957) argument that prevention should be counted among the criteria. For a detailed discussion of the evolution of causal criteria, see Lower and Kanarek (1983). 15

Statisticians' views on the relationship between statistical associ­

ation and causality, and the extent to which statistical associations demon­ strated in either a single study or several studies (e.g., meta-analysis; see Chapter 16), indicate cause, vary widely (Pearson, 1911; Cox and Wermuth, 1996). Pearl (2000) discusses this issue in detail.

(1) Statistically u nassociated (2) Statistically associated

__ non·causally

associated

....... causally associated

¥

....

i nd i rectly associated d i rectly associated

Fig. 3.1 Types of association between disease and hypothesized causal factors.

Response and explanatory variables

A response variable is one that is affected by another (explanatory) variable. In epidemiological invest­ igations, disease is often the response variable. For example, when studying the effects of dry cat food on the occurrence of urolithiasis, cat food is the explan­ atory variable and urolithiasis is the response variable.

Types of association Association is the degree of dependence or independ­ ence between two variables. There are two main types of association (Figure 3 . 1 ):

1. 2.

non-statistical association; statistical association.

Non-statistical association

A non-statistical association between a disease and a hypothesized causal factor is an association that arises by chance; that is, the frequency of joint occurrence of the disease and factor is no greater than would be expected by chance. For example, Mycoplasma felis has been isolated from the eyes of some cats with con­ junctivitis. This represents an association between the mycoplasma and conjunctivitis in these cats. However, surveys have shown that M. felis also can be recovered from the conjunctivae of 80% of apparently normal cats (Blackmore et aI., 1971 ). Analysis of these findings revealed that the association between conjunctivitis and the presence of M. felis arose by chance: the mycoplasma could be present in healthy cats as well in those with conjunctivitis. In such circumstances, where a chance, non-statistical association occurs, a factor cannot be inferred to be causal. Statistical association

Variables are positively statistically associated when they occur together more frequently than would be expected by chance. They are negatively statistically associated when they occur together less frequently than would be expected by chance. Positive statistical associations may therefore indic­ ate a causal relationship. However, not all factors that

Types of association

/

Abomasal mucosal h.perPlasia

Abomasal mucosal hyperplasia and infection with

H. contortus are risk factors for anaemia, that is, their

I

Infection with

lI

Haemonchus contortus

�A!aemia (a)

(b)

Fig.3.2 Path d iagrams i nd icating the paradigm (a) and an example (b) of causal and non-causal statistical associations. A = Cause of d i sease (explanatory variable); B and C = man ifestations of d i sease (response variables); -----. causal assoc iation; .. - - _ . non-causal assoc iation.

are positively statistically associated with a disease are necessarily causal. This can be understood with the aid of a simple path diagram (Figure 3 .2a). The explanatory variable, A, is the cause of a disease. The response vari­ ables, B and C, are two manifestations of the disease. In these circumstances, there is a statistical causal asso­ ciation between A and B, and between A and C. There is also a positive statistical association between the two response variables, B and C, arising from their separate associations with A, but this is a non-causal association. An example of these associations is given in Figure 3.2b. If infection of cattle with Haemonchus contortus were being investigated, then the following positive statistical associations could be found: •

• •

between the presence of the parasite and abomasal mucosal hyperplasia; between the presence of the parasite and anaemia; between abomasal mucosal hyperplasia and anaemia.

The first two associations are causal and the third non-causal.

1.

A

.. B

2.

3. Fig.3.3 Path d iagrams indicating the parad igm (a) and examples (b) of direct and i nd i rect causal assoc iations: 1 and 2 = direct causal associations; 3 = indirect causal assoc iation (A with C), d i rect causal association (B with C); 4 = d i rect and indirect causal association (A with C).

Trauma � Bruise

C

�Enteritis

B�

Infection with canine parvovirus

A -..B-"C

Leptospirosis

A 4.

presence increases the risk of anaemia. Similarly, in cats, lack of skin pigmentation results in white fur and also increased ultraviolet irradiation of the skin. The latter is associated with cutaneous squamous cell carcinoma (Dorn et al., 1971 ), and white fur is a risk factor for this condition. Risk factors therefore may be either causal or non­ causal. (Some authors reserve 'risk factor' exclusively for causal factors, and use 'risk indicator' or 'risk marker' to describe both causally and non-causally associated factors: Last, 2001 .) A knowledge of risk factors is useful in identifying populations at which veterinary attention should be directed. Thus, high milk yield is a risk factor for ketosis in dairy cattle. When developing preventive measures it is important to identify those risk factors that are causal, against which control should be directed, and those that are non-causal and will not therefore affect the develop­ ment of disease. Explanatory and response variables can be causally associated either directly or indirectly (Figure 3.3). Path diagrams 1 and 2 illustrate direct causal asso­ ciations. Indirect associations are characterized by an intervening variable. Path diagram 3 illustrates an indirect causal association between A and C where the effect of A is entirely through the intervening variable B, whose effect is direct. This is equivalent to saying that A and B operate at different levels, therefore either A or B can be described as the cause of C. Leptospirosis, for example, causes haemoglobinuria by haemolysing red blood cells; a clinician would say that leptospirosis causes the haemoglobinuria, whereas a pathologist might attribute it to intra­ vascular haemolysis. Path diagram 4 in Figure 3.3 illustrates the situation where one explanatory variable, A, has not only a

Infection with Salmonella spp.

A �

(a)

----. Haemolysis -.. Haemoglobinuria

Rabies in bats

I --------... C

,� B

:. I

Rabies in humans Rabies in foxes

� (b)

Causality

direct causal association with a response variable, C, but also an indirect effect on C by influencing another variable, B. For example, in the US people have con­ tracted rabies by inhalation on entering caves where rabies-infected bats roost. They can also contract rabies from foxes that are infected by living in bat-infested caves.

(a)

Confou nd i n g

(b)

Confounding (Latin: confundere to mix together) is the effect of an extraneous variable that can wholly or partly account for an apparent association between variables. Confounding can produce a spurious asso­ ciation between study variables, or can mask a real association. A variable that confounds is called a con­ founding variable or confounder. A confounding variable is distributed non-randomly (i.e., is positively or negatively correlated with the explanatory and response variables that are being studied). A confounding variable generally must16:

/�

�"� Leptospirosis in dairy farmers

Size of dairy herd (confounder)

be a risk factor for the disease that is being studied; and be associated with the explanatory variable, but not be a consequence of exposure to it.

Examples to illustrate the concept

An investigation of leptospirosis in dairy farmers in New Zealand (Mackintosh et al., 1980) revealed that wearing an apron during milking was associated with an increased risk of contracting leptospirosis. Further work showed that the larger the herd being milked, the greater the chance of contracting leptospirosis. It also was found that farmers with large herds tended to wear aprons more frequently for milking than farmers with small herds. The association between the wearing of aprons and leptospirosis was not causal but was produced spuriously by the confounding effect of large herd size (Figure 3 .4a), because large herd size was associated with leptospirosis, and also with the wearing of aprons. Figure 3 .4b illustrates a similar confounding effect in relation to respiratory disease in pigs (Willeberg, 1 980b). A statistical association was demonstrated between fan ventilation and respiratory disease. This was not because fan ventilation caused respiratory disease. The association resulted from the

10

Criteria

for confounding are given in standard texts (e.g.,

Schlesselman, 1982), but there is controversy over conflicting definitions of confounding, and therefore over the conditions required (Kass and Greenland, 1991; Weinberg, 1993; Shapiro, 1997).

Fan ventilation of pig house

/

=

Weari ng an apron

Size of pig herd (confounder)

"� Respiratory disease In pigs �,

Fig. 3.4 Examples of confounding: (a) large dairy herds in relation to leptosp irosis in dairy farmers and the wearing of m i l king aprons; (b) large pig herds in relation to respi ratory d i sease in pigs and fan ventilation. � 'Real' association; .. - - - - spurious association.

confounding effect of herd size: large herds are more likely to develop respiratory disease than small herds, and are also more likely to have fan ventilation rather than natural ventilation. These two examples have been selected to illustrate confounding in situations where the spurious asso­ ciation is obviously rather implausible. However, in many situations, confounding is less obvious, but must be considered, for example, in observational studies that test causal hypotheses (see Chapter 15).

Causal models The associations and interactions between direct and indirect causes can be viewed in two ways, producing two causal 'models'. Causal model 1

The relationship of causes to their effects allows classification of causes into two types: 'sufficient' and 'necessary' (Rothman, 1 976). A cause is sufficient if it inevitably produces an effect (assuming that nothing happens that interrupts the development of the effect, such as death or prophy­ laxis). A sufficient cause virtually always comprises a range of component causes; disease therefore is multifactorial. Frequently, however, one component is commonly described, in general parlance, as the

Causal models

cause17. For example, distemper virus is referred to as the cause of distemper, although the sufficient cause actually involves exposure to the virus, lack of immunity and, possibly, other components. It is not necessary to identify all components of a sufficient cause to prevent disease because removal of one com­ ponent may render the cause insufficient. For example, an improvement in floor design can prevent foot abscesses in pigs even though the main pyogenic bacteria are not identified. A particular disease may be produced by different sufficient causes. The different sufficient causes may have certain component causes in common, or they may not. If a cause is a component of every sufficient cause, then it is necessary18. Therefore, a necessary cause must always be present to produce an effect. In Figure 3.5a, A is the only necessary cause, because it is the only component appearing in all of the sufficient causes. The remaining causes (B-J) are not necessary because there are some sufficient causes with­ out them. This concept is exemplified in Figure 3 .5b, which depicts hypothesized sufficient causes of pneumonic pasteurellosis in cattle. Infection with Pasteurella spp. is the necessary cause, but other com­ ponent causes, including lack of immunity, are required for induction of the disease. Another example of a cause that is necessary but not sufficient is infection with Actinobacillus ligneresi, which must occur before actinobacillosis ('wooden tongue') can develop. However, other factors that dam­ age the buccal mucosae (e.g. sharp, abrasive vegeta­ tion) must be present before the disease develops. In the absence of these factors, the bacterium can be present without disease developing. It is obvious that necessary causes are frequently related to the definition of a disease; for example, lead is a necessary cause of lead poisoning, and P. multocida is a necessary cause of pneumonic pasteurellosis. A cause may be necessary, sufficient, neither, or both, but it is unusual for a single component cause

17 Philosophers are uneasy with such a definition. Note, for instance, Mill's 'argument from caprice': 'Nothing can better show the absence of any

Sufficient cause 1

single out a few as the "causes", calling the rest mere "causal factors" or "causal

Again, the philosopher would be uneasy. Just because one com­

ponent has always been present in all cases, it does not follow that it is the causally operative/necessary component, or that it is a necessary component at all - what if the next case lacks this component?

Sufficient

Sufficient

2

3

(b) Fig. 3.5 Scheme for the causes of d i sease (causal model 1 ) . (a) Parad igm. (b) Hypothetical example for bovine pneu monic pasteurel losis. glob-: Lack of specific globu l i ns; stress : adrenal

stress of environmental origin (e.g., weather); Past.: presence of Mannheimia (Pasteurella) spp.; m i c robe : presence of vi ruses or

mycoplasmata; cell - : lack of cel l u l ar i m m u nity. «a) From Rothman, 1 976; (b) modified from Martin et al., 1 987.)

to be both necessary and sufficient. One example is exposure to large doses of gamma radiation with the subsequent development of radiation sickness. Component causes therefore include factors that have been classified as: •

under human control, or those we deem good or bad, or just those we want to talk IS

Sufficient

cause

cause

conditions" ... We may select the abnormal or extraordinary causes, or those about. I have nothing to say about these principles of invidious discrimination.'

Sufficient

cause

1

porary authors such as Lewis (1986): 'We sometimes single out one among all the causes of some event and call it "the" cause, as if there were no others. Or we

3

®®®

conditions, than the capricious manner in which we select from among the

argument has won the philosophical field, and is echoed by contem­

2

Sufficient cause

(a)

scientific ground for the distinctioll between the cause of a phenomenon and its conditions that which we choose to denominate the cause.' (Mill, 1868). Mill's

Sufficient cause

predisposing factors, which increase the level of

susceptibility in the host (e.g., age and immune status); enabling factors, which facilitate manifestation of a disease (e.g., housing and nutrition); precipitating factors, which are associated with the definitive onset of disease (e.g., many toxic and infectious agents); reinforcing factors, which tend to aggravate the presence of a disease (e.g., repeated exposure to an infectious agent in the absence of an immune response).

! J

Causality

� 7T � ' f \ , " �7 03 t � � Z;;; '\l l 1 �

Change from Reduced O ;:�'�': f''''

Soil

::::'k'

Rapid grass Nitrogenous Cold W'''

"9e of Nervous Movement Age lactation O�'' S disposition

LOW plant Mg High plant N I High plant K

. • High gut

Increased rate Low gut Mg KINa ratio of passage � of digesta

.� -----... _

Stress

t

HI. h gu�

. non-pro eln

t �

I

Endocrine effects

N

;-I

Increased net magnesium loss

Decreased net

magnesium absorption

--.

Fall in blood magnesium

Level 5

Level 4

Level 3

Level 2 Levell

Hypomagnesaemia

Fig. 3.6

Causal web of bovine hypomagnesaemia (causal model 2 ) .

Pneumonia is an example of a disease that has sufficient causes, none of which has a necessary com­ ponent. Pneumonia may have been produced in one case by heat stress where a dry, dusty environment allowed microscopic particulate matter to reach the alveoli. Cold stress could produce a clinically similar result. Multifactorial syndromes such as pneumonia can have many sufficient causes, although no single component cause is necessary. Part of the reason is taxonomic: pneumonia is a loosely connected group of diseases whose classification (see Chapter 9) is based on lesions (inflammation of the lungs), rather than specific causes; the lesions can be produced by many different causes. When a disease is classified according to aetiology, there is, by definition, usually only one major cause, which therefore is likely to be neces­ sary. Examples include lead poisoning, actinobacil­ losis and pasteurellosis, mentioned above, and many 'simple' infectious diseases, such as tuberculosis and brucellosis. The object of epidemiological investigations of cause is the identification of sufficient causes and their component causes. Removal of one or more compon­ ents from a sufficient cause will then prevent disease produced by that sufficient cause. Causal model 2

Direct and indirect causes represent a chain of actions, with the indirect causes activating the direct causes (e.g., Figure 3 .3, path diagram 3). When many such relationships occur, a number of factors can act at

the same level (but not necessarily at the same intens­ ity), and there may be several levels, producing a 'web of causation'. Again, disease is multifactorial. Figure 3.6 illustrates the causal web of bovine hypomagnesaemia.

Formulating a causal hypothesis The first step in any epidemiological investigation of cause is descriptive. A description of time, place, and population is useful initially. Time

Associations with year, season, month, day, or even hour in the case of food poisoning investigations, should be considered. Such details may provide information on climatic influences, incubation periods and sources of infection. For example, an outbreak of salmonellosis in a group of cattle may be associated with the introduction of infected cattle feed. Place

The geographical distribution of a disease may indic­ ate an association with local geological, management or ecological factors, for example nutritionally defi­ cient soil or arthropod transmitters of infection. Epi­ demiological maps (see Chapter 4) are a valuable aid to identifying geographical associations. For example, mapping of the location of cattle fatalities in South Africa, linked to meteorological data, revealed that the

Formulating a causal hypothesis

fatalities were due to ingestion of grass contaminated with copper from a nearby copper mine (Gummow et al., 1 991 ) (addressed more fully in Chapter 22). Population

The type of animal that is affected often is of consider­ able importance. Hereford cattle are more susceptible to squamous cell carcinoma of the eye than other breeds, suggesting that the cause may be partly genetic. In many parts of the world, meat workers are affected more often by Q Fever than are other people, implying a source of infection in meat-processing plants. When the major facts have been established, alternat­ ive causal hypotheses can be formulated. An epidemio­ logical investigation is similar to any detective novel that unfolds a list of 'suspects' (possible causal factors), some of which may be non-statistically associated with a disease, and some statistically associated with the disease, either causally or non-causally.

Methods of deri v i n g

a

hypothes i s

There are four major methods of arriving at a hypothesis:

1. method of difference; 2.

method of agreement;

3. method of concomitant variation; 4. method of analogy.

with the greater frequency of bovine spongiform en­ cephalopathy (Wilesmith, 1 993). This added credence to the hypothesis that the causal agent was transmitted in meat and bone meal in concentrate rations. A defect of a hypothesis based on the method of dif­ ference is that several different factors usually may be incriminated as possible causes. The value of a hypo­ thesis generated by this method is reduced if many alternative hypotheses can be formulated. For example, a comparison of the different disease patterns of pigs in Africa and Denmark would involve a large number of variables, many of which could be hypothesized as causal. In contrast, the marked occurrence of mannosi­ dosis in Angus cattle (Jolly and Townsley, 1 980), com­ pared with the absence of this disease in other breeds, strongly suggests that a genetic factor is the cause. Method of agreement

The method of agreement (Mill's canon 2) reasons that, if a factor is common to a number of different circum­ stances in which a disease is present, then the factor may be the cause of the disease. Thus, if a batch of meat and bone meal was associated with salmonellosis on widely different types of pig farms, and this was the only circumstance in common, then the causal hypo­ thesis - that disease was caused by contamination of that batch - is strengthened. A second example relates to bovine hyperkeratosis which was identified in cattle in the US (Schwabe et al., 1 977). The disease was called 'X disease' because ini­ tially the cause was unknown. It occurred in different circumstances: •

Method of difference

The method of difference (Mill's canon 1) argues that, if the frequency of a disease is different in two different circumstances, and a factor is present in one cir­ cumstance but is absent from the other, then the factor may be suspected of being causal. For instance, Wood (1978) noted an increased occurrence of stillbirths in pigs in one of three farrowing houses. The only dif­ ference between this house and the other two was a different type of burner on its gas heaters. A hypo­ thesis was formulated: that the different type of burner caused the stillbirths. Subsequently, the burners were shown to be defective and producing large amounts of carbon monoxide; the carbon monoxide was assumed to cause the stillbirths. The occurrence of stillbirths decreased when the faulty burners were removed, thus supporting the hypothesis. Similarly, bovine spongiform encephalopathy occurred to a different extent on the Channel Islands (Jersey and Guernsey), and meat and bone meal was used more frequently in feedstuffs on the island

I;

• •

in cattle that were fed sliced bread; in calves that had been licking lubricating oil; in cattle that were in contact with wood preservative.

The bread slicing machine was lubricated with a sim­ ilar oil to that which had been licked by the calves. The lubricating oil and the wood preservative both contained chlorinated naphthalene. This chemical was common to the different circumstances and sub­ sequently was shown to cause hyperkeratosis. Method of concomitant variation

The method of concomitant variation (Mill's canon 5) involves a search for a factor, the frequency or strength of which varies continuously with the frequency of the disease in different situations. Thus, the distance over which cattle are transported before slaughter appears to be related to the occurrence of bruises in their car­ casses (Meischke et al., 1 974). Similarly, there appear to be relationships between the occurrence of squamous cell carcinoma of the skin of animals and the intensity

Causality

Table 3.1 The relationship between frequency of m i l king and serological evidence of exposure to leptosp i rosis in dairy farm personnel in the Manawatu region of New Zealand. Frequency ofmilking

Ser%gicalleptospirosis

of cows by personnel Present

Absent

Total number

Percentage of personnel with

of personnel

serological leptospirosis

61

1 16

1 77

34.5

1 -8 ti mes/week

4

11

15

26.7

Rarely or never

20

20

0 .0

9 times/week

Table 3.2 The relationship between number of cigarettes smoked per day and deaths from l u ng cancer in British doctors, 1 95 1 -6 1 . (From Doll and H i l l, 1 964a.) Cigarettes/day in 195/

None 1 -14

Annual lung cancer death

rate/I 000 (1951-61) 0.07 0 .54

1 5-24

1 .39

225

2 .27

of ultraviolet radiation, between the occurrence of bovine hypomagnesaemia and pasture levels of mag­ nesium, and between infection of dairy personnel with leptospires and the frequency with which the person­ nel milk cows (Table 3.1). The classical medical epi­ demiological investigation of the association between smoking and lung cancer (Doll and Hill, 1 964a,b) also illustrates this method of reasoning (Table 3.2): the number of deaths due to lung cancer is proportional to the number of cigarettes smoked per day19. Method of analogy

This method of reasoning involves comparison of the pattern of the disease under study with that of a dis­ ease that already is understood, because the cause of a disease that is understood may also be the cause of another poorly understood disease with a similar pattern. For example, some mammary tumours of mice are known to be caused by a virus, therefore some mammary tumours of dogs may have a viral cause. The climatic conditions associated with outbreaks of Kikuyu grass poisoning of cattle may suggest a myco­ toxin as the cause because the circumstance is similar to those circumstances present in other mycotoxicoses (Bryson, 1 982). Bovine petechial fever, caused by Cytoecetes ondiri, is present in a limited area of Kenya (Snodgrass, 1974). The mode of transmission of this

19

This seminal investigation eventually became a 50-year study

(Doll ct al., 2004).

infectious agent is unknown. However, other mem­ bers of the genus Cytoecetes are known to be trans­ mitted by arthropods, and geographic limitation is a feature of arthropod transmitted diseases. Therefore, using the method of analogy, it has been suggested that C. ondiri may be transmitted by arthropods. Evidence by analogy is not, in the strictest sense, evidence of fact, It can point to probabilities, and can confirm conclusions that may be reached by other means; but it can be dangerously misleading (and was not considered sound enough by Mill to be included as a canon). A classical example is the inference made by the 19th century medical epidemiologist, John Snow, that yellow fever was transmitted by sewage (Snow, 1 855) . He had already demonstrated that cholera was transmitted by sewage, and then observed that cholera and yellow fever were both associated with over­ crowding. He then inferred that cholera and yellow fever had similar modes of transmission, whereas the latter actually is transmitted by an arthropod rather than by contaminated sewage.

Pri n c i p l es for estab l i s h i n g cause: Hi l l 's criteria The British medical statistician, Austin Bradford Hill, proposed several criteria for establishing a causal asso­ ciation (Hill, 1965), including: • • • • •

the time sequence of the events; the strength of the association; biological gradient; consistency; compatibility with existing knowledge.

Time sequence

Cause must precede effect. In a bacteriological survey, Millar and Francis (1 974) found an increased occur­ rence of various infections in barren mares compared with others whose reproductive function was normal. However, unless the bacterial infections were present before the mares became infertile, it would be incorrect to infer that the bacterial infections caused infertil­ ity. The causal pathway may have been in the other

Formulating a causal hypothesis

direction: absence of normal reproductive cyclic activity may allow previously harmless infections to flourish. Strength of association

If a factor is causal, then there will be a strong positive statistical association between the factor and the disease.

l)

syndrome (see Figure 9.3d), and, earlier in this chapter, the latter has been shown to be a suspect method of reasoning. A fuller discussion of reasoning and causal inference in general is given by Taylor (1967) and Pinto and Blair (1993), and, in the context of epidemiology, by Buck (1975), Maclure (1985), Weed (1 986), Evans (1993) and Rothman and Greenland (1998). The testing of hypotheses using observational studies is described in Chapter 15.

Biological gradient

If a dose-response relationship can be found between a factor and a disease, the plausibility of a factor being causal is increased. This is the basis of reasoning by the method of concomitant variation. Examples have already been cited: frequency of milking in relation to leptospirosis (see Table 3.1), and smoking in relation to lung cancer (see Table 3.2).

Fu rther read i n g Doll, R. (2002) Proof of causality: deduction from epidemio­ logical observation. Perspectives in Biology and Medicine, 45, 499-515 Evans, A.S. (1993) Causation and Disease: A Chronological

Journey. Plenum Publishing Corporation,New York Falkow, S. (1988) Molecular Koch's postulates applied to microbial pathogenicity. Reviews of Infectious Diseases, 10,

Consistency

If an association exists in a number of different circum­ stances, then a causal relationship is probable. This is the basis of reasoning by the method of agreement. An example is bovine hyperkeratosis, mentioned above.

Suppl. 2,S274-S276. (Modification of Koch's postulates to suit

the genetic basis of microbial pathogenicity) Goodstein, D. (2000) How science works. In: Reference

Manual on Scientific Evidence, 2nd edn, pp. 67-82. Federal Judicial Center, Washington. (A brief, selective discussion of

scientific method) Jeffreys, H. (1973) Scientific Inference. Cambridge University

Compatibility with existing knowledge

It is more reasonable to infer that a factor causes a disease if a plausible biological mechanism has been identified than if such a mechanism is not known. Thus, smoking can be suggested as a likely cause of lung cancer because other chemical and environmen­ tal pollutants are known to have a carcinogenic effect on laboratory animals. Similarly, if a mycotoxin were present in animal foodstuffs, then it might be expected to produce characteristic liver damage. On the other hand, the survey of leptospirosis of dairy farmers, men­ tioned earlier, showed a positive association between wearing an apron and having a leptospiral titre. This finding was not compatible with either existing know­ ledge or common sense, and a factor that might have confounded the result was sought and found. Hill also included specificity of response (a single cause leads to a single effect) and analogy in his set of criteria2o. However, the former is faulted (Susser, 1977): some causes are known to induce more than one

Press,Cambridge Last, J.M. (Ed.) (2001) A Dictionary of Epidemiology, 4th edn. Oxford University Press,New York Lower, G.M. (1983) Systematic epidemiologic theory: con­ ceptual foundations and axiomatic elements. Medical Hypotheses, 11, 195-215. (A concise discussion of causality, and causal criteria) Rothman, K.J. and Greenland,S. (1998) Modern Epidemiology, 2nd edn. Lippincott-Raven,Philadelphia Susser, M. (1973) Causal Thinking in the Health Sciences.

Concepts and Strategies of Epidemiology. Oxford University Press,New York, London and Toronto Susser, M. (1977) Judgment and causal inference: criteria in epidemiologic studies. American Journal of Epidemiology, 105,1-15

Tarski,A. (1995) Introduction to Logic and to the Methodology of

Deductive Sciences. Dover Publications,New York Taylor,R. (1967) Causation. In: The Encyclopedia of Philosophy, Vol. 2. Ed. Edwards, P., pp.

56-66. The Macmillan

Company and The Free Press,New York Vineis, P. (2004) Causality in epidemiology. In: A History of

Epidemiologic Methods and Concepts. Ed. Morabia, A., pp. 337-349. Birkhauser Verlag, Basel

20

Specificity of response, having its origins in Koch's postulates, had

already been argued as being central to causal inference (Yerushalmy and Palmer, 1959), and was cited in the debate on the relationship between smoking and lung cancer (Berkson, 1960, 1962).

Describing disease occurrence

This chapter discusses the types of animal population that are encountered in veterinary medicine, and describes the methods of expressing the amount and temporal and spatial distribution of disease in these populations.

Some bas i c terms Endemic occurrence

'Endemic' is used in two senses to describe:

1. 2.

the usual frequency of occurrence of a disease in a population; the constant presence of a disease in a population.

Thus, the term implies a stable state; if a disease is well understood, then its endemic level is often predictable. The term 'endemic' can be applied not only to overt disease but also to disease in the absence of clinical signs and to levels of circulating antibodies. Therefore, the exact context in which the term is used should always be defined. For example, laboratory mice kept under conventional systems of 'non-barrier mainten­ ance' (i.e., with no special precautions being taken to prevent entry and spread of infection into the popula­ tion) are invariably infected with the nematode Syphacia obvelata. Infection of 100% of the mice would be consid­ ered the usual level of occurrence, that is, the endemic level of infection. When a disease is continuously pre­ sent to a high level, affecting all age-groups equally, it is hyperendemic. In contrast, the endemic level of actino­ bacillosis in a dairy herd is likely to be less than 1 % . 'Endemic' i s applied not only t o infectious diseases but also to non-infectious ones: the veterinary meat hygienist is just as concerned with the endemic level of carcass bruising as is the veterinary practitioner with the endemic level of pneumonia in pigs.

When endemic disease is described, the affected population and its location should be specified. Thus, although bovine tuberculosis is endemic in badgers in south-west England, the infection apparently is not endemic in all badger populations in the UK (Little et al., 1 982). Epidemic occurrence

'Epidemic' originally was used only to describe a sudden, usually unpredictable, increase in the number of cases of an infectious disease in a population. In modern epidemiology, an epidemic is an occurrence of an infectious or non-infectious disease to a level in excess of the expected (i.e., endemic) level. Thus, infection with S. obvelata should be absent from specific-pathogen-free (SPF) mice kept under strict barrier conditions where precautions are taken to prevent entry and spread of infectious agents in the colony. If an infected mouse gained entry to the colony, the infection would be transmitted through­ out the resident population and an epidemic of the nematode infection would occur. Such an infection in SPF mice colonies would be unusually frequent, that is, epidemic. Similarly, if cattle grazed on rough pas­ ture, which could abrade their mouths, there might be an increase in the number of cases of actinobacillosis. Although only 2% of the animals might become infected, this would be an unusually high (epidemic) level compared with the endemic level of 1 % in the herd. Thus, an epidemic need not involve a large number of individuals. When an epidemic occurs, the population must have been subjected to one or more factors that were not present previously. In the example of the SPF mouse colony that became infected with S. obvelata, the factor was a breakdown in barrier maintenance and the entry

Describing d isease occurrence

of an infected mouse. In the case of the herd with actinobacillosis, the new factor was an increased consumption of vegetation that could cause buccal abrasions. The popular conception of an epidemic frequently is an outbreak of disease that is noticed immediately. However, some epidemics may go undetected for some time after their occurrence. Thus, in London, in 1952, the deaths of 4000 people were associated with a particularly severe smog (fog intensified by smoke). The deaths occurred at the same time as the Smithfield fat stock show (HMSO, 1954). Although an epidemic of severe respiratory disease in the cattle was recognized immediately, and was associated with the air pollution caused by the smog, the epidemic of human respir­ atory disease was not appreciated until statistics recording human deaths were published more than a year later. In contrast, some epidemics may be exaggerated. An increased number of deaths in foxes occurred in the UK in the late 1950s. This apparent epidemic of a 'new' fatal disease received considerable publicity and every dead fox was assumed to have died from the disease. Subsequent laboratory analyses identified chlorinated hydrocarbon poisoning as the cause of the increased fox fatality, but only 40% of foxes submitted for post­ mortem examination had died from the poisoning. The other 60% had died of endemic diseases that had not previously stimulated general interest (Blackmore, 1964). This example illustrates that the endemic level of disease in a population has to be known before an epidemic can be recognized. Pandemic occurrence

A pandemic is a widespread epidemic that usually affects a large proportion of the population. Many countries may be affected. Pandemics of rinderpest (see Table 1 .1 ), foot-and-mouth disease, and African swine fever have been the cause of considerable financial loss. By the 1970s, rinderpest was found only in north-west Africa and the Indian subcontinent, but the disease became pandemic in Africa and the Middle East during the early 1980s (Sasaki, 1991), and became the target of a global eradication campaign (Wojciechowski, 1991), which is reaching a successful climax (Table 1 .4). In the late 1970s, a pandemic of parvovirus infection occurred in dogs in many parts of the world (Carmichael and Binn, 1981). Serious human pandemics have included plague (the Black Death), which spread throughout Europe in 13481, cholera 1

in the 19th century, influenza soon after the First World War, and, currently, HIV / AIDS (particularly in Africa). Sporadic occurrence

A sporadic outbreak of disease is one that occurs irregu­ larly and haphazardly. This implies that appropriate circumstances have occurred locally, producing small, localized outbreaks. Foot-and-mouth disease is not endemic in the UK. A sporadic outbreak, thought to be associated with the importation of infected Argentine lamb that entered the animal food chain, occurred initially in Oswestry in October 1967 (Hugh-Jones, 1972). Unfortunately, this incident, and several subsequent ones associated with the imported lamb, resulted in an epidemic, which was not eliminated until the middle of 1968 (Figure 4.1a). Similarly, the more widespread epidemic of foot-and-mouth disease that occurred in the UK in 2001 (Figure 4.1b) began as a sporadic outbreak in a pig herd at Heddon-on-the-Wall in Northumbria (DEFRA, 2002b; Mansley et al., 2003), and was most likely caused by contamination of swill by illegally imported meat. However, in both epidemics, the disease did not become endemic because of veterinary intervention. Conversely, in 1969, a single sporadic case of rabies occurred in a dog in the UK after it had completed the statutory 6-month quarantine period (Haig, 1977). No other animal was infected and so this sporadic outbreak was confined to the original case. Thus 'sporadic' can indicate either a single case or a cluster of cases of a disease or infection (without obvious disease) that is not normally present in an area. Infection with Leptospira interrogans, serovar pomona, is endemic in domestic pigs in New Zealand. The bacterium is also frequently the cause of sporadic epidemics of abortion in cattle. Infected cattle excrete the bacterium in their urine only for approximately 3 months. The bacterium therefore cannot usually be maintained, and so become endemic, in the herd. If a cow becomes infected with the bacterium by direct or indirect contact with pigs, this constitutes sporadic infection. This animal may now become a short-term source of infection to other pregnant cattle in the herd, and a sporadic epidemic of abortion, of 3 or 4 months' duration, is likely to occur. Post-infection leptospiral antibodies persist for many years in cattle, and spor­ adic infection with the bacterium is not uncommon; 18% of New Zealand cattle have been reported to have

lords weaker. Consequently, wealth was sought in commerce, and the The pandemic eliminated nearly a third of the population, but popu­

great cities of Amsterdam. Florence, London, Paris, Vienna and Venice

lation decline continued long after. In 1450, Europe's population was

developed. In Italy, this produced the urban cultural climate in which The

probably nearly half of what it had been in the early 14th century. Thus,

Renaissance could be born and flourish (Holmes, 1996) - illustrating that

agricultural labour became scarce, labourers became stronger, and land-

disease can have consequences far beyond the bounds of health.

III

Describing disease occurrence 80

(a)

'" -"

70

Q)

60

50

co

-B� '0

� Q) .0

E

� z

40 30 20 10 March

1967

April

May

1968

60

(b)

50

-" co

(J)

�0 '0 0;

.a E � z

40

30

20

10

2001

October

Fig. 4.1 Epidemics of foot-and-mouth d i sease in the U K : n u m ber of outbreaks per day. (a) 1 967-68. (From HMSO, 1 969); (b) 2001. (From DEFRA, 2002b. © Crown copyright; Reproduced by kind permission of D E F RA.)

detectable antibodies to this organism. Thus, although infection and the abortion that may ensue are sporadic, there is an endemic level of antibody in the bovine population (Hathaway, 1981). Outbreaks

The Office In ternational des Epizooties defines an out­ break as 'an occurrence of disease in an agricultural establishment, breeding establishment or premises, including all buildings as well as adjoining premises, where animals are present', the term generally imply­ ing that several animals are affected. Livestock in developed countries are usually kept as separated populations (see below) and so 'outbreak' can be applied unambiguously to an occurrence of disease on

an individual farm. For example, the epidemic of foot­ and-mouth disease in the UK in 2001 comprised 2030 infected premises (i.e., outbreaks), which all originated from a single infected pig farm. In contrast, the term sometimes also is used in the context of a single source, irrespective of the number or premises involved. Thus, in the US in 2002-03, exotic Newcastle disease occurred in 21 commercial flocks in California, and over 1 000 'backyard flocks', including some in the neighbouring states of Arizona and Nevada. This was documented as only one outbreak because it was con­ sidered to have arisen from a single introduction of the disease. Subsequently, a second outbreak, involving only one premises, was recorded in Texas (some dis­ tance from the first outbreak); this was determined to be a separate introduction, based on DNA sequencing

Describing disease occurrence

Table 4.1

i C)

Criteria for declaring an outbreak of foot-and-mouth d isease. (From European Com m ission, 2002.)

An outbreak shall be declared where a hold i ng meets one or more of the following criteria: 1.

foot-and-mouth d i sease v i rus has been isolated from an animal, any product derived from that a n i mal, o r its environment;

2.

c l i n ical signs consistent with foot-and-mouth d isease are observed in an a n i mal of a susceptible species, and the vi rus antigen or v i rus ribonucleic acid (RNA) specific to one or more of the serotypes of foot-and-mouth d i sease virus has been detected and identified in samples col lected from the an imal or its cohorts;

3.

c l i n ical signs cons i stent with foot-and-mouth d i sease are observed in a n a n i mal of a susceptible species and the an imal or its cohorts are positive for antibody to foot-and-mouth d i sease vi rus structural or non - structural proteins, provided that previous vaccination, residual maternal antibodies or non-specific reactions can be excl uded as possible causes of seropositiv ity;

4.

virus antigen or vi rus RNA specific to one or more of the serotypes of foot-and-mouth d isease v i rus has been detected and identified i n samples co l l ected from a n i mals o f suscepti ble species a n d the a n i mals are positive for anti body t o foot-and-mouth d i sease v i rus structural or non - structural protei ns, provided that in the case of antibodies to structural prote i n s previous vaccination, res idual maternal antibodies or non-specific reactions can be excl uded as possi ble cau ses of seropositivity;

5.

an epidemiological l i nk has been establ ished to a confirmed foot-and-mouth d isease outbreak and at least one of the fol l owi ng cond itions applies: (a) (b) (c)

one or more a n i mals are positive for antibody to foot-and-mouth d i sease v i ru s structural o r non-structural protei ns, provided that previous vaccination, residual maternal antibodies or non-specific reactions can be excl uded as possible causes of seropositivity; v i rus antigen or v i rus RNA specific to one o r more of the serotypes of foot-a nd-mouth d i sease vi rus has been detected and identified i n samples collected from o n e or more a n i mals o f susceptible species; serological evidence of active infection with foot-and-mouth d i sease by detection of seroconversion from negative to positive for antibody to foot-and-mouth d i sease v i rus structural or non-structural prote i ns has been estab l i shed in one or more a n i m als of suscepti ble species, and previous vaccination, residual maternal antibodies or non-specific reactions can be excluded as poss ible causes of seropositivity.

Where a previously seronegative status can not be reasonably expected, this detection of seroconversion i s to be carried out in paired samples col l ected from the same a n i mals on two or more occasions at least 5 days apart, in the case of structural protei ns, and at least 21 days apart, i n the case o f non-structural proteins.

differences between the two virus strains that were isolated from each outbreak. Moreover, definition of 'outbreak' may include criteria other than the presence of clinical cases, and may be tailored to specific infec­ tions (Table 4.1). I n developing countries, animal populations are frequently contiguous (see below) and so it may be difficult to define the limits of one outbreak. An outbreak is then considered as occurring in part of a territory in which, taking local conditions into account, it cannot be guaranteed that both susceptible and unsusceptible animals have not had direct contact with affected or susceptible animals. For example, in certain areas of Africa, an outbreak means the occurrence of disease within a sixteenth square degree; the occur­ rence is still referred to as an outbreak, even though the disease may occur in several places within the same sixteenth square degree. (Note that the area within a sixteenth square degree is not constant: it varies with latitude.)

the amount of disease can be described. Furthermore, it is usually desirable to describe when and where disease occurs, and to relate the number of diseased animals to the size of the population at risk of devel­ oping disease so that a disease's importance can be assessed. A report of 10 cases of infectious enteritis in a cattery, for example, does not indicate the true extent of the problem unless the report is considered in terms of the number of cats in the cattery: there may be only 10 cats present, in which case all of the cats are affected, or there may be 1 00 cats, in which case only a small proportion of the cats is affected. The amount of disease is the morbidity (Latin: mor­ bus disease); the number of deaths is the mortality. The times of occurrence of cases of a disease constitute its temporal distribution, whereas places of occurrence comprise its spatial distribution. The measurement and description of the size of populations and their characteristics constitute demography2 (Greek: demo­ people; -graphia writing, description). =

=

=

Basic concepts of d i sease q u antification A necessary part of the investigation of disease in a population is the counting of affected animals so that

2 A distinction between zoography and demography is not made in this book, for the reasons given in Chapter 2 in relation to epizootiology and epidemiology.

,[I

Describing disease occurrence

T he structure of animal populations The structure of populations influences the extent to which the size of the population at risk can be assessed, as well as affecting the ways in which disease occurs and persists in animals. The organization of animal populations can usually be described as either con tiguous or separated. ­

Contiguous pop u l ations A contiguous population is one in which there is much contact between individuals in the population and members of other populations. Contiguous popu­ lations therefore predispose to transfer and persistence of infectious diseases over large areas because of the inherent mixing and movement of animals. Most human populations are contiguous because there is mixing of individuals by travel. Populations of small domestic animals also are usually contiguous. Dogs and cats that are not confined to houses move freely within cities, coming into contact with other urban, suburban and rural animals of their own and different species3. African nomadic tribes similarly own animals that comprise contiguous groups. Many wild animals belong to this category, too. Assessing the size of contiguous populations

It is often difficult to assess the size of contiguous animal populations. Only limited demographic data about small domestic animals are available; for ex­ ample, from Kennel Club registers (Tedor and Reif, 1978; Wong and Lee, 1985). In some developed countries, dogs must be legally registered, but this is a difficult law to enforce and so many dogs may not be recorded. There are pet registries that record and identify animals, for example, by ear or leg tattooing (Anon., 1984), but these records are voluntary and so exclude the majority of animals. Increased uptake of identifica­ tion of companion animals by 'microchips', designed to an international standard (Anon., 1 995; Ingwersen, 2000), should facilitate improved enumeration and tracing of these animals4. Over half a million animals were implanted with microchips in the UK within the ten years up to 2000 (Anon., 2000).

3

Such animals are classified as 'free-roaming' (Slater, 2001), a category

that includes strays (i.e., recently lost or abandoned animals) as well as unrestrained, but owned, animals. 4

Microchips are an accurate means of identification of animals,

provided they are properly implanted (Sorensen e/ ai., 1 995; Fry and

Green, 1999). However, the use of different standards in the US and Europe currently hampers international identification of all 'chipped' animals (Fearon, 2004).

Some studies have been undertaken to establish the size and other characteristics of small animal popula­ tions (Table 4.2). However, such animals frequently are kept in small numbers - often only one animal per household. It is therefore necessary to contact many owners to gain information about relatively few animals (i.e., the animal:owner ratio is low). This can be a difficult and costly exercise. The results may also be distorted by the lack of information on undetect­ able segments of the population such as stray, semi­ domesticated and feral animals. Limited demographic data can be obtained from animal-cemetery records (e.g., Hayashidani et al., 1988, 1989) and information held by pet insurance companies (e.g., Bonnett et al., 1997; Egenvall et al., 2000). Non-thoroughbred horses and ponies kept as leisure animals similarly are difficult to count, and their enumeration is frequently indirect. In the UK, for example, estimation of population size has been based on the number of farriers (McClintock, 1988), the amount of shoeing steel produced (Horse and Hound, 1 992), aerial counts (Barr et al., 1986), and surveys of private households (McClintock, 1988; Horse and Hound, 1992). These methods have shortcomings. The first counted farriers, assuming that each shod 250 horses, and ignored unshod horses; the second assumed an average of four new sets of shoes per horse per year, again ignoring unshod horses; the aerial survey omitted horses indoors; and the household surveys excluded some categories of animals such as those in riding centres. However, each produced sim­ ilar figures (for thoroughbred and non-thoroughbred horses, combined), ranging from 500 000-560 000 animals, suggesting valid, but conservative, estimates. In the US, a sample survey of equine operations has provided information on the age and type of horse (USDA, 1998). The requirement for horse 'passports' within the European Union (EUROPA, 2000; Sluyter, 2001; HMSO, 2004) - although primarily designed to protect the health of those who eat horsemeat by preventing horses, dosed with any medicines that are not intended for use in food-producing animals, from entering the human food chain - should lead to better characteriza­ tion of equine populations. Populations of wild animals can be enumerated either directly or indirectly. Direct methods involve observation of individual animals, and include aerial and ground counts (Seber, 1973; Norton-Griffiths, 1978; Southwood, 1978; Buckland et al., 1 993). A common method is capture-release-recapture in which animals are caught, marked and released. A second sample is then captured. The numbers of marked animals recap­ tured in the second sample is then related to the num­ ber initially marked. The simplest index for estimating the number of individuals (Lincoln, 1930) is:

The structure of animal populations

Table 4.2

,!

Some demographic stud ies of dog and cat populations.

Country/region

Characteristics recorded

Source

Bali

Type and characteristics of urban pet owners h i p*

Margawa n i and Robertson ( 1 995)

Canada: Ontario

B reed, age, owner characteristicst

Lesl i e et al. ( 1 994)

Cyprus

Population size

Pappaioanou et al. ( 1 984)

Europe

Population size (by cou ntry) For U K : regional d i stribution, owner characteristics

Anderson ( 1 983)

Malaysia

Breed, sex, l itter size, seasonal d istribution of whelping

Wong and Lee ( 1 985)

Netherlands

Population size*

Lumeij et al. ( 1 998)

Norway

For Bernese mountain dog, boxer, Bichon frise: population size, sex, age, age-spec ific mortality

Moe et al. (200 1 )

P h i l i ppi nes

Density of rural dogs

Robinson et al. ( 1 996); C h i l d s et al. ( 1 998)

Sweden

B reed-spec ific morta l ity Breed, sex, age, owner c haracteristics

Bonnett et al. ( 1 997) Egenvall et al. ( 1 999); Hedhammar et al. ( 1 999); Sal lander et al. (200 1 )

UK

Sex, age, diet Breed Breed, sex, age

Fennell ( 1 975) Edney and Sm ith ( 1 986) Thrusfield ( 1 989)

US

Age, health status Free-roaming populations

Lund et al. ( 1 999) Levy et al. (2003)

US: Boston

Age at death, breed, sex

Bronson ( 1 9 8 1 , 1 982)

US: Cal ifornia

Breed, sex, age, owner characteristics Breed, sex, age� Owner characteristics Breed, sex, age owner characteristics

Dorn et al. ( 1 967b); Franti and Kraus ( 1 974) Schneider and Vaida ( 1 975) Franti et al. ( 1 974) Franti et al. ( 1 980) Schneider ( 1 975)

Population size US: I l l inois

Sex, age, reproductive h i story, owner characteristics

G riffiths and Brenner ( 1 9 7 7)

U S : Indiana

Population size Sex, age, owner characteristics

Lengerich et al. ( 1 992) Teclaw et al. ( 1 992)

US: Kansas

Age, population dynamics

Nasser and Mosier ( 1 980)

US: Nevada

Age, population dynamics

Nasser et al. ( 1 984)

US: New Jersey

Breed, sex, age

Cohen et al. ( 1 959)

US: Ohio

Breed, sex, age, owner characteristics

Schnu rrenberger et al. ( 1 961 )

Zimbabwe

Popu lation size, sex, age, owner characteristics

Butler and B i ngham (2000)

* Also reports ownersh i p of birds and exotic species. t Owner characteristics vary between studies, and i nclude age, occupation, location (urban versus rural), number and age of c h i l d ren, and type of dwe l l ing. � Also reports owners h i p of horses.

an

N=­ r

where:

N = estimated population size;

a = number of individuals initially marked; n number of individuals in the second sample; =

r

= number of marked individuals recaptured in the second sample.

Capture-release-recapture techniques have also been applied to estimating the size of dog populations (Beck, 1 973; Anvik et ai., 1974; Heussner et ai., 1978); and these and other marking techniques can also pro­ vide information on the movement, home range and territories of wild animals, which can be relevant to disease transmission (see Chapter 7). The marking of bait, for example, has facilitated identification of badgers' territories that overlap with dairy farms in

Describing disease occurrence

Table 4.3

Hold ings by size of herd or flock: U K, J u ne, 1 99 7 . (From HMSO, 1 998.)

No. of holdi ngs No. of cows

1-< 7 0 2 2 60 8 556

1 0-

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120 I"iii E 'c V>

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E

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1 1 0 l100 190 80 70 60 50 40 30 20 10 0

:J

t co '"

b',

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n n

Site of infection

Fig. 4.4 The d i stribution of hydatid cysts i n organs of 765 Somalian cattle i n Kuwa it: an example of a bar chart. (Modified from Behbehani and Hassounah, 1 976.)

In a time trend graph the vertical position of each point represents the number of cases; the horizontal position corresponds to the midpoint of the time interval in which the cases were recorded. In Figure 4.5, for instance, the vertical coordinate of each point is the number of new cases of anthrax and the horizontal coordinate is the midpoint of the weekly intervals for which cases of anthrax were reported. The plotting of epidemics in this way produces epidemic curves (see Figure 4 . 1 and Chapter 8) Time lines

Time lines depict disease and related events (e.g., implementation of control procedures) in chronolog­ ical order, along a horizontal line representing the passage of time. They are a simple and useful way of visualizing key events (e.g., Figure 4.6).

Mapping A common method of displaying the geographical (spatial) distribution of disease and related factors is by drawing maps (cartography). This is of value not only in the recording of areas where diseases exist but also in investigating the mode and direction of trans­ mission of infectious diseases. For example, the spatial distribution of cases of foot-and-mouth disease during the British outbreak in 1 967 suggested that the infec­ tion may have been disseminated by wind (Smith and Hugh-Jones, 1969). Subsequent investigations have supported this idea (Hugh-Jones and Wright, 1970; Sellers and Gloster, 1980). Maps can also suggest possible causes of diseases of unknown aetiology. Mapping indicated that tumours (notably of the jaw) in sheep in Yorkshire clustered in areas where bracken was common (McCrea and Head, 1978). This led to the hypothesis that bracken causes tumours. Subsequently, the hypothesis was supported by experimental investigation (McCrea and Head, 1981). Similarly, comparison of the maps of hypocupraemia in cattle (Leech et al., 1982) with a geo­ chemical atlas (Webb et al., 1978) has indicated areas in England and Wales where bovine copper deficiency may be caused by excess dietary molybdenum. At their simplest, maps may be qualitative, indicat­ ing location without specifying the amount of disease. They can also be quantitative, displaying the number of cases of disease (the numerator in proportions, rates and ratios), the population at risk (the denominator), and prevalence and incidence (i.e., including both numerator and denominator).

Describing disease occurrence 12 11 10 9 8

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6

1 3 20 27

3

Mar

10

1 7 24

Apr

8

1 5 22 29 5

May

12

Jun

t t

A

B

Weeks end i ng

Fig. 4.5 An anthrax outbreak i n cattle i n England, 1 January-1 2 June 1 9 7 7, associ ated w i t h a batch o f feedstuff: a n example o f a t i m e trend graph. A = Feedstuff unl oaded at docks; B = Feedstuff arrived at m i l l s. (Modified from MAFF, 1 9 77.)

First I P confirmed

UK declared free of FMD by OlE 23/1/02

20/2/0 1

EU export ban

2 1 /2/01

Last I P

30/9/01

I I

: National l ivestock I I

::

I I I I

movement ban 23/2/01

.. t

I I

First IP confirmed

1/3/01

Last I P

23/5/01

Contiguous cull beg ins

24/3/0 1

3 km cull beg ins

22/3/01

3-10 km

surveillance zone serological sampling ends

3 1/7/01

Contiguous cattle cull ends

26/4/0 1

3 km cull ends

1 5/5/01

Scotland declared free by EU

1 1/9/01

Regional serosurveillance ends

3-10 km 5/9/01 surveillance zone serological Regional sampling serosurvei l lance beg ins beg ins 8/7/01

I

Pig-meat exports begin

2/1 1/01

Lamb-meat exports begin

2211 1/01

1 6/8/0 1

Events in D u mfries and Gal loway: - ; Events in the whole of the U K : - - - + . E U : E u ropean U n ion; I P : Premises confi rmed as affected by foot-and­ mouth d i sease; OlE; Office International des Epizooties. Fig. 4.6 200Sa.)

Time l i ne of the main events in the foot- and-mouth d i sease epidemic in Dumfries and Gal loway, Scotl and, 2001 . (From Thrusfield et al.,

Mapping

_ o c::J

oS"loA-Jr-

mm c::J �

Very (';ommon Common Frequt.'nt I nfreq uent Scarce Apparently absent o r unrecorded

> 50 sl'tts per 10 km sq 31

50

,.

16

30

"

6

15

1

5

December 1 976 .

Miles 0 10 ,

!

Fig. 4.7 Density of badger sells in Great Brita i n : an example of an isoplethic map (geographic base). (From Zuckerman, 1 980.)

Map bases

Maps can be constructed according to the shape of a country or region, in which case they are drawn to a geographic base. Alternatively, they can be drawn to represent the size of the population concerned, that is, to a demographic (isodemographic) base (Forster, 1966), in which morbidity and mortality information is presented in relation to population size. Demographic maps require accurate information on both the numer­ ators and denominators in morbidity and mortality values and are not common in veterinary medicine because this information is often missing.

G eogra p h i c base m aps

Figure 4.7 is an example of a geographic base map, It is

a 'conventional' map of Great Britain, showing the shape of the country. Most atlases consist of geographic base maps. There are several types of geographic base map, each with a different purpose, and displaying informa­ tion in varying detail. Point (dot or location) maps

These maps illustrate outbreaks of disease in discrete locations, by circles, squares, dots or other symbols.

disease occurrence

Longitude (OW)

- - - - --

9

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7 \

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km 50

D isease occurrence:

0 Endemic S1 Only in very wet years

HOBART

Fig. 4.8 Outbreaks of bl uetongue in Portuga l ; J u l y 1 95 6 : an example of a point map. (From Sellers et al., 1 9 78.)

Fig. 4.1 0 Fasciol iasis i n Austra l i a : an example of a d istribution map. (Modified from Barger et al., 1 9 78.)

An example is Figure 4.8, where the solid circles with adjacent names indicate the sites of outbreaks of blue­ tongue in Portugal. Point maps are qualitative; they do not indicate the extent of the outbreaks, which could each involve any number of animals. Point maps can be refined by using arrows to indicate direction of spread of disease. A series of point maps, displaying occurrence at different times, can indicate the direction of spread of an outbreak of disease. Additionally, point maps can be given a quantitative dimension (if data

are available) by varying the density of the dots in proportion to the amount of disease (Figure 4.9).

Fig. 4.9

Distribution maps

A distribution map is constructed to show the area over which disease occurs. An example is given in Figure 4.10, illustrating areas in south-east Australia in which fascioliasis is continually present (endemic areas) and those that only experience the disease in wet

Prevalence of heartworm infection in the US, 1 99 5 . (From 501 1 and Kn ight, 1 995.)

Mapping

• 1 CASE

I S CASES

"Ii

30 CASES

Fig. 4.1 1 Reported cases of rabies in skunks in the US, by county, 1 990: an example of a proportional c i rc l e map. The area of each c i rcle i s proportional t o t h e n u mber o f cases i n each county. (From U h aa et al., 1 992.)

years. Further examples, showing the world distribu­ tion of the major animal virus diseases, are presented by Odend'hal (1983).

the administrative boundaries of the areas over which the displayed values are averaged. Isoplethic maps

Proportional circle maps

Morbidity and mortality can be depicted using circles whose area is proportional to the amount of disease or deaths (Figure 4.11). If the large values are substan­ tially greater than the small values, the values can be represented by proportional spheres whose volume is proportional to the magnitude of the depicted char­ acteristic. (Shading is used to give the impression of spheres on a two-dimensional map.) Choroplethic maps

It is also possible to display quantitative information as discrete shaded units of area, graded in intensity to represent the variability of the mapped data. The units can be formed from grid lines, but are commonly administrative areas such as parishes, shires, counties or states. Maps that portray information in this way are choroplethic (Greek: charas an area, a region; plethos a throng, a crowd, the population). Figure 4.12 is an example. Choroplethic maps display quantitative data, but the boundaries between different recorded values are artificial. They are not the actual boundaries between, for example, high and low prevalence; they are merely

True boundaries between different values can be depicted by joining all points of equal value by a line, such as joining points of equal height to produce the familiar contour map. Maps produced this way are isoplethic (Greek: iso equal). Lines joining points of equal morbidity are isomorbs, and those joining points of equal mortality are isomorts. If these lines are to be constructed, accurate estimates of both the num­ ber of cases of disease (numerator) and the size of the population at risk (denominator) over an area must be known. Figure 4.7 is an isoplethic map showing badger density in Great Britain, drawn in relation to bovine tuberculosis. In this example, the 'contours' are the boundaries between different ranges of badger density. Medical mapping is discussed in detail by Cliff and Haggett (1988). =

=

=

G eograp h i cal i n formation systems Disease distribution can b e mapped and analysed using geographical information systems (GIS) (Maguire, 199 1 ) . These are computerized systems for collecting, storing, managing, interrogating and

Describing disease occurrence

D < 25 per cent --

Local Government Boundaries

a 26-50 per cent !ITII!Il 5 1 -7 5 per cent � > 75 per cent

VICTORIA

Fig. 4. 1 2

Prevalence of fluke-affected l ivers by s h i re, Victoria, Austral ia, 1 977-78: an example of a choroplethic map. (From Watt, 1 980.)

displaying spatial data. They have a range of powerful functions in addition to simple mapping; these include graphical analysis based on spatial location, statistical analysis and modelling. Structure of G I S

Data that are input may b e cartographic data, describ­ ing the location of features; and textual attribute data, describing characteristics of the features. These types of data may be primary or secondary. Primary data may be directly sensed from field sketching, inter­ views and measurements. Alternatively, they may be remotely sensed (Hay et ai., 2000), that is, collected by a device not in direct contact with the object that is being sensed (e.g., a photographic camera). Meteorological satellites have also been used to detect habitats of ticks, mosquitoes, trematodes (Hugh-Jones, 1 989) and tsetse flies (Rogers, 1 991). The GIS then store these geographically referenced data in a database management system in a form that can be graphically queried and summarized. Cartographic data must be stored in digital form on computers. The digital maps are stored in two basic formats: grid-based (raster-based) and vector-based.

In grid-based systems, information is stored uniformly in relation to each cell that forms the grid (Figure 4.13). In vector-based systems, points and lines (arcs) are used to represent geographical features, the lines being composed of their respective straight-line segments. Areas enclosed by lines (e.g., farms) are termed polygons. A digitizing tablet is used to convert maps to a digital format for vector-based storage. This is an electronic board and pointer that accurately transcribes a map to digital format. A scanner is used for raster­ based storage. Grid-based systems store and manipulate regional and remotely sensed data conveniently, but data pro­ cessing is relatively slow if high resolution is required. In contrast, vector-based systems have inherently high resolution but are complex to implement. Many cur­ rent systems can analyse both vector and raster data. Applications of G I S

Applications o f GIS (Sanson et ai., 1991 b ) include: •

cartography, with the advantage over traditional techniques that special-purpose maps can be produced and updated rapidly;

Mapping

km squares controlled under the interim strategy

Iffil

km squares with control prior to 1986 with no control under the interim strategy

£b 2 8 « 7 6 5 4 3 2 1

10 1 1 1 2 1 3+

Fig. 5.5

Age distribution of a total canine hospital population (bars) and age-apecific rates (graph) for can i ne neop lasia: U n iversity of Pennsylvania, 1 952-1 964. (From Reif, 1 98 3 . )

increased insulin requirements of diabetic bitches during oestrus. Similarly, the neutering of bitches decreases the likelihood of mammary carcinoma developing (Schneider et al., 1 969), perhaps from the effect of oestrogens on this tumour (see Chapter 18). Occupational determinants

Sex-associated occupational hazards, although more relevant to human than animal disease, can be identified occasionally in animals, where animal use is equated with occupation. Thus, the increased risk of contracting heartworm infection by male dogs relative to bitches (Selby et al., 1 980) may result from increased 'occupational' exposure of male dogs during hunting to the mosquito that transmits the infection. Social and ethological determinants

Behavioural patterns may account for bite wound abscesses being more common in male than female cats. Behaviour can also affect the likelihood of trans­ mission of infection from one species to another. Thus, in New Zealand, opossums stand their ground when confronted by cattle, thereby increasing the chance of aerosol transmission (see Chapter 6) of tuberculosis from infected opossums to cattle by inhalation. In contrast, in the UK, badgers' immediate response to threatening behaviour is to retreat, and so aerosol transmission of tuberculosis from infected badgers is less likely (Benham and Broom, 1989).

Genetic differences in disease incidence may be inherited either by being sex-linked, sex-limited, or sex-influenced. Sex-linked inheritance is commonly associated with Mendelian inheritance, and occurs when the DNA responsible for a disease is carried on either the X or Y sex chromosomes. Canine haemophilia A and B, for example, are associated with the X chromosome and are inherited recessively, the defects being predominant in males (Patterson and Medway, 1 966). Sex-limited inheritance occurs when the DNA responsible for the disease is not in the sex chromosomes, but the disease is expressed only in one sex, for example cryptorchidism in dogs. In sex­ influenced inheritance, the threshold for the overt expression of a characteristic (based on the multi­ factorial genetic model: Figure 5.3) is lower in one sex than the other, therefore, there is an excess incidence in one sex over the other. Canine patent ductus arteriosus (see Chapter 18) may be an example. In many diseases, there may be excess disease occurrence in one sex over the other, but either a genetic component has not been identified clearly or the method of inheritance has not been established. Examples that are reported to occur predominantly in male dogs include epilepsy (Bielfelt et al., 1971), melanoma and pharyngeal fibrosarcoma (Cohen et al., 1 964). Some diseases may be apparently sex-associated, but are actually associated with other determinants that are related to gender. For instance (Schwabe et al., 1977), the increased mortality rate in male dairy calves may appear to be sex-associated. However, the real association is with husbandry: male dairy calves may not be given as much attention as females because they are worth less (in this instance husbandry, therefore, is a confounder: see Chapter 3).

Species and breed Species and breeds vary in their susceptibility and responses to different infectious agents, and therefore in the role they play in disease transmission. Dogs, for example, do not develop heartwater. Pigs are harder to infect with foot-and-mouth disease virus via the respiratory tract than cattle and sheep (Sellers, 1971; Donaldson and Alexandersen, 2001 ) . Thus, cattle are the species most likely to be infected by between-farm spread of airborne virus, because of their extreme susceptibility to airborne infection and higher respir­ atory tidal volume (Donaldson et al., 1982; Donaldson, 1 987). Pigs are not only less susceptible to airborne virus but also, because of their lower tidal volume and the practice of housing them indoors, are less likely to

Host determinants

encounter sufficient virus to initiate clinical disease. In contrast, if infection does occur, pigs excrete vast quantities of airborne virus (one pig being equivalent to 3000 cattle) and so are important sources of airborne virus during epidemics because they are often kept in large numbers. (See also Chapter 6.) Rottweilers and Dobermann Pinschers react more severely to canine parvovirus enteritis than other breeds (Glickman et al., 1985), and boxers appear to be more susceptible than other breeds to mycotic diseases, such as coccidioidomycosis (Maddy, 1958) (for a distribution map of the fungus see Figure 7.2). Different breeds of poultry vary in their susceptibility to a range of viruses (Bumstead, 1998; Hassan et al., 2004). The reasons for species susceptibility are many and not fully understood. The efficacy of the immune mech­ anism against an infectious agent may be important. Thus, humans are not usually susceptible to infection with Babesia spp. but splenectomized individuals can develop the disease. Different species have been shown to have different receptors for infectious agents on the cell surface. This is particularly important with viruses, which must enter the host cell. Monkeys are not susceptible to poliovirus because they do not have the 'right' cell receptors. Removal of the virus capsid allows the virus to divide lytically in monkey cells if it is first made to enter them. Susceptibility can vary within a species, too. Thus, only certain pigs are sus­ ceptible to the strain of Escherichia coli possessing the K88 antigen because susceptibility is determined by the presence of an intestinal receptor that is specified by one or more genes (Vogeli et al., 1992). Phylogenetically closely related animals are likely to be susceptible to infection by the same agent, albeit with different signs. Herpesvirus B causes labial vesicular lesions in non-human primates, but fatal encephalitis in man. The rider to this - that phylogen­ etically closely related agents infect the same species of animal - is not, however, generally true. Measles, distemper and rinderpest are closely related para­ myxoviruses, yet usually infect quite different species: man, dogs and cattle, respectively. Apparently new diseases can develop when a species or breed is placed in a new ecosystem (see Chapter 7) that contains a pathogen that has a well bal­ anced relationship with local species or breeds. In such circumstances inapparent infection (discussed later in this chapter) is common in the local animals but clinical disease occurs in the exotic ones. This hap­ pened in South Africa, when European breeds of sheep were exposed to bluetongue virus. The agent did not produce clinical signs in the indigenous sheep, but caused severe disease in imported Merino sheep. Similarly, malaria developed as a clinical disease in early European visitors to West Africa, whereas

gI

the local population was tolerant of the parasite. Resistance to the tick Boophilus microplus is greater in indigenous Zebu cattle (Bas indicus) than in European cattle (Bas taurus) (Brossard, 1 998), and the importation of European cattle to West Africa also accentuated the problem of dermatophilosis. There is also species and breed variation in the occurrence of non-infectious diseases. Thus, British breeds of sheep develop intestinal carcinoma more fre­ quently than fine wool breeds, Hereford cattle develop ocular squamous cell carcinoma more commonly than other breeds (see Chapter 4), and there is considerable variation in canine and feline breed predisposition to skin tumours (Goldschmidt and Schofer, 1994). Many diseases having distinct associations with a particular familial line or breed are considered to be primarily genetic (Ubbink et al., 1 998b). Patterson (1 980) has described over 1 00 such diseases in the dog. A genetic causal component is more likely when dis­ ease incidence is higher in pedigree animals than in crossbreds. Examples include congenital cardiovascu­ lar defects (Patterson, 1 968) and valvular heart disease (Thrusfield et al., 1985) in dogs. Diseases may be present in a range of breeds, because the breeds are genetically related. Boston ter­ riers and bull terriers show a high risk of developing mastocytoma, which may be related to their common origin (Peters, 1969). In contrast, the risk of a particular breed developing a disease may vary between coun­ tries, indicating different genetic 'pools' (or a different environment or method of management). Thus, Das and Tashjian (1965) found an increased risk of devel­ oping valvular heart disease in cocker spaniels in North America, whereas, in Scotland, Thrusfield et al. (1985) did not detect an increased risk in that breed. In contrast, valvular heart disease is commoner in cavalier King Charles spaniels in Scotland (Thrusfield et al., 1985) than in Australia (Malik et al., 1992). Gough and Thomas (2003) document breed dispositions to diseases in dogs and cats.

Other host d eterm i n a nts Size and conformation

Size, independent of particular breed associations, has been identified as a disease determinant. Hip dys­ plasia and osteosarcoma are more common in large than small breeds of dog (Tjalma, 1966). Interestingly, the latter disease is also more common in large than small children (Fraumeni, 1 967). The conformation of animals may similarly increase the risk of some diseases. For instance, cows with a small pelvic outlet relative to their size (e.g., Chianina and Belgian blue) are predisposed to dystokia. Conformation may also

/1/

Determinants of disease

have less direct effects. Thus, some calves cannot suckle their dams because the latter have large, bulbous teats (Logan et al., 1974). This can result in the calves being hypogammaglobulinaemic, with the increased risk of fatal colibacillosis. Coat colour

Predisposition to some diseases is associated with coat colour, which is heritable and a risk indicator. For example, white cats have a high risk of developing cutaneous squamous cell carcinoma (Dorn et al., 1971) related to the lack of pigment, which protects the skin from the carcinogenic effects of the sun's ultraviolet radiation. In contrast, canine melanomas occur mainly in deeply pigmented animals (Brodey, 1 970). White cats often have a genetic defect associated with deaf­ ness (Bergsma and Brown, 1 971 ). White hair colour is also associated with congenital deafness in Dalmatians (Anderson et ai., 1 968) .

Agent determinants Vi ru le nce a n d pathoge n i c ity Infectious agents vary in their ability to infect and to induce disease in animals2• The ability to infect is related to the inherent susceptibility of a host and whether or not the host is immune. The ability to induce disease is expressed in terms of virulence and pathogenicity. Virulence is the ability of an infectious agent to cause disease, in a particular host, in terms of severity3. It is also sometimes expressed quantitatively as the ratio of the number of clinical cases to the num­ ber of animals infected (Last, 2001). Case fatality (see Chapter 4) is an indicator of virulence when death is the only outcome. Pathogenicity is sometimes incor­ rectly used as a synonym for virulence, with virulence reserved for variations in the disease-inducing poten­ tial of different strains of the same organism. However, 'pathogenicity' refers to the quality of disease induc­ tion (Stedman, 1 989). Thus, the protozoan parasite Naegleria fowleri is pathogenic to man in warm, but not in cold, water, pathogenicity being governed in this instance by environment. Pathogenicity also may be quantified as the ratio of the number of individuals developing clinical illness to the number exposed to infection (Last, 2001 ). 2 This is also true for plant pathogens (Mills et ai., 1995).

3

The conventional wisdom is that parasites evolve into less virulent

forms because, in killing their hosts, lethal parasites appear to 'commit suicid e'. However, recent evidence (Ebert and Mangin, 1 995) suggests that parasite evolution involves a subtle balance between virulence and transmission rate.

Pathogenicity and virulence are commonly intrinsic characteristics of an infectious agent and are either phenotypically or genotypically conditioned. Pheno­ typic changes are transient, and are lost in succeeding generations. For example, Newcastle disease virus, cultivated in the chorioallantois of hens' eggs, is more virulent to chicks than virus that is cultivated in calf kidney cells. Genotypic changes result from a change in the DNA (and RNA, in RNA viruses) of the micro­ bial genome (the agent's total genetic complement). Most pathogenic bacteria express their virulence genes only when they are inside the host; the conditions in the host somehow facilitating expression of these genes. Pathogenicity and virulence are determined by a variety of host and agent characteristics. Bacterial viru­ lence and pathogenicity are determined by a relatively small group of factors ('common themes'), including toxin and adhesin production, and common themes for invasion of the host and resistance to the clearance and defence mechanisms of the host (Finlay and Falkow, 1997). An agent may achieve pathogenicity, or increase virulence, by a change in antigenic com­ position to a type to which the host is not genetically or immunologically resistant. However antigenic changes are not always the cause of changes in pathogenicity. They may simply be indicators of such changes, the determinants being associated with the production of inhibitory, toxic or other substances (e.g., exotoxins and endotoxins) and the immune­ mediated damage that may ensue (Biberstein, 1999). Genotypic changes also can alter the sensitivity of bacteria to antibiotics. Types of genotypic change

Various genotypic changes can occur in infectious agents (Table 5.3). Major ones include mutation, recombination, conjugation, transduction and transformation.

Mutation is an alteration in the sequence of nucleic acids in the genome of a cell or virus particle. There may be either point mutation of one base, resulting in misreading of succeeding codon triplets, or deletion mutation, where whole segments of genome are removed. Deletion mutants are more likely to occur because they result in changes without redundant genetic material. Frequent mutation may produce antigenic diversity, which may induce recurrent out­ breaks of disease in a population that is not immune to the new antigen. Within the same organism, mutation rates can vary for different genetic markers by a factor of 1 000. Sites within the genome that frequently mutate are termed 'hot spots' . If these spots code for virulence determinants and antigens in the infec­ tious agent, then the agent can change virulence and

Agent determinants

i, :

Table 5.3 Potential sou rces of genetic variabil ity in bacterial and vi rus pop u l ations, (Modified from Trends in Ecology and Evolution, 1 0, Schrag, S.J . and Wiener, P. Emerging i nfectious d i seases: what are the relative roles of ecology and evolution?, 3 1 9-324 © (1 995), with perm ission from Elsevier.) Bacteria

Mutation: Mutation rate i s approximately 1 0- 9 _1 0- 6 per base

pair. Poi nt mutations, deletions, i nsertions and i nvers ions can lead to sign ificant changes i n viru lence factors (e.g., adhesion abil ity, tox in production). Antigenic drift can a l low bacterial pathogens to ' h ide' from mamma l i a n immune systems.

Transposition: Transposons are segments of DNA that can be i ntegrated i nto new sites on the same or different DNA molecules from thei r orig i n ; conj ugative transposons are elements that can promote their own transfer from one bacterial cell to

another. Transformation: Uptake and integration i nto bacterial

chromosome of exogenous DNA. Plasmid exchange: Transfer of plasm ids between bacterial cel ls. Conjugation: Plasmid-med iated chromosome transfer between bacterial cells.

Viruses

Mutation: RNA v i ruses have sign ificantly h igher mutation rates than DNA viruses or bacteria, because of the greater i nstabil ity of RNA molecules and the h igher error rates of RNA replication enzymes. Po int mutations can generate rapid antigenic variation. Recombination between viruses: I n traspecific and i n terspecific recomb i n ation has been observed in some RNA and DNA viruses. Recombination with host genes: Recom b i nation can occ u r in

DNA v i ruses that i ntegrate i nto host c h romosomes or in the DNA provi ru s step of retrovi rus repl ication. If the host c h romosome has previously i ncorporated pieces of virus DNA, reco m b i nation can result i n the i ntegration of both host and virus genes i nto vi rus genetic material. Reassortment of virus segments: I n RNA vi ruses with segmented genomes (e.g., i nfluenza viruses) reassortment of segments among progeny rapidly leads to h igh levels of genetic variabil ity with i n populations.

Lysogeny: I ncorporation of phage genes i nto bacterial genome via phage i ntegration (e.g., Escherichia coli 0 1 57). Transduction: Phage-mediated transfer of sma l l portions of

bacterial DNA.

antigens frequently. If mutation occurs at sites that are not associated with either virulence or antigenic type, then changes in these two characteristics are rare. Sometimes only one or two mutations is sufficient to convert a relatively harmless bacterium or virus into a highly virulent form (Rosqvist et al., 1988). The switch from virulence to non-virulence which is reversible - is sometimes termed phase varia­ tion. This can occur with a high frequency; appro­ ximately 1 in 106 in Bordetella pertussis (the cause of whooping cough in children), for example. The phase variation is manifested in changes in colonial char­ acteristics, and similar changes occur in Bordetella bronchiseptica, the cause of canine 'kennel cough', (Thrusfield, 1992), in which infections may range from the clinically inapparent to the overt (Bemis et al., 1977; McKiernan et al., 1984; and see below 'Gradient of infection' ). Recombination is the reassortment of segments of a genome that occurs when two microbes exchange genetic material. Thus, influenza A viruses have a genome that is packaged in each virion (virus particle) as eight strands of RNA. Influenza viruses are divided into groups based on the structure of two major anti­ gens: the haemagglutinin and neuraminidase (see also Table 1 7.6). Reassortment between current human and avian strains of the virus (possibly in pigs) is likely to

produce recombinants with novel haemagglutinin and neuraminidase combinations (Webster et al., 1992). Major changes are referred to as 'shift' and minor changes as 'drift' . The major changes are responsible for the periodic - approximately decadal - pandemics of influenza in man (Kaplan, 1 982; Webster, 1993). (Note that antigenic drift also occurs in trypanosomes, but by a totally different mechanism. The superficial cell membrane is shed to reveal new antigens4. The epidemiological result, though, is similar: new antigens, therefore a partially or totally susceptible population.) Recombination may also occur in the orbiviruses (e.g., African horse sickness and blue­ tongue) where the precise mechanism is not known, and the term 'genetic reassortment' has been applied (Gorman et al ., 1 979).

4

African trypanosomes can spend a long time in the blood of their

mammalian host, where they are exposed to the immune system and are thought to take advantage of it to modulate their own numbers. Their major immunogenic protein is the variant surface glycoprotein (VSG). Trypanosomes escape antibody-mediated destruction through periodic changes of the expressed VSG gene from a repertoire of 1 000 genes (Barry and McCulloch, 2001; Gibson, 2001; Vanhamme et aI., 2001; Barry and

Carrington, 2004).

Il"!

Determinants of disease

Conjugation (Clewell, 1993) involves transmission of genetic material - usually in the form of a plasmid5 from one bacterium to another, by a conjugal mech­ anism (i.e., they touch) through a sex pilus6. The greatest practical effect of conjugation is in conferring resistance to antibiotics in both 'established' and emerging and re-emerging pathogens (McCormick, 1 998); for example, gentamycin resistance in Staphylo­ coccus spp. (Schaberg et al., 1985), which may pose a particular problem in nosocomial infections7. Con­ jugally mediated drug resistance may therefore be an important determinant of the effectiveness of therapy when infections occur, and there is increasing evid­ ence that some antibiotic-resistant strains of zoonotic bacteria have evolved in farm livestock (Fey et al., 2000; Willems et al., 2000)8 . Conjugation occurs in many bacteria, including Bordetella bronchiseptica, E. coli, and Clostridium, Pasteurella, Proteus, Salmonella, Shigella and Streptococcus spp. Transduction (Snyder and Champness, 1 997) is the transfer of a small portion of genome from one bac­ terium to another, 'accidentally', by a bacterial virus (bacteriophage)9. Again, resistance factors, as well as surface antigens, may be transferred in this way. It occurs in Shigella, Pseudomonas and Proteus spp. Transformation (Snyder and Champness, 1997) involves release of DNA from one bacterial cell and then its entry into another cell of the same bacterial species. It occurs spontaneously in Neisseria spp. but, to occur in other bacterial species, DNA has to be extracted in the laboratory. (This type of trans­ formation should not be confused with the in vitro production of malignant cells, which is also called transformation.) In addition to these five methods of genetic altera­ tion, infection by more than one type of virus particle may be necessary to produce disease. Such infections do not strictly involve a change in a virus genome, rather a complementation of it, which may render a non-pathogenic virus particle pathogenic. This occurs in some plant virus infections because several plant viruses have split genomes that are packaged in

5

Plasmids are small, autonomously replicating molecules in bacterial

cells. h

7

Plasmids also can be transferred non-conjugally (Storrs et ai., 1988).

Nosocomial infections are those that are acquired in hospitals or clin­

ics (Greek: 'nosokomeian'

=

hospital). In human and (probably) veteri­

nary hospitals, the most common are those of the urinary tract, followed by pneumonias, surgical site infections, and bacteraemias (Emori and Gaynes, 1 993; Greene, 1 998b). H

There is also evidence that the process is reversible, when in-feed

separate particles. Each particle carries a portion of the total genome which is, itself, non-infectious, but which contributes to the whole infectious unit. For example, tobacco rattle virus has two virions: one containing a promoting gene, and the other containing replication and maturation genes. All three genes, and therefore both types of virion, are necessary to instigate the suc­ cessful infection of a tobacco plant. In animals, Rous sarcoma virus has capsid proteins that are genetically determined by a separate helper virus. Similarly, some adeno-associated viruses require an adenovirus for infectivity. The different particles present in human hepatitis B fall into this double infection group too. Infection with immunosuppresive viruses can exacerbate other infections (e.g., rinderpest infection aggravates haemoprotozoan infections). Conversely, infection by one virus may prevent infection by, or lessen the virulence of, a second virus. This occurs when the first virus induces the host's cells to release an inhibitory substance now known as interferon. The ways in which virulence and pathogenicity affect the transmission and maintenance of infection are discussed in Chapter 6. Genotypic variability and microbial taxonomy

Initially, classification of microbes was based on phys­ ical and chemical properties; for example, buoyant density and susceptibility to heat inactivation to define genera of the virus family, Picornaviridae, which includes the foot-and-mouth disease virus species. Subsequently, nucleotide sequencing and other micro­ bial characteristics have been used to classify microbes in a manner that may reflect, more accurately, vari­ ation in pathogenicity and virulence. Thus, foot-and­ mouth disease virus occurs as seven serotypes - A, 0, C, Southern African Territories (SAT) 1, SAT 2, SAT 3, and Asia 1 - defined by the inability of infection or vaccination to confer immunity against other serotypes. Substantial genetically determined antigenic variation exists within each serotype (particularly types A and 0), and is associated with varying virulencelO. The genetic variation in microbes may also provide valuable clues to the origin of epidemics. The type 0 foot-and-mouth disease viruses, for instance, exhibit genetically and geographically distinct evolutionary lineages (topotypes) (Samuel and Knowles, 2001). Using a 15% nucleotide-sequence difference as the upper limit defining a single topotype, eight topotypes of type 0 have been identified: European/South American (Euro-SA), Middle East/South Asia (ME­ SA), South East Asia (SEA), Cathay, East Africa (EA),

antibiotics are subsequently banned (Ferber, 2002).

" There are two types of transduction: generalized and specialized. In

the former, any region of the bacterial DNA can be transferred; whereas,

in the latter, only certain genes close to the phage's attachment site on the bacterial chromosome can be transferred.

10

The variation is so substantial that each isolate may be unique

(Clavijo and Kitching, 2003).

Agent determinants

Ii )

I ncreasing severity of disease

C l i n ical signs Signs in animal

No signs

No signs Death (Subc l in i ca i

(Severe

( M i l d disease)

d i sease)

d i sease)

Type of infection

Status of animal

Fig. 5.6

N o infection

I napparent

Overt infection

infection

I nsusceptible or i mmune

Suscepti b l e

G radient of i nfection: the various responses of an a n i m a l to chal lenge by an i nfectious agent.

West Africa (WA), Indonesia 1 (ISA-1) and Indonesia 2 (ISA-2). The 2001 epidemic in the UK was caused by the PanAsia strain, a genetic sublineage of the ME-SA topotype, which emerged in India in 1990 before spreading throughout Asia and into the Middle East, South Africa and southern Europe (Kitching, 1 998). Identification of this strain therefore supported the hypothesis that meat, illegally imported from the Far East, may have been the source of the epidemic (DEFRA, 2002b).

G rad ient of i nfection 'Gradient of infection' refers to the variety of responses of an animal to challenge by an infectious agent (Fig­ ure 5.6) and therefore represents the combined effect of an agent's pathogenicity and virulence, and host char­ acteristics such as susceptibility and pathological and clinical reactions. These responses affect the further availability of the agent to other susceptible animals, and the ability of the veterinarian to detect, and there­ fore to treat and control, the infection. If an animal is either insusceptible or immune, then infection and significant replication and shedding of an agent do not usually occur and the animal is not important in the transmission of infection to others.

which produces a clinical case, with replication and shedding of agent. The inapparently infected animal poses a considerable problem to the disease controller because it is impossible to detect without auxiliary diagnostic aids such as antigen detection or serology. For example, sheep may show either no or transient clinical signs of infection with foot-and-mouth disease virus (Kitching and Hughes, 2002), although they may excrete virus (Sharma, 1978). Demonstration of infection by serology is therefore recommended in this species (Donaldson, 2000). Subclinical infection occurs without overt clinical signs. Some authors use this term and inapparent infection synonymously. Others ascribe a loss of pro­ ductivity to subclinical infection, which is absent from inapparent infection. 'Subclinical' can also be applied to non-infectious conditions, such as hypomagnesae­ mia, where there may be no clinical signs. Clinical infection

Clinical infection produces clinical signs. Disease may be mild. If the disease is very mild with an illness too indefinite to permit a clinical diagnosis, then it is termed an abortive reaction. Thus, the spectrum of response to foot-and-mouth disease virus infection in sheep may result in only mild signs of foot-and-mouth

Inapparent (silent) infection

This is infection of a susceptible host without clinical signsll . The infection may run a similar course to that

11

Some authorities use the term 'unapparent' synonymously (e.g.,

Sutmoller and Olascoaga, 2002).

Determinants of disease

disease (Bolton, 1 968; Kitching and Hughes, 2002), leading to difficulty in unequivocal diagnosis (Ayres et al., 2001; De la Rua et al., 2001). Laboratory diagnosis is therefore prudent (and probably necessary) to confirm a diagnosis in this species, and to avoid misclassifying unaffected sheep as affected12. There is a gradation to severe disease, which is called a frank clinical reaction, when the intensity is sufficient to allow a clinical diagnosis. The spectrum of response to foot-and-mouth disease virus infection in sheep may therefore also include clear clinical signs, often associated with times of stress such as parturi­ tion (Brown, 2002; Reid, 2002; Tyson, 2002). The severest reaction results in death. Paradoxically, death is the logical climax of some infections because it is the only means by which the agent can be released to infect other animals. An example is infection with Trichinella spiralis, which is transmitted exclusively by flesh eating. Inapparent and mild clinical infections may indicate an adaptation of some antiquity between host and parasite; the relationship between bluetongue virus and indigenous South African sheep has already been cited.

Outcome of infection Clinical disease may result in the development of a long-standing chronic clinical infection, recovery, or death. Chronically infected cases are potential sources of an infectious agent. Death usually removes an animal as a source of infection, although there are important exceptions such as infection with T. spiralis, and anthrax infection where carcasses contaminate the soil. Recovery may result in sterile immunity follow­ ing an effective host response, which removes all of the infectious agent from the body. Animals that have sterile immunity no longer constitute a threat to the susceptible population. Two states, however, are important determinants: 1. 2.

the carrier state; latent infection.

The carrier state

'Carrier' is used loosely to describe several situations. In a broad sense, a carrier is any animal that sheds an infectious agent without demonstrating clinical signs. Thus, an inapparently or subclinically infected animal may be a carrier, and may shed agent, either continu12

This is particularly important if animals incorrectly classified as

diseased on clinical examination alone ('false-positives': see Chapter 17) are subject to mandatory slaughter.

ously or intermittently. The periods for which animals are carriers vary. They are rarely lifelong, but carriers may be important sources of infection to susceptible animals during these periods. Incubatory carriers are animals that excrete agent during the disease's incubation period. For instance, dogs usually shed rabies virus in their saliva for up to 5 days before clinical signs of rabies develop (Fox, 1958), and periods as long as 14 days have been reported (Fekadu and Baer, 1980). Thus, in countries in which rabies is endemic, the World Health Organiza­ tion recommends that dogs and cats that have bitten a person should be confined for 10 days; this protocol is designed to determine if the bitten person was exposed to rabies virus. Convalescent carriers are animals that shed agent when they are recovering from a disease, and the agent may then persist for prolonged periods. A carrier of foot-and-mouth disease virus is precisely defined as an animal from which the virus can be isolated from oropharyngeal fluid samples, collected by probang, for periods greater than 28 days after virus challenge (Salt, 1994). It occurs in cattle and sheep following clinical and subclinical disease, the latter commonly fol­ lowing challenge with low titres of virus, and in cattle with partial immunity (Sutmoller et al., 1968), such cir­ cumstances occurring in areas in which the disease is endemic. Persistence also may occur in vaccinated cat­ tle that are subsequently challenged. The oropharynx is the primary site of replication of virus in cattle, whereas, in sheep, virus is most frequently isolated from the tonsillar region. However, virus titres are low, and decline, falling below the level considered necessary for transmission (Donaldson and Kitching, 1989). The duration of the carrier state varies between spe­ cies, with sheep and goats carrying foot-and-mouth disease virus for up to 9 months, cattle for up to 3 years, and the African buffalo for at least 5 years; whereas pigs do not act as carriers. The frequency of develop­ ment of the carrier state in nature also appears to be species-related. Thus, up to 50% of cattle have been recorded as carriers for 6 months following epidemics (Sutmoller and Gaggero, 1965), whereas the carrier state in sheep and goats has been rarely reported naturally (Anderson et al., 1976; Hancock and Prado, 1993; Donaldson, 2000). Although virus-laden oropharyngeal fluid from car­ rier animals can infect cattle and pigs experimentally (van Bekkum, 1973), many experiments have failed to demonstrate transmission from carrier animals to in­ contact susceptible animals (Davies, 2002; Sutmoller and Olascoaga, 2002). Similarly, there is a paucity of evidence that carriers can transmit infection in

The carrier state in foot-and-mouth disease

Agent determinants

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or an area of poorly drained land for Fasciola hepatica infection of cattle. Biocenosis

A biocenosis is the collection of living organisms in a biotope. The organisms include plants, animals and the microorganisms in the biotope. Sometimes biotic community is used synonymously with biocenosis. On other occasions, 'biotic community' refers to a large biocenosis. Major biotic communities are biomes.

The relationship between the population density of mice

and the prevalence of fox rabies. The relationship arises from a predator/prey relationship between faxes and mice (see text). (From Sinnecker, 1976.)

Types of ecosystem Three types o f ecosystem can be identified, according to their origin: autochthonous, anthropurgic and synanthropic.

density of mice (a prey). Figure 7.10 illustrates this rela­ tionship, using demographic and disease prevalence data collected in Germany. There are also similarities between predator/prey interactions and parasite/host interactions. For ex­ ample, cyclic patterns of measles and other childhood diseases (Yorke and London, 1973) are equivalent to Lotka-Volterra cycles because the development of immunity by infected individuals is equivalent, in its effect on parasite populations, to the effects of removal of prey on predator populations.

Autochthonous ecosystems

'Autochthonous' derives from the Greek adjective autos, meaning 'oneself' or 'itself'; the Greek noun chthon, meaning 'the earth' or 'the land'; and the adjectival suffix -ous, meaning 'deriving from'. Hence an auto­ chthonous ecosystem is one 'coming from the land itself'. Examples are to be found in biomes such as tropical rain forests and deserts. Anthropurgic ecosystems

Ecosystems The relationship between animals linked by food chains defines the variety of animals in a particular area. Similarly, climate and vegetation govern the dis­ tribution of plants and therefore of the animals that live off them. These areas are characterized by the animals and plants that occupy them, and by their physical and climatic features. This unique interact­ ing complex is called an ecosystem (Tansley, 1935). The components of an ecosystem can be considered seperately, and ecosystems themselves can vary in size. Various terms have been devised to describe these components (Schwabe, 1984) including biotope and biocenosis.

Biotope A biotope is the smallest spatial unit providing uni­ form conditions for life. An organism's biotope there­ fore describes its location. This contrasts with a niche, which describes the functional position of an organism in a community. A biotope can vary in size. For example, it may be the caeca of a chicken for coccidia,

,Anthropurgic' is derived from the Greek noun anthropos, meaning 'man': and the Greek verb root erg, meaning 'to work at, to create, to produce'. Thus, an anthropurgic ecosystem is one created by man (strictly, it can also mean 'creating man'). Examples are those found in cultivated pastures and towns. Some authors use 'anthropogenic' (Greek: gen'be produced') in a similar context. =

Synanthropic ecosystems

'Synanthropic' originates from the Greek preposition syn, meaning 'along with, together with'; and the Greek noun anthropos, meaning 'man'. Thus, a synan­ thropic ecosystem is one that is in contact with man. An example is a rubbish tip, harbouring a variety of vermin. It follows that some synanthropic ecosystems, such as rubbish tips, are anthropurgic. Synanthropic ecosystems facilitate the transmission of zoonotic infections from their lower animal hosts to man. For example, the brown rat, Rattus norvegicus, inhabits rubbish dumps and can be inapparently infected with Leptospira, serovar ballum. Humans in proximity to rubbish dumps that harbour infected rats may therefore be infected with the bacterium.

Natural country ,

/

Forest

Ape

Ape

A e

Savannah Human settlements Fig. 7.1 1

The transmission of yellow fever

An ecological climax

An ecological climax traditionally is said to have occurred when plants, animals, microbes, soil and macroclimate (see Chapter 5) have evolved to a stable, balanced relationship7. Characteristically, when infections are present, they too are stable and therefore are usually endemic. Also, the balance between host and parasite usually results in inapparent infections. Such stable situations can be disrupted, frequently by man, resulting in epidemics. For example, bluetongue, a virus disease of sheep, was recognized only after the importation of European breeds of sheep to South Africa towards the end of the 19th century (Neitz, 1948). The virus, however, was present in indigenous sheep before that time, but was p art of an ecological climax in which it only produced mapparent infections. The importation of exotic sheep represented a disturbance of the stable climax. A climax involving endemic infectious agents indic­ ates that all factors for maintenance and transmission of the agent are present. Sometimes changes in local ecology may tip the balance in favour of parasites, thus increasing disease incidence. For example, the sea­ sonal periodicity of foot-and-mouth disease in South America may result from seasonal increases in the size of the susceptible cattle population when animals are brought into an endemic area for fattening (Rosenberg et al., 1980). Ecological interfaces

An ecological interface is a junction of two ecosystems. Infectious diseases can be transmitted across these interfaces. An example is the transmission of yellow fever, an arbovirus disease of man. The virus is main­ tained in apes in Africa in an autochthonous forest

In some ecosystems (e.g., tropical rain forests) an ecological climax is

determined exclusively by plant! arthropod relationships ( Janzen, 1971; Way, 1977).

'-

,

Plantation cycle

�A. simpson i....

�A. aegypti

Town

Town cycle

Man

secondary host). (From Sinnecker, 1976.)

7

Virgin forest cycle

"'

1-- - - - - Cultivated land

between apes (primary hosts) and man (the

/ A. africanus ---

Ape

ecosystem in the forest canopy (Figure 7.1 1 ) . The canopy-dwelling mosquito, Aedes africanus, transmits the virus between apes. The mosquito A. simpsoni bridges the interface between the autochthonous forest ecosystem and the anthropurgic cultivated savannahs. his n:osquito therefore maintains a plantation cycle m WhICh man and apes may be infected. Finally, the urban mosquito, A. aegypti, can maintain an urban cycle in man. People who enter forests may also contract the infection from A. african us. Several diseases can be propagated across the inter­ face between wildlife ecosystems and cultivated land stocked with domesticated animals (Bengis et al., 2002; see also Table 6.9). Sylvatic foci of infection may con­ . stItute refractory problems to eradication of disease in livestock (e.g., tuberculosis in badgers: see Chapter 2), as well as increasing the frequency of disease in companion animals (e.g., epidemics of rabies in raccoons related to the increased occurrence of rabies in domestic cats: Gordon et al., 2004).

!

Ecological mosaics

An ecological mosaic is a modified patch of vegetation, created by man, within a biome that has reached a climax. Infection may spread from wild animals to man in such circumstances. For example (Schwabe, 1984), the helminth infection, loiasis, is transmitted by arthro­ pods between man, living in small forest clearings, and canopy-dwelling monkeys. Similarly, clearing of the forest canopy encourages a close cover of weeds on the ground, creating conditions that are favourable for the incursion of field rats with mites infected with scrub typhus, which form mite islands and the result­ ing local areas of endemic scrub typhus (Audy, 1961). However, transmission does not always occur in the mosaics because suitable vectors may not be available. Thus, in Malaya, man lives unharmed in forests in mosaics with monkeys infected with a variety of species of Plasmodium (a protozoon) that are patho­ genic to man. Transmission to man from monkeys

IL l

The p('rll n,Jv of disease

does not occur because vectors that bite both types of primate are not present in the ecosystem.

on its limitation to particular ecosystems. An area that has ecological, social and environmental conditions that can support a disease is a nosogenic territory (Greek: noso- sickness, disease; gen- to produce, to create). A nosoarea is a noso genic territory in which a particular disease is present. Thus, Britain is a noso­ genic territory for rabies and foot-and-mouth disease, but is not a nosoarea for these diseases, because the microbes are prevented from entering the country by quarantine of imported animals. Diseases that show strict geographical boundaries within an ecosystem or series of ecosystems are nidal because they are confined to a specific nidus. Salmonellosis is endemic in most parts of the world because virtually all verteb­ rates and some invertebrates (see Table 6.S) can act as hosts for the various species of Salmonella. Rabies, when maintained in foxes, is endemic in a large zone around the northern hemisphere because this large area supports a fox population of high density (Figure 7.1 2). The nosoarea for coccidioidomycosis was described earlier in this chapter (see Figure 7.2). When diseases are vector-transmitted, they are often restricted to more precise geographical boundaries than other infectious diseases. This is because the ecosystem has to satisfy the requirements of both the vertebrate host and the arthropod vector. Thus, Rocky Mountain spotted fever, a rickettsial disease of rodents transmitted by ticks, is essentially restricted to particu­ lar areas of North America, as the name of the disease suggests. At the opposite end of the spectrum from diseases with a wide distribution are those that may be confined to relatively small areas within a town or on a =

Landscape epidemiology The study of diseases in relation to the ecosystems in which they are found is landscape epidemiology. Terms conveying the same meaning are medical ecology, horizontal epidemiology (Ferris, 1967) and medical geography. Investigations are frequently qual­ itative, involving the study of the ecological factors that affect the occurrence, maintenance and, in the case of infectious agents, transmission of disease. This contrasts with the study of quantitative associations between specific diseases and hypothesized factors - sometimes termed 'vertical' epidemiology - as described in Chapters 14, IS, 18 and 19. Landscape epi­ demiology was developed by the Russian, Pavlovsky (1964), and later expanded by Audy (1958, 1960, 1962) and Galuzo (1975); it involves application of the ecological concepts described above in the study of disease.

Nida l ity The Russian steppe biome was the home of the great plagues such as rinderpest. Many arthropod­ transmitted infections present in the steppes were also limited to distinct geographical areas. These foci were natural homes of these diseases and were called nidi (Latin: nidus nest). The presence of a nidus depends =

Fig. 7.1 2

N osoarea (shaded) of endemic fox rabies. (From W i n kler, 1975.)

=

Landscape epidemiology

I ;' \

»" '"

a:

10

Kyasanur Forest disease

0.8

1 .0

Relative population de n sity Fig. 7. 1 3

Relationship between the relative population density and

prevalence of Leptospira, serovar ballum, infection in the brown rat ( Rattus norvegicus). (Simplified from Blackmore and HathawaY, 1980.)

Tularaemia

In 1967 in Sweden, an epidemic of tularaemia occurred with more than 2000 human cases and a high mortality rate of hares (Borg and Hugoson, 1980). This epi-

Kyasanur Forest disease is caused by an arbovirus. Symptoms in humans include headache, fever, back and limb pains, vomiting, diarrhoea and intestinal bleeding. Death due to dehydration can occur in untreated cases. It is apparently restricted to an area 600 miles square in the Indian state of Mysore. The virus endemically and inapparently infects some small mammals, including rats and shrews, in the local rain forest. The virus is transmitted by several species of tick (Singh et al., 1964), only one of which, Haemaphysalis spinigera, will infest humans. The usual host of the tick is the ox. Thus, when humans create ecological mosaics by cultivating areas for rice, their cattle roam into the surrounding rain forest and

Landscape epidemiology

may become infested with virus-infected ticks. Dense populations of ticks therefore build up around villages and, when infected, these ticks can transmit the infec­ tion to humans (Hoogstraal, 1966).

Further reading Aguirre, A.A., Ostfeld, RS., Tabor, G.M., House, e. and Pearl, M.e. (2002) Conservation Medicine: Ecological Health in Practice. Oxford University Press, Oxford. (A study of human and animal diseases in an ecological context) Bengis, RG. (Coordinator) (2002) Infectious diseases of wildlife. Revue Scientifique et Technique, Office International des Epizooties, 21, 1-402 Bokma, B.H. and Blouin, E. (Eds) (2004) Impact of Ecological Changes on Tropical Animal Health and Disease Control, Annals of the New York Academy of Sciences, Vol. 1026. New York Academy of Sciences, New York Burnet, F.M. and White, D.O. (1962) Natural History of Infectious Disease. Cambridge University Press, Cambridge Bush, A.O., Fernandez, J.e., Esch, G.W. and Seed, R (Eds) (2001) Parasitism: The Diversity and Ecology of Animal Parasites. Cambridge University Press, Cambridge Chadwick, D.J. and Goode, J. (Eds) (1997) Antibiotic Resistance: Origins, Evolution, Selection and Spread. CIBA Foundation Symposium 207. John Wiley, Chichester Cherrett, J.M. (Ed.) (1989) Ecological Concepts. Blackwell Scientific Publications, Oxford. (A general ecology text, which also includes a discussion of predator/prey and host/ pathogen interactions) Crawley, M.J. (Ed.) (1992) Natural Enemies: the Population Biology of Predators, Parasites and Diseases. Blackwell Scientific Publications, Oxford Daszak, P., Cunningham, A.A. and Pepper, I.L. (1998) Emerging infectious diseases of wildlife - threats to bio­ diversity and human health. Science, 287, 443- 449 Deem, S.L., Kilbourn, A.M., Wolfe, N.D., Cook, RA. and Karesh, W.B. (2000) Conservation medicine. Annals of the New York Academy of Sciences, 916, 370-377 Desowitz, RS. (1981) New Guinea Tapeworms and Jewish Grandmothers. Tales of Parasites and People. W. Norton and Company, New York and London. (Essays on ecological and anthropological aspects of some parasitic diseases) Dieckmann, U., Metz, A.J., Sabelis, M.W. and Sigmund, K (Eds) (2002) Adaptive Dynamics of Infectious Diseases: In Pursuit of Virulence Management. Cambridge University Press, Cambridge. (A comprehensive presentation of the evolu­ tionary ecology of infectious diseases) Edwards, M.A. and McDonnell, U. (Eds) (1982) Animal Disease in Relation to Animal Conservation. Symposia of the Zoological Society of London No. SO. Academic Press, London Ewald, P.W. (1994) Evolution of Infectious Diseases. Oxford University Press, Oxford Fayer, R (1998) Global change and emerging infectious diseases. Journal of Parasitology, 86, 1174 -1181 Galuzo, I.G. (197S) Landscape epidemiology (epizootio­ logy). Advances in Veterinary Science and Comparative Medicine, 19, 73-96

1 ; ')

Gibbs, E.P.J. and Bokma, B.H. (Eds) (2002) The Domestic Animal/Wildlife Interface: Issues for Disease Control, Conserva­ tion, Sustainable Food Production, and Emerging Diseases. Annals of the New York Academy of Sciences, Vol. 969. New York Academy of Sciences, New York. (Includes discussions of disease transmission across ecological interfaces) Grenfell, B.T. and Dobson, A.P. (Eds) (199S) Ecology of Infectious Diseases in Natural Populations. Cambridge University Press, Cambridge Grenfell, B.T., Pybus, O.G., Gog, J.R, Wood, J.L.N., Daly, J.M., Mumford, J.A. and Holmes, E.e. (2004) Unifying the epidemiological and evolutionary dynamics of pathogens. Science, 305, 327-332 Hastings, A. (2004) Population Biology, 2nd edn. Springer­ Verlag, New York. (A basic text on population biology, with emphasis on simple mathematical models) Hudson, P.J., Rizzoli, A., Grenfell, B.T., Heesterbeek, H. and Dobson, A.P. (Eds) (2002) The Ecology of Wildlife Diseases. Oxford University Press, Oxford Learmonth, A. (1988) Disease Ecology: An Introduction. Basil Blackwell, Oxford. (A text focussing on human diseases, but also covering some zoonoses) Levin, B.R, Lipsitch, M.N. and Bonhoeffer, S. (1999) Population biology, evolution, and infectious disease: convergence and synthesis. Science, 283, 806- 809. (A discussion of population biology in the context of molecular epidemiology, pathogenesis, and disease control) Lord, RD. (1973) Ecological strategies for the prevention and control of health problems. Bulletin of the Pan American Health Organization, 17, 19-34 Lower, G.M. (1984) The ecology of infectious and neoplastic disease: a conceptual unification. Ecology of Disease, 2, 397-407 May, RM. (1981) Population biology of parasitic infections. In: The Current Status and Future of Parasitology. Eds Warren, KS. and Purcell, E., pp. 208-23S. Josiah Macy Jnr. Foundation, New York Morse, S.S. (Ed.) (1993) Emerging Viruses. Oxford University Press, New York Osofsky, S.A. (Ed.) (200S) Conservation and Development Interventions at the Wildlife/Livestock Interface. Occasional Paper of the IUCN, Species Survival Commission No. 30. IUCN Gland, Switzerland /Cambridge. (Includes a discus­ sion of diseases in wildlife and associated domestic species) Pavlovsky, E.N. (1964) Prirodnaya Ochagovost Transmis­ sivnykh Bolezney v Svyazi s Landshoftnoy Epidemiologiey Zooantroponozov. Translated as Natural Nidality of Trans­ missible Disease with Special Reference to the Landscape Epidemiology of Zooanthroponoses. PIous, F.K (translator), Levine, N.D. (Ed.) (1966). University of Illinois Press, Urbana Pastoret, P.-P., Thiry, E., Brochier, B., Schwers, A., Thomas, I. and Dubuisson, J. (1988) Diseases of wild animals transmissible to domestic animals. Revue Scientifique et Technique, Office International des Epizooties, 7, 70S-736 Rapport, D.J. (1999) Epidemiology and ecosystem health: natural bridges. Ecosystem Health, 5, 174-180 Rapport, D., Costanza, R, Epstein, P.R, Gaudet, C. and Levins, R (Eds) (1993) Ecosystem Health. Blackwell Science, Oxford. (A discussion of the impact of environmental change on ecosystems, including human and animal disease)

I ,h

The ecology of disease

Ricklefs, R.E. and Miller, G.L. (2000) Ecology, 4th edn. W.H. Freeman, New York. ( A general ecology text, which also includes a discussion of parasitism and disease)

Schneider, R. (1991) Wildlife epidemiology. In: Waltner­ Toews, D. (Ed.) Veterinary Epidemiology in the Real World: a Canadian Potpourri, pp. 41-47. Canadian Association of Veterinary Epidemiology and Preventive Medicine, Ontario Veterinary College, Guelph. (A concise discussion of the role of disease in regulating animal populations)

Schrag, S.J. and Wiener, P. (1995) Emerging infectious dis­ eases: what are the relative roles of ecology and evolution? Trends in Ecology and Evolution, 10, 319-324

Schwabe, c.E. (1984) Veterinary Medicine and Human Health, 3rd edn. Williams and Wilkins, Baltimore. (Includes a section on medical ecology)

Sinnecker, H. (1976) General Epidemiology Walker, N. (trans­ lator). John Wiley and Sons, London. (An ecological approach to epidemiology)

Sterns, S. (Ed.) (1999) Evolution in Health and Disease. Oxford University Press, Oxford Williams, E.5. and Barker, I.K. (Eds) (2001) Infectious Diseases of Wild Mammals, 2nd edn. Manson Publishing, London Wobeser, G.A. (1994) Investigation and Management of Disease in Wild Animals. Plenum Press, New York

Patterns of disease

Methods of expressing the temporal and spatial dis­ tribution of disease were described in Chapter 4. The various patterns of disease that can be detected when disease distribution is recorded are discussed in this chapter. A considerable bulk of mathematical theory has been formulated to explain disease patterns (e.g., Bailey, 1975). Most of this is beyond the scope of this book, but a brief introduction will be given in this chapter. Additionally, the application of mathematics to the development of predictive models, of practical value to disease control, is described in Chapter 19. Epidemic curves

The representation of the number of new cases of a disease by a graph, with the number of new cases on the vertical axis and calendar time on the horizontal axis, is the most common means of expressing disease occurrence. The graph of an epidemic in this way pro­ duces an epidemic curve. Figure 8.1 depicts the vari­ ous parts of an epidemic curve, stylized to a symmetric shape for the purpose of illustration. Epidemic curves are given for foot-and-mouth disease in Figure 4.1, with the number of new outbreaks (Appendix I) approximately indicating the number of new cases. Note that the culmination point (peak) is shifted to the left, that is, the curve is positively skewed.

Thus, a highly infectious agent with a short incubation period infecting a population with a large proportion of susceptible animals at high density produces a curve with a steep initial slope on a relatively small time scale, representing a rapid spread of infection among the population. A minimum density of susceptible animals is required to allow a contact-transmitted epidemic to commence. This is called the threshold level, and is defined mathematically by Kendall's Threshold Theorem (in Discussion to Bartlett, 1957). Figure 8.2 illustrates application of the theorem in relation to rabies in foxes. Above a certain density of susceptible animals, one infected fox can, on average, infect more than one susceptible fox, and an epidemic can occur; the greater the density, the steeper the slope of the progressive stage of the epidemic curve. Few thres­ hold values relating to animal diseases are known. Culmination point

OJ +"

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Factors affecting the shape of the curve

The shape of the curve and the time scale depend on: • the incubation period of the disease; • the infectivity of the agent; • the proportion of susceptible animals in the population; • the distance between animals (i.e., animal density).

1i""

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Fig. 8.1 Components of an epidemic curve (stylized to a symmetric shape). The horizontal dotted line i ndicates the average number of new cases. (From S i nnecker, 1 976.)

I Ii)

Patterns of disease

.!!! '"

E

c '"

al �

u

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'7.) 1 � � "' ; 1 -.� , 1 indicates that an epidemic is increasing, whereas an EDR < 1 points to a decline. Figure 8.4 plots the EDR of foot-and-mouth disease in Dumfries and Galloway, during the epidemic in the UK in 2001, plotted daily, using a 7-day interval. The EDR dropped below one on 21 March, and subse­ quently there were transient increases above one at the

Date

end of March and early in April. However, these last two peaks should not be interpreted as failures in dis­ ease control. They resulted from eruption of disease in new areas north-west of Dumfries and south and south-east of Dalbeattie, rather than recrudescence in the initial focus in the south-east of the region (see Figure 4.14). This highlights the importance of express­ ing disease occurrence both temporally and spatially, and recognizes the need to collect and analyse field data during an epidemic. Common source and propagating epidemics

A common source epidemic is one in which all cases are infected from a source that is common to all

140

Patterns of disease

period, then it is difficult to differentiate between a propagating epidemic and a series of point-source epidemics. Sartwell ( 1950, 1966) describes a suitable technique of differentiation, based on the statistical distribution of incubation periods.

32 30

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The Reed-Frost model

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The shape of the epidemic curve in a propagating epidemic in a defined population can be mathematic­ ally modelled (Bailey, 1975). One of the basic models is the Reed-Frost model (Abbey, 1952; Frost, 1976). In this model's classical simple form, the population is divided into three groups, comprising:

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8-12

13-17 23-27 18-22 28-1 July

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August

Fig.8.5 A point-source epidemi c : h uman leptospirosis associated with contaminated water supply, Rostov-on-Don, USSR, 1 955. (From lanovitch et a/., 1 957.)

individuals. If the period of exposure is brief, then a common source epidemic is a point-source (or, more briefly, just a point) epidemic. A food-poisoning out­ break, in which a single batch of food is contaminated, is a typical point-source epidemic. Figure 8.5 illustrates a point-source epidemic of human leptospirosis in the USSR in 1955 associated with the contamination of the water supply with the urine of infected dogs. An epidemic of leptospirosis was occurring in dogs, and contaminated urine was discharged on to fields. A cloud-burst occurred on 28 June during a brief period of heavy rainfall. This washed off the topsoil. Some of the soil entered a water pumping station inspection shaft which was open for repair. Thus, the water supply was contaminated, and resulted in the human epidemic. A propagating epidemic is an epidemic caused by an infectious agent in which initial (i.e., primary) cases excrete the agent, and thus infect susceptible indi­ viduals, which constitute secondary cases. Epidemics of foot-and-mouth disease are examples ( Figure 4.1). One of the primary cases is frequently the index case, that is, the first case to come to the attention of investigators. The time interval between peaks of successive tem­ poral clusters of cases, separating the primary from subsequent secondary cases, reflects the incubation period of the infection. Typically, all cases of a point­ source epidemic occur within one incubation period of the causal agent. Thus, if the period between sub­ sequent peaks is less than the most common incubation

infected animals (cases); susceptible animals; 3. immune animals. The number of individuals in each group determines the shape of the epidemic curve and the pattern of immunity in the population. Assuming that the period of infectiousness of infected animals is short, and the incubation period or latent period is constant, then, starting with a single case (or several simultaneously infected cases), new cases will occur in a series of stages. Cases occurring at each stage can be expected to have a binomial dis­ tribution (see Chapter 12), depending on the number of susceptible and infectious animals at the previous stage. A chain of binomial distributions thus can be expected; this model is therefore termed a 'chain­ binomial model'. The model also assumes that all infected animals develop disease, become infectious in the next stage, and then become immune. The model is constructed using the formula: Ct+1

=

S p _qCt),

where: t

the time period: usually defined as the incuba­ tion period or latent period of the infectious agent (ideally, the serial interval of infection: see Chapter 6); Ct+1 the number of infectious cases in time period, =

=

t+ 1; St the number of susceptible animals in the time period, t; q the probability (see Chapter 12) of an individual not making effective contact. =

=

The value, q, is given by ( 1 - p), where p the probab­ ility of a specific individual making effective contact (see Chapter 6) with another individual wh�ch would result in infection if one were susceptible and the other were infectious. The term ( 1 - qCt) arises because it represents the probability that at least one of the Ct =

Table 8.1

Simu lation of an epidemic using the classical Reed-Frost model.

Time (t)

0 1 2 3 4 5

Number of Cases (Ct)

Number of susceptible animals (St)

6 29 54 11 0

1 00 94 65 11 0 0

Number of immune animals (It)

0 7

36 90 1 01

Totals

Probability of effective

pSt

1 01 1 01 1 01 1 01 1 01 1 01

0.06 0.06 0 .06 0.06 0.06 0.06

6.00 5.64 3.90 0.66 0.00 0.00

contact(p)

110

infectious cases makes effective contact. The magni­ tude of p is a matter of chance, and depends on a variety of factors, including those already described in Chapter 6. It is usually estimated empirically from real epidemics (Bailey, 1975). If, at time t (the beginning of an epidemic), there are 100 susceptible animals, no immune animals, and one case, then St =100 and Ct =1. If P = 0.06, then q =0-0.06) = 0.94.

2

At time t+ 1:

3

4

5

6

7

8

Time (t)

Cl+l = 1000-0.941) =6,

An epidem ic curve, number of susceptible animals and number of i mmune animals s i m ulated by the classical Reed-Frost model. Cases; -+- i mmune ani mals; -x- susceptible animals. (Data from Table 8.1.) Fig. 8.6

-e-

and 51+1 =100 - 6 = 94.

At time t + 2: Ct+2 = 940- 0.946 ) =29,

and St+2 = 94 -29 =65.

At time t +3: Ct+3 = 650-0.94 29) =54,

and St+3 = 65 -54 = II,

and so on. The number of immune animals at any time period is the cumulative total of infected animals during the preceding time periods. Thus, at time t + I, the number of immune animals 1t+1= 1 (the 1 case from time t = 0 ); at time t + 2, 11+2 =6 + 1 = 7; at time t + 3, 11+3 = 7 + 29 = 36, and so on. Table 8.1 presents the results of the Reed-Frost model, using the above parameters, for the complete

course of the modelled epidemic. The results are also plotted in Figure 8.6. Note that an epidemic can only occur when p x St > I, and declines (or cannot initially occur) when p x St < 1. The likelihood of an epidemic occurring, and the shape of the epidemic curve, are therefore functions of the probability of effective con­ tact and the number of susceptible animals. The proportion of the population that is susceptible is often used as a general guide to the likelihood of an infection spreading - commonly, at least 20-30% of the population; with the corollary that, if 70-80% of the population is immune, infection will not spread. Although the latter level of protection will prevent a major epidemic, infection can spread with a relatively low proportion of susceptible animals if there are sufficient susceptible animals to render p x St greater than 1. Figure 8.7 depicts epidemic curves that are simulated using various values for the number of susceptible and immune animals, and the parameter, p. A number of immune animals at the beginning of an epidemic can decrease the amplitude of the epidemic and delay its peak; a change in effective contact can also alter the amplitude. The basic Reed-Frost model can be modified to include control components, such as vaccination with

Patterns of disease

1 . amplitude - decreasing intensity from type 1 to type 3; 2. peakedness (concentration of cases) - also decreasing, from type 1 to type 3; 3. skewness - noticeable in type 1, but decreasing in succeeding types.

600 '" Q) '" '" "

'0 G; .0 E

" z

4 00

200

0 0

2

3

4

5

6

7

9

8

10

Time (I) Initial number of susceptible animals

Initial number of immune animals

Probability of effective contact

1000 600 600

0 4 00 4 00

0.007 0.007 0.015

-.-

-+-x-

Some epidemic curves simulated by the classical Reed-Frost model. Population size 1 000; a si ngle case is i ntroduced into the population. Fig.8.7

=

Type 1

Type 2

Type 3

Time Fig. 8.8 Kendall's concept of changing wave shape over time. (From C l iff and Haggett, 1 988.)

a varying duration of immunity (Carpenter, 1988), and varying periods of infectiousness (Bailey, 1975)3 . Kendal l 's waves

Some epidemics - notably those caused by viruses occur as a series of outbreaks which can be considered as a series of epidemic waves: a wave-train. Three types of wave, representing particular stages of a con­ tinuum, were identified by Kendall (1957); these are called Kendall's waves ( Figure 8.8). There are three main differences between these waves (Cliff and Haggett, 1988):

3 Some models of the age distribution of cancer also show remarkable similarities to the Reed-Frost model (Burch, 1966), reflecting underlying biological similarities. Contact between an infectious and a susceptible individual is similar to an environmental carcinogen effectively 'hitting' a cell; and the conversion of a susceptible individual to a case is similar to a mutation that converts a normal cell to a malignant one (see Chapter 5).

The shape of each wave in the wave-train at a given time or place in a population at risk of size S depends on the rate of infection, {3, and the rate of removal, f.1. Removal occurs when infected animals die, are isolated, or recover and become immune. These two parameters are related in a third, Sc: the relative removal rate.

The relative removal rate defines a critical susceptible threshold population size whose magnitude com­ pared with S determines the wave's shape. When S is much greater than Sc a type 1 wave occurs. Type 3 ' waves occur when the number of animals at risk is low, and consequently S is only slightly greater than Sc. These waves are characterized by relatively lengthy outbreaks of low amplitude. Type 2 waves are inter­ mediate to types 1 and 3. The shape of the waves changes as an epidemic spreads over time and space. This is exemplified by the epidemic of the virus disease, Newcastle disease, which occurred in England and Wales in 1970-71, and which is charted in Figures 8.9 and 8.10. The infection is spread by movement of live birds and other animals, fomites, poultry products and airborne transmission (Calnek, 1991). Although the disease is preventable by vaccination, the previous epidemic had occurred 6 years earlier and the subsequent casual attitude to vaccination resulted in a level of population immunity well below the 75% required to prevent a major epi­ demic. The epidemic began in the East of England and spread westwards. Initially, the amplitude was great, but succeeding waves showed a transition over time and space from type 1 to type 3; locations 1, 2 and 3 in Figure 8.9 corresponding to the wave types predicted by Kendall. The contours in Figure 8.1 0 are time con­ tours of 1 5-day periods (15 days is a rough multiple of the average incubation period, calculated from a range of 3-10 days). Thus, the contour with the value 9 marks the 135th day of the epidemic. These contours suggest that the 'velocity' of the epidemic temporarily decreased as the epidemic moved westwards. The changes in the shape of these waves must result from a decrease in the value of S/Sc over time and space. This could occur either because S decreases and/or Sc increases. An increase in the latter could occur because of a change in the value of the removal rate, f.1, but this is unlikely for a specific disease. Alternatively, the rate of infection, {3, could increase,

I ,I l

Epidemic curves

Newcastle d isease epidemic of 1 970-71 in England and Wales. (From Cl iff and Haggett, 1 988.) Fig. 8. 9

a I a

kilo�tru i

miles

i

200

100

i

�:.:;.:��(i";i;'i"'J. Spread vectors

/ Time

_---.l>

Fig. 8.1 0 Progress of the Newcastle d isease epidemic of 1970-71 in England and Wales from its origins to the rest of the country. (From Cliff and Haggett, 1 988.)

"

(

periods (each 15 days long)

(a)

Cyc l i cal tre n d s

(c)

Cyclical trends ( Figure 8.1 1 c) are associated with regu­ lar, periodic fluctuations in the level of disease occur­ rence. They are associated with periodic changes in the size of the susceptible host population and/or effective contact, and may produce recurrent epidemics or endemic pulsations (regular, predictable cyclical fluctuations). Thus, the 3- to 4-year cycle of foot-and­ mouth disease in Paraguay (see Figure 8.17), and the predicted 4-year periodicity of fox rabies in Britain, with a contact rate of 1.9 (see Figure 19.4a), probably are related to the time taken for the susceptible population to reach the threshold level.

Time

Time

1\

Seasonal trends

Time Fig. 8.1 1 Temporal trends in d i sease occurrence. (a) Long-term trend : (1) with equ i l i brium between i nfectious agent and host; (2) host/agent interaction biased to the host; (3) host/agent interaction biased to the agent. (b) Short-term trend. (c) Cycl ical trend. (From Sinnecker, 1976.)

but this is equally unlikely, necessitating a change in virulence or infectiousness of the agent during the course of the epidemic. Thus, the most probable reason for the change in the wave shape is a reduction in S, which could plausibly be brought about by isolation of animals and vaccination. This is consistent with the pattern of the Newcastle disease epidemic, in which increased vaccinations and mandatory restrictions on poultry movement during the epidemic would have decreased the value of S.

Trends in the temporal distribution of disease

A seasonal trend is a special case of a cyclical trend, where the periodic fluctuations in disease incidence are related to particular seasons. Fluctuations may be caused by changes in host density, management prac­ tices, survival of infectious agents, vector dynamics and other ecological factors. Thus, before eradication, rinderpest occurred in Africa more commonly in the dry than the wet season because animals congregated at water holes, increasing the local animal density. The prevalence of Lassa virus infection of the multi­ mammate mouse (see Chapter 6) is related to density­ dependent variations in mortality, competition with other rodents, and seasonal factors. The mouse may seek shelter in homes during the wet season, and this may partly explain the increased incidence of human Lassa fever during the wet season. Rat plague demonstrates a seasonal incidence, being associated with climatically determined fluctuations in the population size of certain fleas that are vectors of the disease. Additionally, the rat population increases during the interepidemic season, thereby exacerbating the seasonal trend (Pollitzer and Meyer, 1961 ). Myxomatosis in lowland rabbits in the UK has a two-peaked annual cycle, with a main autumnal peak between August and December, and a subsidiary peak in February ( Figure 8.12). This is the result of several

The temporal changes and fluctuations in disease occurrence can be classified into three major trends ( Figure 8.1 1 ): 1. 2. 3.

short-term; cyclical (including seasonal); long-term (secular).

.l!l :0 40 ..Q � 1:l Q)

U Q)

:g

20

� 0

Short-term trends

Short-term trends ( Figure 8.1 1 b) are typical epidemics, which have already been discussed.

Monthly percentage of l ive-trapped farmland rabbits infected with myxomatosis, Hampshi re, U K, 1971-78. (Redrawn from Ross et a/., 1989.) Fig. 8.1 2

Trends in the temporal distribution of disease

'"

OJ u 0 �

OJ .0

E

:0 Z

200 180 160 140 120 100 80 60 40 20 0

14 r;

196 ...;...;

1.§.3

1,2.9

35 '" .'=!

E

OJ

-a

'0.

1J-5

OJ -a

76

r-

� ��

56

r-

2l 0 c. � '0 0; .0 E :0 z

30 25 20 15 10 5

c OJ --,

.0 OJ LL

OJ

::2'

OJ

::J «

a. Q.) (f)

+-' U 0

> 0 Z

u QJ 0

Sep

Month of onset

Bar chart depicting the seasonal occurrence of human leptospirosis i n the US. (From Diesch and E l l i nghausen, 1 975.)

Fig. 8.1 3

ecological factors, including mass movement of fleas and seasonal fluctuations in the abundance of rabbits (Ross et ai., 1989). In Spain, clinical myxomatosis occurs in the winter and spring, corresponding to the recruitment of young susceptible rabbits (Calvete et ai., 2002).

Leptospirosis is more common in the summer and early autumn than the winter in temperate climates ( Figure 8.13) because the warm, moist conditions dur­ ing the summer predispose to survival of the pathogen (Diesch and Ellinghausen, 1975; Ward, 2002). In contrast, transmissible gastroenteritis of pigs is more common in winter than summer ( Figure 8.14). This may be because the survival time of the virus is very short in summer because of the stronger ultra­ violet light and higher temperatures then (Haelterman, 1963).

In the US, feline panleucopenia shows a seasonal peak in August and September (Reif, 1976). This is associated with a peak in the number of births in the cat population in June, which increases the number of susceptible cats in the population at risk. The kittens are protected passively by maternal antibody for approximately the first 2 months of life, therefore the peak 'herd' susceptibility occurs 2 months after the birth peak. Such seasonal fluctuations are less likely in canine than in feline populations because births of puppies are distributed more evenly throughout the year than those of kittens (Tedor and Reif, 1978). Some non-infectious diseases may also show seasonal trends. Thus, bovine hypomagnesaemia is common in spring and is associated, among other factors, with low levels of magnesium in rapidly growing pastures (see Figure 3.6).

Oct

Nov

Dec

Jan

Months (weekly intervals)

Seasonal trend of transmissible gastroenteritis of pigs: reported epidemics i n I l l inois, 1 968-69. (From Ferris, 1 97 1 .)

Fig. 8.1 4

Sometimes seasonal determinants may be uni­ dentified. For example, canine diabetes mellitus, like human insulin-dependent diabetes, is more common in winter than summer (Marmor et ai., 1982). Lon g-te rm (sec u l ar) trends

Secular trends ( Figure 8.1 1 a) occur over a long period of time and represent a long-term interaction be­ tween host and parasite. If a balance occurs, then a stable, endemic level of disease is maintained (1 in Figure 8.lla); if the interaction is biased to the host, then there is a gradual decrease in disease occurrence ( 2 ); and if the interaction is biased to the parasite, there is a gradual increase in disease occurrence (3). Figure 8.15 illustrates a reported increasing long­ term trend in the annual prevalence of rabies in Total

10 000

� o

5000

Dogs

,-------,

Wildlife

] E " c

1000

�o

500

C. 0> a:

'--,

,

, ,

,

Year Fig. 8.1 5 An example of a secular trend: reported cases of rabies i n the U S , 1 946-65. (From West, 1 972.)

/Ie,

Patterns of disease

wildlife in the US, whereas the prevalence in dogs is decreasing due to adequate control. 'Reported' is emphasized to stress that accurate estimation of trends is open to errors, some of which are described below. Upward trends may also result from the inter­ vention of man and changing human habits. Such trends occur with the so-called 'diseases of civilization' and 'urbanization' in man, (e.g., coronary heart disease) and the diseases of intensive production in animals. Secular decreases in morbidity may be the product of prophylaxis (e.g., vaccination). Mortality may show a secular decrease due to improved therapeutic techniques. True and fa l se c h a n ges i n morbid ity and morta l ity

The temporal changes that occur in recorded morbid­ ity and mortality rates may be either true or false. The recording of mortality rates is rarer in veterinary than in human medicine because recording death in animals is not compulsory. Thus, details of trends in mortality in animals are usually unavailable. The common measures of morbidity - prevalence, cumulative incidence and incidence rate - comprise a numerator (number of cases) and a denominator ('popu­ lation at risk' for first two measures, and 'animal-years at risk', or a suitable approximation, for the third Chapter 4). Changes in either numerator or denomin­ ator induce changes in these measures that may be either true or false (Table 8.2). True changes in risk and an incidence density can affect these recorded measures and prevalence; additionally, changes in disease duration affect prevalence (see Chapter 4). A major cause of false changes is variation in the recognition and reporting of disease. Thus, the in­ creasing secular trend in wildlife rabies in the US Reasons for true and false temporal changes in i ncidence and prevalence accord ing to changes in the n umerator (cases) and denominator (an imal-years at risk etc./population at risk).

Table 8.2

True changes

Incidence: Prevalence:

change in incidence (a) change in incidence (b) change in d u ration of d isease

False changes

Prevalence and incidence: 1.

Errors i n the n umerator: (a) changes in the recognition of disease (b) changes in the procedu res for classifying disease

2.

Errors i n the denominator: (a) errors in enumeration of the a n i mal-years at risk etc./population at risk

between 1946 and 1965 ( Figure 8.15) may have resulted from increased recognition and reporting of affected animals, rather than a genuine increase in incidence. In the US, reports of feline heartworm disease have increased over the years (Guerrero et al., 1992), but it is difficult to say if this is due to increased awareness, improved methods of diagnosis, or a true rise in the disease's incidence. Similarly, apparent increases in parietal chronic pleuritis in Danish abattoirs can be explained by an increased frequency of detection resulting from increased diagnostic sensitivity (En0e et al., 2003).

The sampling of an animal population to record morbidity is also subject to inherent variation in the samples (see Chapter 12), and so appropriate statistical analysis should be undertaken (see Chapter 13). Apparently changing patterns therefore should be interpreted with due regard to the possibility that they are artificial. Detecti ng tem poral trends: t i m e series analysis

Short-term, seasonal and secular changes are temporal trends that can occur simultaneously, and may be mixed with random variation. In such circumstances, the various changes can be identified by statistical investigation. One method, originally applied in com­ merce, that is used in epidemiology to detect temporal trends, is time series analysis. A time series is a record of events that occur over a period of time; cases of disease are typical events. The events are plotted as points on a graph, with 'time' along the horizontal axis. Table 8.3, for instance, records the percentage of sheep lungs condemned monthly because of pneumonia or pleurisy at a Scottish slaughterhouse. Figure 8.16a plots these monthly values. There is considerable variation in the location of the points, but, by eye, an annual cycle is suggested and there appears to be a slight secular trend of increased prevalence from 1979 to 1983. Trends in these data may be detected by three methods: 1. 2. 3.

free-hand drawing; calculation of rolling (moving) averages; regression analysis;

the object being to identify, and, if required, to remove, random variation, seasonal and secular trends. Free-hand drawing

The joining of points by eye is an obvious, easy method of indicating a trend. However, it is susceptible to sub­ jective interpretation and cannot counteract random variation readily.

Trends in the 'no����" distribution of disease

J .t/

Percentage of sheep l u ngs condemned monthly because of pneumonia and/or pleurisy, and average monthly and yearly percentage condemnation rates ( 1 979-83) at a Scottish abattoi r. (From Simmons and Cuthbertson, 1 985.)

Table 8.3

1 979 1 980 1 981 1 982 1 983 Average monthly 'Yo condemnation rate

jun% ju/%

Aug% Sep%

jan %

Feb %

Mar%

Apr %

May %

0.33 0.40 0.48 0.72 0.71

0.24 0.38 0.58 0.71 ' 0.64

0.46 0.39 0.62 0.75' 0.48

0.57 0.65 0.75 0.85 0.84

0.65 0.58 0.51 0.45 0.38

0.23 0.49 0.44 0.34 0.48

0.27 0.49 0.2 1 0.26 0.69

0.37 0. 1 9 0.1 7 0.43 0.80

0.53

0.51

0.54

0.73

0.5 1

0.40

0.38

0.39

Oct %

Nov%

Dec %

Year/y% condemnation rate

0.14 0.27 0. 1 8 0.95 1.09

0.30 0.34 0.2 1 0.60 0.76

0.24 0.30 0.35 1 .4 1 1 .25

0.1 4 0.44 0.2 7 0.63 0.97

0.33 0.41 0.40 0.68 0.76

0.53

0.44

0.71

0.49

, Estimated

1.50

%

]

1.25 E � 1.00 c: o

C< c:

v =

0.243

+

0.OO889x

0.75

.3 0.50 "#

0.25

.

1979

(a)

u

1.5

1980

1981

1982

1983

(b)

1979

1980

1981

1982

1983

%

� 1.2 E � 1.0 c: o

� 0.7 C< c:

'

.3 0.5 "#

.'

0.25 o.001J.,.r.,-rW ,"',"M''"''"' ''W'WWA"',"''W,"�'o_''o''om,oo,o,"�om'MO" .M., » ,,,,0>«n:>,,,prnp,,t

Disease E m e rgency Control Centres

External locations, e.g. U n iversities

System users' PCs r u n n i n g web browser

L:J

n�

V"','"

H o l d i n g detai l s Herd details

l"" "" N etwork

O.t, ,,,, d ,.,1

� �

g g:�",

Labo ratory systems

li 0

Details of i nfected pre m i ses,

system

Fig. 1 1 .1 3

0.

gg ;==

movement restrictions

I nformation

Census Data entry

Disease Control System ---,

. M i l k producer deta i l s

Geographical

D

D-

Agricultural

;==

Database servers

'----------------------' ' iti On s Of

i nfected areas

t{

system

Stock n u m bers

q

Raw data

by species

Statistics systems

Management Information

Systems Holding details,

disease status, �v'm'"t �"dct;o",

Animal Movement Licensing System

The structure of the D i sease Control System i n formation syste m . (Modified from a figu re suppl ied by R. Muggeridge, Department for

Environment, Food and Rural Affai rs, London.)

having to install and administer specialized software on hundreds of microcomputers. Multiple Web and database servers are used to guard against failure, and to spread the processing load to avoid performance bottlenecks. Outbreak-specific data, such as details of suspected and confirmed cases, records of documents served on premises, visits made, cases of slaughter and carcass disposal, are recorded in the DeS database. Data entry screens and a wide variety of predefined reports and queries allow outbreak data to be exported to other DEFRA systems in a variety of formats. Exchange of data between Des and GISs enable outbreak data to be plotted, and definitions of infected and at-risk areas, which change with the spread of the disease and the progress of work to eradicate it. Exchanges between DEFRA's laboratory systems serve to update DeS with results of sample testing; and export of data to finan­ cial systems validates compensation payments. The DeS database includes details of over 400 000 agricultural holdings and other relevant business loca­ tions. Details of over 80 000 further locations, includ­ ing rented land and common grazing together with links between holdings such as common ownership of stock, are also recorded.

The use of DeS during the 2001 epidemic is a valu­ able example of the need to continually modify informa­ tion systems in the light of experience. For example, Vetnet' s tracing and verification system (VTVS) could only effectively trace cattle (all of which have an ear tag number), whereas sheep (which do not have indi­ vidual ear tag numbers) could only be traced in batches and, when broken up, became progressively more difficult to trace. In addition, initially, vehicles and personnel could not be traced (exemplifying the third of Finagle'S 'Laws': the information one needs is not what one can get), yet tracing is a key component of outbreak investigation and control (see Chapter 22). Moreover, at the beginning of the 2001 epidemic, both DeS and VTVS were fledgling systems, the former still being developed following its initial use during the 2000 UK swine fever epidemic. Although training in the use of DeS commenced relatively early in the epi­ demic, it was difficult for the full complement of staff to attend training sessions because of the massive additional workload on permanent administrative staff induced by the epidemic6. This therefore also 6

Permanent staff of necessity were supplemented by temporary staff

(see Figure 22.1).

Veterinary recording schemes

emphasizes the need for adequate training and staff­ ing before an information system can be effectively utilized.

l .l

Featherston, RH. (1997) Benefits of a national database for patient medical records. Journal of the American Veterinary Medical Association, 210, 173-174 Frerichs, RR and Selwyn, B.J. (2002) Microcomputers,

F u rther Read i n g

the Internet, and epidemiology. In: Oxford Textbook of Public Health, 4th edn. Vol. 2. Eds Detels, R, McEwen, J.,

Association for Veterinary Informatics Newsletter. http://

versity Press, Oxford

www.avinformatics.org

Beaglehole, R and Tanaka, H., pp. 745-758. Oxford Uni­ Menzies, P.I., Meek, AH., Stahlbaum, B.W. and Etherington,

Atkinson, I. (1971) Handbook for Interviewers. Great Britain

W.G. (1988) An assessment of the utility of micro­

Office of Population Census and Surveys. Social Survey

computers and dairy herd management software for

Division, Her Majesty's Stationery Office, London Bennett, AE. and Ritchie, K. (1975) Questionnaires in Medi­

cine: a Guide to Their Design and Use. Oxford University Press, London Blood, D.C and Brightling, P. (1988) Veterinary Information

Management. Bailliere Tindall, London Boynton, P.M. (2004) Administering, analysing, and report­

dairy farms and veterinary practices. Canadian Veterinary

Journal, 29, 287-293 Morris, RS. (Ed.) (1991) Epidemiological information sys­ tems. Revue Scientifique et Technique, Office International des

Epizooties, 10, 1-231 Morris, RS., Nimis, G. and Stein, T.E. (1986) The computer as a tool in epidemiological studies - an appraisal of trends.

ing your questionnaire. British Medical Journal, 328, 1372-

In: Proceedings of the 4th International Symposium on

1375

Veterinary Epidemiology and Economics, Singapore,

Cimino, J.J. (1998) Desiderata for controlled medical vocabu­ laries in the twenty-first century. Methods of Information

in Medicine, 37, 394- 403. (A review of medical terminology, with particular reference to computerized data recording and retrieval) Clements, ACA, Pfeiffer, D.U., Otte, M.J., Morteo, K. and Chen, L. (2002) A global livestock production and health atlas (GLiPHA) for interactive presentation, integration

18-22 November 1985, pp. 34-39. (A discussion of data collection, storage and analysis with microcomputers) Moser, CA and Kalton, G. (1971) Survey Methods in Social Investigation, 2nd edn. Heinemann Educational Books, London Payne, S.L. (1951) The Art of Asking Questions. Princeton University Press, Princeton Pollari, F.L., Bonnett, BN., Allen, D.G., Bamsey, S.C and

and analysis of livestock data. Preventive Veterinary Medi­

Martin, S.W. (1996) Quality of computerized medical

cine, 56, 19 -32

record abstract data at a veterinary teaching hospital.

Date, CJ. (2000) An Introduction to Database Systems, 7th edn. Addison-Wesley Publishing, Reading, Massachusetts Dillman, D.A (1978) Mail and Telephone Surveys: the Total

Design Method. John Wiley, New York

Preventive Veterinary Medicine, 27, 141-154 Revie, CW., McKendrick, I., Irwin, T., Gu, Y., Reid, S.J.W. and Gettinby, G. (1996) The application of hybrid informa­ tion systems to decision support in the veterinary and

of information systems in developing countries. World

agricultural domains. In: Society for Veterinary Epidemio­ logy and Preventive Medicine, Proceedings, Glasgow, 27-29

Animal Review, 3, 19-24

March 1996, Eds Thrusfield, M.V. and Goodall, E.A,

Dohoo, I.R (1994) Specific issues concerning the application

Ellis, P.R (1993) Information systems in disease control pro­

pp. 48-57

grams. In: Diagnosis and Epidemiology of Foot-and-Mouth

Smith, RD. (2003) The application of information technology

Disease in Southeast Asia. Eds Copland, J.W., Gleeson, L.J.

to the teaching of veterinary epidemiology and public

and Chamnanpood, C, pp. 111-115. Australian Centre for

health. Journal of Veterinary Medical Education, 30 (4), 344-

International Agricultural Research, Canberra FAO (1999) Manual on Livestock Disease Surveillance and

350 United States Department of Agriculture (1982) International

Information Systems. FAO Animal Health Manual No. 8.

Directory of Animal Health and Disease Data Banks. National

Food and Agriculture Organization of the United Nations,

Agriculture Library, United States Department of Agri­

Rome

culture, Miscellaneous Publication No. 1423

Presenting numerical data

The epidemiologist makes inferences from data col­ lected from groups of animals. The data are frequently quantitative, comprising numerical values. A funda­ mental characteristic of numerical biological data is their inherent variability. The weights of 100 Friesian cows, for example, will not be identical; there will be a range of values. If the 100 cows were a sample of a much larger group - say the national herd - then a dif­ ferent sample of 100, drawn from the same national herd, is almost certain to have a different set of weight values. Variability is of importance to the epidemiologist in two circumstances: when a sample is taken and when different groups of animals are being compared. In the first circumstance, it is necessary to assess to what extent the sample's values are representative of those in the larger population from which the sample was drawn. This is relevant to surveys, which are discussed in the next chapter. In the second circumstance, it is often necessary to decide whether or not a difference between two groups can be attributed to a particular factor. In epidemiology this frequently involves detect­ ing an association between disease and hypothesized causal factors, and is discussed in Chapters 14 and 15. For example, if the effect of ketosis on milk yield were being investigated, then two groups of cows - one comprising cows with ketosis and one consisting of cows without ketosis - could be compared with respect to milk yield. A detected difference in yield could be due to: the effect of ketosis; inherent natural variation in milk yield between the two groups; confounding variables (see Chapter 3) such as breed: cows of different breeds may be present in different proportions in each group, when the different breeds produce different milk yields. •

In this example, the second and third reasons for the difference can confuse the investigation by contribut­ ing to differences in the milk yields of the two groups. Statistical methods exist to separate the effects of the factors that are being investigated from random variation and confounding. Essentially, these involve estimating the probability of an event taking place. Probability is a numerical measure taking values between zero and 1 . An event that is impossible has a probability of zero, whereas an event that is certain has a probability of 1 . Probability also may be thought of as the frequency of certain events relative to the total number of events that can occur. Thus, the probability of throwing a 'head' with an unbiased coin is 1/2 (0.5). The probability of throwing either a 'head' or a 'tail' (i.e., the total probability) is 1 . Similarly, prevalence (see Chapter 4) is a measure of probability. A specific prevalence value is an estimation of conditional prob­ ability; a male sex-specific prevalence of 30% means that there is a probability of 0.3 of any one animal having a disease at a given point in time, conditional on its being male. This chapter deals with the probability distributions of numerical data that are the basis of many statistical tests (some of which are described in Chapter 13) and with the methods of displaying numerical values. The statistical content of this book is not comprehensive; it is designed to give the reader a basic knowledge of some relevant concepts and techniques. The reader who is unfamiliar with elementary mathematical notation should first consult Appendix II.

Some basic definitions

Any observable event that can vary. Variables may be either continuous or discrete (see

Variable

Some descriptive statistics

Chapter 9). An example of a continuous variable is the weight of an animal. An example of a discrete variable is the number of cases of disease. In some circum­ stances, the numerical values of the variable are called

Table 1 2.1

variates.

4.2

5.3

5.6

6.0

6.4

4.6

5.3

5.7

6.0

6.4

4.7

5 .4**

5.7

6.1

6.4

4.8

5 .4

5.7

6.1

6.5

4.9

5.4

5 .9*

6.1

6.5

5.1

5.4

5.9

6.1

6.5

5.2

5.4

5.9

6.1 **

6.8

5.2

5.5

5 .9

6.2

6.8

5.2 5.3

5.5 5.5

6.0

6.3 6.4

6.8

Any variable that is being considered in an investigation. Study variable

A response variable is one that is affected by another (explanatory) variable; for instance, an animal's weight may be a response variable and food intake an explanatory vari­ able, because weight is assumed to depend on the amount of food consumed. In epidemiological invest­ igations, disease often is considered as the response variable; for example, when studying the effects of dry cat food (the explanatory variable) on the incidence of feline urolithiasis. There may also be circumstances in which disease is considered as the explanatory vari­ able, for instance when studying the effect of disease on weight. Response variables are sometimes called dependent variables and explanatory variables are called independent variables. Response and explanatory variables

A quantity that can differ in different cir­ cumstances, but is constant in the case that is being considered. It may be a constant in a mathematical formula or model. For example, a survey may be designed to detect a minimum disease prevalence, such as 20%. Although prevalence can vary, the minimum detectable prevalence is defined for the objectives of the survey as a single unvarying value, and is there­ fore a parameter of the survey, which is incorpor­ ated in the appropriate formula to detect the specified minimum disease prevalence (see Chapter 13). A parameter may also be a measurable characteristic of a population such as the average milk yield of a herd of dairy cows.

Specimen 3-week wea n i ng weights (kg) of two groups

(A and B) of piglets.

Group A

6.0

n = 49; X= 5 . 76 kg; 5= 0.60 kg;

Q2 = 5.9

Group 8

kg; SIR = 0 . 3 5 kg.

2.6

4.3

4.6

4.8

5.3

3.4

4.3

4.6

5 .0

5.5

3.6

4.3**

4.6

5 .0

5.5

3 .8

4.4

4.6

5.0

5.6

3.9

4.4

4.7*

5.0

5 .6

4.0

4.4

4.7

5.1

5 .6

4.0

4.4

4.7

5 . 1 **

5 .6

4.1

4.5

4.8

5.2

5.7

4.1

4.5

4.8

5.2

6.3

4.2

4.5

4.8

5.2

n = 49 ; x = 4.69 k g ; 5 = 0.67 kg;

Q2 = 4.7

Parameter

kg; SIR = 0.40 kg.

* Median ** Quartiles

Table 1 2.2

G rouped freq uency d i stribution for t h e 3-week weaning

weights of piglets i n G roup B of Table 1 2. 1 .

Weight (kg)

Number o fpiglets

2 .6-3.0 3 . 1 -3 . 5 3 .6-4.0

5

4.1 -4.5

13

4.6-5.0

15

5 . 1 -5 . 5

8

5 .6-6.0

5

6. 1 -6 . 5

Data set

A collection of data.

The initial measurements that form the basis of analyses.

Raw data

Some descriptive statistics

Table 1 2 . 1 lists sample weights of two groups (A and B) of piglets, when weaned at 3 weeks of age. These can be considered as random samples of a much larger group of piglets; namely, all piglets at 3 weeks of age. The inherent variability is obvious. The number of piglets with weights within defined intervals (i.e., the group frequency distribution of the weights) for

Group B is recorded in Table 1 2 .2 and depicted in Figure 12.1 . This figure, which summarizes the data, is called a histogram. The intervals on the horizontal axis are 0.5 kg wide. The number of piglets within each interval is proportional to the area of the vertical bars. H the intervals on the horizontal axis are equal, as in this example, then the number of piglets within each interval is also proportional to the height of the bars. Alternatively, the vertical plots and the mid-points of the horizontal intervals can be joined, rather than con­ structing bars, in which case a frequency polygon is constructed. These data can be summarized further by the use of descriptive statistics that are measures of position and spread of the histogram.

)Jh

Presenting numerical data 17 16 15 14

'**'.

13 12 11 Cl '0. 1 0 '0 ... 9 '"

(l) .0

E

:l Z

8 7 6 5 4 3

=

2

3

2

4

5

6

7

Wei g ht ( k g ) Fig. 1 2.1

The lower and upper quartiles, Q1 and Q3' respect­ ively, are defined as the two values that are mid-way between the lower and upper extreme values and the median. For Groups A and B they are marked with two asterisks, Thus, 25% of values fall below Ql' and 75% of values lie above it; Q1 is therefore the 25th centile. Similarly, 75% of values fall below Q3 and 25% of values lie above it; Q3 is therefore the 75th centile. Quartiles may be located between two values; notably, when there is an even number of observa­ tions. Interpolation is then required. If there are n observations, the first quartile (Ql) is the observation at position (n + 1)/4; the second quartile (median: Q) is the observation at position 2(n + 1)/4; and the third quartile (Q3) is the observation at position 3(n + 1)/4. For example, suppose n 10. Then 00 + 1)/4 = 2.75, and Q1 is between the second and third observations (call them x2 and x3), three-quarters of the way up. Thus, Q1 = x2 + 0.75(x3 - x2). Similarly, 00 + 1)/2 = 5.5, and Q2 is between the fifth and sixth observations, half-way up. Thus, Q2 = Xs + 0.5(x6 - xs)' where Xs and X6 are the fifth and sixth observations. Again, since 300 + 1)/4 = 8.25, Q3 = Xs + 0.25 (x9 - xs)' where Xs and X9 are the eighth and ninth observations. Consider this data set, comprising six observations: 9, 12, 16, 22, 27, 31. The first quartile (Ql) is the observation at position (n + 1)/4 = 7/4 1.75. Q1 is between the first and second observations, three-quarters of the way up: 9 + 0.7502 - 9) 9 + 2.25 = 11.25. The median (Q2) is the observation at position 2(n + 1)/4 = 14/4 = 3.5. Q2 is between the third and fourth observations, half of the way up: 16 + 0.5(22 - 16) = 16 + 3 = 19. The third quartile (Q3) is the observation at position 3(n + 1)/4 = 21/4 = 5.25. Q3 is between the fifth and sixth observations, one-quarter of the way up: 27 + 0.25(31 - 27) = 27 + 1 28.

Observed d i stribution of the weights of the 49 p iglets i n

Group B dep icted as a h i stogram (rectangles) a n d fitted 'Normal ' curve (smooth curve). (Data from Table 72. 7 .)

Measu res of pos ition

=

A commonly adopted measure of position is the mean of the sample, denoted by i (pronounced 'x-bar'). It is calculated using: LX i=­ n

where n is the number of values in the random sample. In Table 1 2 . 1 , n = 49 in each group, and i = 5.76 kg in Group A, and 4.69 kg in Group B. Each sample has been assumed, implicitly, to have been drawn from a much larger population; thus, the mean of the sample is only an estimate of the true popu­ lation mean, fl. Only if all the population is invest­ igated can the parameter fl be known. As the sample size increases, i will be a better estimator of fl; that is, the precision of i as an estimator of fl will increase. The median of the sample, sometimes denoted by Q2' is another measure of position. It is the value below which half, and therefore above which half, of the observations lie. It divides the distribution into equal, ordered subgroups and is termed a quantile. Quantiles that divide the distribution into hundredths are centiles (percentiles). The median therefore is the 50th centile (percentile). The median values in Table 1 2 . 1 for Groups A and B, respectively, are marked with an asterisk, Again, the sample median is an estimator of the true popula­ tion median. '*'.

=

=

Measu res of spread

Measures of spread are a little more difficult to cal­ culate than those of position. Two examples of simple measures of spread are the range and the mean of the absolute deviations of the individual values from the mean. However, these measures often do not distin­ guish different sets of data. A commonly adopted measure is the sample vari­ 2 ance, S , which is calculated by: 52

=

L(x - i) n-l

2

Statistical distributions

This formula may be rewritten in a form that is more easily calculated with small calculators, namely: I x2 - I (I x)2 / n ) S2 = n-l The square root of the sample variance is called the sample standard deviation. Using the values from Table 12.1, Group B, and the formula for s2 above, the sample standard deviation, s, is given by: I x2 - I( I x)2/n}

p.

I -2 Fig. 1 2.2

/J, a,

n-l

I

- 2u

z

I I I I I I I I I I

� 68% �

I - u

p.

I I I I I I I I I I

I

p. +

I -1

u

I

f' +

I 2

2u

)1

X Z

A Normal density curve showing the relationsh i p between

and the proportion of observations for Normal ly d i stributed

data.

1100.27 - (229.82/49) 48 = � 21.62/48 = 0.67 kg. Just as the sample mean is an estimate of the popu­ lation mean, so the sample variance and sample standard deviation are estimates of the population variance, 0"2 and the population standard deviation, 0" (sigma). When summary statistics are presented, the sample standard deviation should be presented as well as the sample mean in order to indicate the variability within the population. A measure of spread that often accompanies the median is the semi-interquartile range (SIR). This is half of the range between the quartiles, Q1 and Q3 : SIR = Q3 - Ql .

2

This is an estimator for the

population

semi­

interquartile range.

Alternatively, and increasingly, a sample may be summarized by a five-point summary consisting of the minimum, lower quartile, median, upper quartile and maximum.

This bell shape is typical of a family of frequency dis­ tributions known as the Normal family of distributions. It is better spelled with an upper case N to avoid con­ fusion with other meanings of the word. Another name for this distribution is the Gaussian distribution. This distribution is described by two parameters: its mean, j1, and its standard deviation, 0". The Normal curve can be used as a smooth approx­ imation to a histogram based on a sample of values, as in Figure 12.1, or as the paradigm of the population distribution of a variable. The latter can be described mathematically as a density function (Samuels, 1989), and plotted graphically as a density curve, which can be interpreted quantitatively in terms of areas under the curve (Figure 12.2). All Normal curves can be made equivalent with respect to areas under them by rescaling the horizontal axis. The rescaled variable is denoted by z, the standardized Normal deviate: x - j1

Z = -- . 0"

The values z = 0, 1, 2, 3 therefore correspond to x = j1, j1 + 0", j1 + 20" and j1 + 30", respectively, derived thus: j1 - j1 if x = j1, z = -- = O; 0"

Statistical distributions

j1 + 0"- j1 . If x = j1 + O", z = 0"

The Normal d i stribution

if x = j1 + 20", Z =

If many piglets were weighed, rather than just the 49 in the data set shown in Table 12.1, and if the intervals used in the histogram in Figure 12.1 were reduced, then the bars would become narrower. Eventually, the cor­ responding frequency polygon would trace a smooth curve. One such curve has been fitted over the bars in Figure 12.1, using a computer program, which identi­ fies the curve, using the weights in Table 12.1. The curve has one peak in the middle and is symmetrical.

if x = j1 + 30", Z =

j1 + 20"- j1 0" j1 + 30"- j1 0"

0"/0"= 1; 20"/0"= 2; 30"/0"= 3.

The Z scale can be used to ascertain the proportion of observations that fall within a specified range of values. Approximately 68% of all Normally distributed values lie within one standard deviation of the mean of the population from which they were sampled (j1 - O"to j1 + 0"; Z = -1 to Z = 1), and 95% within approximately

) I ()

Presenting numerical data

Table 1 2.3

Possible series of calves born to a cow d u ri ng three

successive u n iparous gestations (M

=

male; F = female).

gestation

Second gestation

gestation

First

Third

Total male

Total female 0

M

M

M

3

M

M

F

2

M

F

M

2

M

F

F

1

F

M

M

2

F

M

F

F

F

2 2

M F

2 0

3

two standard deviations of the mean (precisely:

11 - 1 .960"to 11 + 1 .960"; Z = -1.96 to Z = 1 .96) (Figure 1 2 .2).

In many cases, the Normal distribution provides a workable approximation to the distribution of biological variables; for this reason it is a very impor­ tant distribution. However, this distribution cannot be applied to all variables. Measurements to which Normality does not apply (although it can do as an approximation for large samples) are counts and ordinal data that only have a small number of intervals on the scale (Figure 9.1). Visual analogue measure­ ments also may not be Normally distributed. The b i no m i a l d i str i bution

This distribution relates to discrete data when there are only two possible outcomes on each occasion; for instance, the sex of a calf at birth can only be either male or female. An example is given in Table 12.3. The two outcomes may be of any kind but, for convenience, here are termed 'success' and 'failure'. On n occasions, the probability Pr(r) of r successes out of n trials is found to be: Pr(r) =

n! r!(n - r)!

pr(1 _ p)n-r

[r = O,I,2 . . . n ; O < p < l]

where p = probability of success on a single occasion assuming no association between the outcomes occur­ ring on different occasions. In this example, two males (outcomes, r = 2) may be born during three pregnan­ cies (occasions, n = 3). If it is assumed that the sex of the first calf does not affect the sex of future calves, and p = 0.52, then the probability, Pr(2), will be: 3! Pr(2) = - (0.52)2 (0.48) [Note: n - r = 1] 2!1!

= 0.39. The value of p can vary considerably between 0 and 1; for example, in some genetically determined diseases.

The Poi sson d i stribution

The Poisson distributionl is concerned with counts. It is applicable when events occur randomly in space or time. Some commonly quoted examples are the dis­ tribution of blood cells in a haemocytometer and the distribution of virus particles infecting cells in tissue culture. This distribution is important in epidemiology because it relates to the spatial and temporal distribu­ tion of disease. The random occurrence of cases of dis­ ease in unit time or in unit area can follow a Poisson distribution. A significant departure from this distribu­ tion therefore indicates temporal and geographical departures from randomness (see Chapter 8). The distribution is characterized by one parameter, A. (lambda): the average count per unit area or per unit time. The probability of counts of r = 0, I, 2, 3, 4, and so on, is given by the formula: e AA.r r! -

Pr(r) =

--

[A. > O, r = O,I,2 .

..]

where e is a constant: the base of natural (Napierian) logarithms = 2.71 8 28. The value of e-A can be found in published tables and is determined on many pocket calculators. For example, suppose that a tissue culture mono­ layer is being infected with virus particles. If there are 1 x 106 cells to which are added 3 x 106 virus particles, then the average count/ cell (A.) is 3. The proportion of cells expected to be infected with, for example, two particles can be calculated using the formula above, with A. = 3 and r = 2. Substituting in the formula: Pr(2) = e-332/2! From tables or a calculator, e-3 = 0.0498.

Thus: Pr(2) = 0.0498 x 32/2! = 0.2241.

This means that the expected proportion of cells infected with two virus particles is 22.41 %. Other d i stributions

There are many other statistical distributions. Some deviate from Normality; some of these deviations are illustrated in Figure 12.3. The mean and median are equal when a variable is symmetrically distributed; and the mean and standard deviation provide good measures of position and spread. However, when frequency distributions deviate from Normality, this 1

The distribution is eponymously named after the 1 9th century

French mathematician, Simeon-Denis Poisson.

Asymmetry

4350 1 30 25 � 20 15 10 5

Kurtosis

(a) negative skewness

c:

0.95, an appropriate formula can be found in Chapter 1 7 ('Confidence intervals for sensitivity and specificity'). Small sample size If only a small-sized sample is available, then nP and n (1 - P) may be less than 5. It is then necessary to calculate exact confidence intervals, based on the binomial distribution (Altman et al., 2000). The values also can be obtained conveniently by consulting Appendix VII. Diseases of low prevalence Some diseases (e.g., tumours) may be rare. If the Normal approximation to the binomial distribution is applied, then a very large sample would be required to estimate a confidence inter­ val accurately. Moreover, Appendix VII can only be used for prevalence values greater than 0.02%. There­ fore, if the estimated prevalence is lower than this, an alternative method, utilizing the Poisson distribu­ tion (see Chapter 12) should be used. For example, a random sample of 2000 dogs may yield two cases of osteosarcoma. The point estimate of the prevalence per 100 000 animals is therefore 2/2000 x 100 000 = 100 cases per 100 000 dogs. To construct a 95% confidence interval, consult columns 4 and 5 of Appendix VIII. The lower limit for two cases (x = 2) is derived from the value of Xu = 0.242 thus: 0.242/2000 x 100 000 = 12 cases per 100 000 animals. The upper limit is derived from the value of Xu = 7.225, thus: 7.225/2000 x 100 000 = 361 cases per 100 000 animals.

If prevalence is being estimated with a diagnostic test whose sensitivity and specificity are known, then a corrected estimate of the true pre­ valence, P, can be made by: Impedect tests

P

=

pT+ specificity - 1 sensitivity + specificity

-

I'

where pT is the test prevalence (Rogan and Gladen, 1978). (The value of 1 is replaced by 100 if the para­ meters are quoted as percentages.) For example, if pT = 0.20, sensitivity (Se) = 0.90 (90%), and specificity (Sp) = 0.95 (95%), then: 0.20 + 0.95 - 1 p= 0.90 + 0.95 - 1 = 0.1765.

-----

where: var P = the variance of the true prevalence pT(1 _pT ) n(Se + Sp - 1)2 where n = sample size. Thus, if the test prevalence, above, was estimated from a sample of 400 animals, n = 400, and: varp = __ 400 x (0.90 + 0.95 - 1)2 0.20 x 0.80 400 X 0.852

__

= 0.000 553 63. Thus, the approximate 95% confidence interval for the true prevalence is: 0.1765 - 1 .96 �O.OOO 553 63, 0.1765 + 1.96 �O.OOO 553 63 = 0.1765 - 0.0461, 0.1765 + 0.0461 = 0.1304, 0.2226; that is, 13.0%, 22.3%. If other confidence intervals are required, then 1 .96 is replaced by the appropriate multiplier (Appendix VI). If the sampling fraction, I, is large (greater than 10%), then the numerator of the variance formula,pT(1 p T ) again should be multiplied by (1 - f). This formula also can be applied when herds or flocks (rather than individual animals) are the sampling units, in which circumstance sensitivity and specificity are replaced by aggregate sensitivity and aggregate specificity (see Chapter 17 and 'Detecting the presence of disease: Imperfect tests', above). _

Systematic sampling

Confidence intervals for prevalence can be calculated for systematic samples using the formulae applied to simple random samples, assuming that there is no periodicity in the samples. More complex formulae should be applied if the latter may be present (Levy and Lemeshow, 1999). Stratified sampling

The simple random sample formulae also are satis­ factory for proportionally allocated stratified sam­ ples. However, if other methods of allocation are

Calculation of confidence intervals

undertaken, more complex formulae are required (Levy and Lemeshow, 1999). Cluster sampling

Confidence intervals for cluster samples need to be calculated differently from those for simple random samples, to take account of the variability that is likely to exist between the groups that constitute the clusters. The data in Table 13.3 will again be used to illustrate how confidence intervals are calculated. The sample estimate, P, has already been calculated in the pre­ ceding section on sample size determination for cluster samples, and was found to be 0.157. An approximate 95% confidence interval may be calculated using the formula11 : P A

-

1.96

{ c�) c(c T

-

1)

, P + 1.96 A

{c�) c(c -

T

- 1)

,

where: c = number of clusters in the sample; T = total number of animals in the sample; and:

where: n = number of animals sampled in each cluster; m = number of diseased animals sampled in each cluster. Now, substitute the values c = 14, T = 3032 and V = 6409 (derived in the preceding section on sample size determination for cluster samples) into the formula:

{

6409 0.157 - 1.96 � 3032 14(14 - 1)

j,

0.157 +

{

6409 1 .96 � 3032 14(14 - 1)

)

0.157 - (1.96 x 0.0046 x �35.214), 0.157 + (1.96 x 0.0046 x �35.214 ) = (0.157 - 0.0535), (0.157 + 0.0535) = 0.1035, 0.2105; that is, 10.35%, 21 .05%.

J

)

Again, if other confidence intervals are required, the appropriate multipliers should be used (Appendix VI). Note that the value for the confidence interval is much wider than that which would have been obtained if the formula for simple random sampling had been inappropriately used 04.4%, 1 7.0% for a 95% confidence interval), illustrating that, for a given sample size, cluster samples usually produce less precise estimates than simple random samples1 2. This formula can be used for both one-stage and two-stage cluster samples. In the former, n = all animals in each cluster, whereas, in the latter, n is a sample of animals in each cluster. A simple rule stating when this Normal-approxima­ tion method for calculating confidence intervals may be applied does not exist. This is because the distribu­ tion of a cluster sample proportion is complex due to the presence of the two variance components (between clusters and between animals within clusters) 1 3. An indication of the validity of the method can be obtained by plotting the frequency distribution of the indi­ vidual cluster prevalence values. If this has a smooth, symmetric distribution, the Normal-approximation method is likely to be valid. Otherwise, the calculated confidence intervals may only be approximate, partic­ ularly if a small number of clusters has been sampled. Thus, a plot of the individual cluster prevalence values in Table 1 3 .3 does not show a smooth distribution, and so the confidence intervals should be regarded as approximate. In such circumstances, an alternative approach to presenting precision would be to simply state the standard error of the cluster sample's overall prevalence (i.e., the value derived in the worked ex­ ample above before being multiplied by the multiplier 1.96: 0.0273). More complex methods of calculating exact confidence intervals are also available (Thomas, 1989), but would require the use of a computer program. Samples with three or more stages require more complicated methods (Levy and Lemeshow, 1999).

=

11 Again, this formula assumes that the fraction of clusters sampled (j) is small (less than 10%). If the fraction is not small, the value V / {e(e - 1)} needs to be multiplied by (1 -n· In this example, f 14/865, 0.016; thus (1 -f) is small and so can be omitted from the formula without affecting the result materially. =

=

12 This is because the variance of the prevalence (i.e., the square of the standard error of a proportion: see Chapter 12) derived by cluster sampling, when there is variability between clusters, is larger than the variance derived when the data are treated as a simple random sample. The ratio of the former variance to the latter is one definition of the design effect. (For other ways of determining the design effect, see Donner and Klar, 2000.) 13 This means that it is unclear when the central limit theorem holds. This theorem states that, as more observations are included, eventually the mean of any distribution will tend towards a Normal distribution, providing its variance is finite. (See also Chapter 12, 'Normal approxima­ tions to the binomial and Poisson distributions' .) The central limit theo­ rem should hold before Normal-approximation methods are used with complete trust. In cluster sampling, the larger the number of clusters and the number of animals, the more likely that the theorem will hold.

Surveys

Further reading

Humphry,KW., Cameron, A. and Gunn, G.J. (2004) A prac­ tical approach to calculate sample size for herd prevalence surveys. Preventive Veterinary Medicine, 65,173-188

Abramson, J.H. and Abramson, Z.H. (1999) Survey Methods

Kish,L. (1995) Survey Sampling. John Wiley,New York Leech, F.B. and Sellers, KC. (1979) Statistical Epidemiology in Veterinary Science. Charles Griffin, London and High Wycombe

in Community Medicine, 5th edn. Churchill Livingstone

Barnett, V. (2002) Sample Survey: Principles and Methods, 3rd edn. Arnold,London Bennett, S., Woods, T., Liyanage, W.M. and Smith, D.L. (1991) A simplified general method for cluster sampling surveys of health in developing countries. World Health Statistics Quarterly, 44,98-106

Levy, P.5. and Lemeshow, S. (1999) Sampling of Populations: Methods and Applications, 3rd edn. John Wiley,New York Lwanga, S.K and Lemeshow, S. (1991) Sample Size Deter­ mination in Health Studies: a Practical Manual. World Health

Casley, J.D. and Lury, D.A. (1981) Data Collection in Developing Countries. Clarendon Press,Oxford Cochran, W.K (1977) Sampling Techniques, 3rd edn. John

Organization,Geneva Moser, c.A. and Kalton, G. (1971) Survey Methods in Social Investigation, 2nd edn. Heinemann Educational Books,

Wiley,New York Condon, J., Kelly, G., Bradshaw, B. and Leonard, N. (2004) Estimation of infection prevalence from correlated binomial samples. Preventive Veterinary Medicine, 64,1-14 Donner, A. and Klar, N. (2000) Design and Analysis of Cluster Randomization Trials in Health Research. Arnold, London Dufour,B.,Pouillot,K and Toma,B. (2001) Proposed criteria to determine whether a territory is free of a given animal disease. Veterinary Research, 32, 545-563 Farver, T.B. (1987) Disease prevalence estimation in animal populations using two-stage sample designs. Preventive

London Salman,M.D. (Ed.) (2003) Animal Disease Surveillance and Survey Systems: Methods and Applications. Iowa State Press,Ames Sergeant, E. and Toribio, J.-A. (2004) Estimation of Animal­ Level Prevalence from Testing of Pooled Samples. AusVet Animal Health Services, PO Box 3180, South Brisbane, QLD 4101,Australia Slater, M.K (1996) Methods and issues in conducting breed­

Veterinary Medicine, 5,1-20 Farver, T.E., Holt, D., Lehenbauer, T. and

Greenley,

W.M. (1997) Application of composite estimation in studies of animal population production with two-stage repeated sample designs. Preventive Veterinary Medicine, 30,109-119 Hadorn, D.C., Rufenacht, J., Hauser, K and Shi.rk, K (2002) Risk-based design of repeated surveys for the documenta­ tion of freedom from non-highly contagious diseases. Preventive Veterinary Medicine, 56,179-192

specific canine health surveys. Preventive Veterinary Medicine, 28, 69-79 Tryfos, P. (1996) Sampling Methods for Applied Research. John Wiley,New York Woods, A.J. (1985) Sampling in animal health surveys. In: Society for Veterinary Epidemiology and Preventive Medicine, Proceedings, Reading, 27-29 March 1985, Ed. Thrusfield,M.V.,pp. 36-54 Yates, F. (1981) Sampling Methods for Censuses and Surveys, 4th edn. Charles Griffin,London and High Wycombe Ziller, M., Selhorst, T., Teuffert, J., Kramer, M. and Schluter, H. (2001) Analysis of sampling strategies to substantiate freedom from disease in large areas. Preventive Veterinary Medicine, 52, 333-343

Demonstrating association

A valuable step in the identification of the cause of a disease is the detection of a statistically significant association between the disease and hypothesized causal factors; this is the basis of the first three of Evans' postulates (see Chapter 3). Some basic principles

Demonstration of association can be approached in three ways. 1. The difference, under two different circumstances, between the mean of the probability distribution of a set of values of a variable can be measured. If there is a significant difference between the means in the two circumstances, the different circum­ stances may lead to an explanation that reflects a causal association. For example, the weights of two groups of piglets, one group of which has developed neonatal diarrhoea and one group of which has not, can be measured. The effect of diar­ rhoea on weight can then be assessed by analysing the difference between the mean weights of the two groups. A similar approach can be adopted when comparing medians. 2. Variables can be categorized, and a significant association sought between various categories. Thus, bitches can be categorized according to whether or not they have physiological urinary incontinence and whether or not they are neutered. Evidence of an association between the syndrome and neutering can then be sought. 3. A correlation between variables can be sought. For instance, the incidence of lameness in cattle and the amount of rainfall can be recorded to investigate whether increased rainfall is signi-

ficantly associated with an increased incidence of lameness. Although approaches 1 and 2 are introduced in this chapter in the context of causal studies, they can be applied in any circumstance in which two groups are being compared. Many of the statistical techniques that adopt these three approaches were developed for use in agricul­ tural science. Their use is confined to epidemiological investigations in this book, but they also have a wide application to experimental and observational bio­ logical and social sciences, and therefore are described in most general statistics textbooks. The principle of a significance test

The bell shape of the Normal distribution (see Fig­ ure 1 2 . 1 ) reveals that there is a probability, albeit a small one, of an observation occurring at the extreme tails of the distribution. This distribution may be used to describe the frequency distribution not only of the values of a continuous variable that has a Normal dis­ tribution but also of the means of repeated samples taken from that population (here termed the 'reference population'). This also includes means of parameters of other distributions, such as the binomial, when Normal approximations are applied. There is, there­ fore, a high probability of the mean of a sample being under the peak, and a much lower probability of this mean being close to either of the two tails. If the mean is close to a tail, this indicates either that the sample is one of those improbable samples taken from the reference population, or, more likely, that it has been drawn from a population with a different population mean.

Demonstrating association

It is necessary to decide when it is improbable that a sample mean has come from the reference population. This decision is taken when the probability, P, of obtaining a value for the sample mean at least as extreme as the one observed, assuming that the sample is drawn from the reference population, is less than a value corresponding to the level of significance. This level is represented by a probability

called a ('alpha'). Conventionally, in biological sci­ ences, a is taken to be 0.05, representing the 5% significance level. In the event of P < 0.05, the result is reported as 'significant P < 0.05' and supports the claim that the sample was not drawn from the refer­ ence population. The 5% significance level is purely conventional. If more caution in inferring a difference were necessary, the 1 % level (P < 0.01) or 0.1 % level (P < 0.001) could be chosen. Some reporting pro­ cedures use *, **, and *** to record significance at these 'critical' levels of 5%, 1 % and 0.1 %, respectively. This decision-making procedure is the principle of a significance test. Significance tests were originally conducted in conjunction with tables that presented only a limited number of significance levels, including the critical ones, and this practice is still common. However, many stat­ istical software packages (see Appendix III) calculate exact P values, and these should always be quoted, if available, in preference to the relevant critical levels. The null hypothesis

In the previous discussion, a statistical test was under­ taken on the basis that the sample came from a popula­ tion with a mean no different from that of the reference population. This constitutes the null hypothesis; the null hypothesis thus is one of no difference. A significant result indicates that the null hypothesis is rejected in favour of an alternative one which states that the sample has been drawn from a population with characteristics that are different from the reference population. Demonstration of a significant difference implies rejection of the null hypothesis. Notice that confidence intervals (see Chapter 12) and the outcomes of significance tests are closely related. For example, suppose that the null hypothesis states a particular value for the mean of a Normal dis­ tribution. A sample is taken and the significance test rejects the null hypothesis at the 5% level. The cor­ responding 95% confidence interval (sample mean ± 2 e.s.e.m.) then will not contain the value of the mean specified by the null hypothesis. Conversely, if the significance test does not reject the null hypothesis at the 5% level, the corresponding 95% confidence interval will contain the value of the mean specified by the null hypothesis.

Errors of i nfere n ce

Five per cent of samples from the reference population lie within the region that would lead to rejection of the null hypothesis at the 5% level. If this happens, it constitutes a rejection of the null hypothesis when the hypothesis is true. This error is an example of a Type I error: false rejection of a true null hypothesis. The probability of a Type I error is just the level of significance discussed abovel . A Type II error is a failure to reject the null hypothesis when it is untrue. The probability of committing this error is called f3 ('beta'). Ideally, both a and f3 should be known by the investigator before the study begins. Depending on the alternative hypothesis, f3 may or may not be determinable. In the previous discussion, if the alternative hypothesis specified the mean of the population from which the sample was drawn, then f3 could be determined for a stated value of a and sample size. However, if the alternative hypothesis only hypo­ thesized that the mean of the population from which the sample was drawn took one of several values, then f3 cannot be calculated. It is known that f3 can be kept small by increasing either a or the sample size. The probabilities of Type I and II errors decrease as sample size increases. For a fixed sample size, the larger the probability of a Type I error is chosen to be, the smaller the probability of a Type II error will be, and vice versa. Two remaining alternative decisions are possible. These represent correct inferences, rather than errors. The first inference is not rejecting the null hypothesis when it is true. The second is rejecting the null hypo­ thesis when it is false (i.e., demonstrating a significant difference). The probability of the latter is called the 'power of a test'; it is denoted by 1 f3. Most tests are calibrated by prescribing the signific­ ance level, a, and the power, 1 f3. -

-

One- and two-tailed tests

The previous discussion has been concerned with demonstrating any differences between a sample and 1 There is a subtle difference between the probability of a Type I error and a P value, which is not usually addressed in introductory texts because elementary statistical practice is usually unaffected by the differ­ ence. Moreover, the statistical approach described here, which focusses on error rates and is termed 'frequentist statistics', attempts to draw a conclusion about the truth of a hypothesis based on the results of a single study. Some statisticians prefer to define probability in the context of ideal populations, in which, in principle, there is an indefinite repetition of measurements, and prefer to focus on the probability distributions of unknowns, given available information: a 'Bayesian' approach (see Chapter 3). Bayesian methods are introduced in Chapter 17 in the context of predictive values and likelihood ratios. For a detailed discussion of these issues, including statistical inference in the context of inductive and deductive reasoning, see Hacking (1975), Casella and Berger (1987) and Goodman (1999a,b).

Some basic principles

a reference population, irrespective of the 'direction' of the difference; that is, whether the sample differs because it comes from a distribution with a mean to the left or right of the mean of the reference population. In this case, the investigator is concerned with signific­ ant departures towards either of the two tails of the distribution. A test that considers these departures is therefore called a two-tailed test. Sometimes, an investigator may be reasonably certain that significant departures only occur in one direction. An example would be investigating whether diarrhoea depressed weight gain in piglets, rather than either depressed or increased it (the latter is very unlikely). This investigation requires a one-tailed test. The 5% significance level in a two-tailed test represents approximately two standard errors to either side of the mean. If the same criterion of approximately two standard errors were used in a one-tailed test, then the actual significance level would only be 2.5% (corres­ ponding to the tail with which the investigator is con­ cerned). Therefore, rejection of the null hypothesis at the 5% level in a one-tailed test requires a deviation corresponding to that required for rejection at the 10% level in a two-tailed test. Significance tests involving other distributions, and conducted on large samples for which Normal approx­ imations to these distributions are valid, often com­ pute values of the standardized Normal deviate, z (see Chapter 12). These are then compared with tabulated values using values of mean and variance specified by the null hypothesis (Appendix XV). Some examples are given later. Independent and related samples

Groups (samples) that are compared may be independ­ ent or related, and different statistical techniques are required for these two circumstances. Independent samples require unpaired tests, whereas related samples require paired tests. Samples are related when: comparisons are made between repeated measure­ ments on the same individuals; they are matched for other variables. An example of the first situation is the measuring of the weights of individual calves one week, and then a week later. Similarly, the completion of two similar questionnaires by the same respondents constitutes related samples. Matching is a feature of some observational studies (see Chapter 15) and clinical trials (see Chapter 16). Pairing can have the benefit of removing a source of variation, therefore providing a more sensitive test than its unpaired counterpart. • •

):1 ()

Parametric and non-parametric techniq u es Parametric tests

Some tests are parametric because they are concerned with the mean, which is one of the parameters of the Normal distribution. Parametric techniques make the following assumptions of the data that are to be analysed: the distribution is Normal; the variables are measured on the interval or ratio scale; that is, they are continuous (see Chapter 9)2 . Additionally: some tests require that the two populations being compared have equal variances; if this is not the case, then these tests must be modified. Table 14.1 lists some commonly used parametric techniques that test hypotheses relating to the mean. This chapter focusses on comparing two populations (i.e., two-sample methods) and correlation. •

Non-parametric tests

If the assumptions of a parametric test cannot be met, then non-parametric techniques should be used. These can be applied to nominal and ordinal data, as well as interval and ratio data. Most of these tests are distribution-free, that is, they do not require assump­ tions such as the underlying distribution being Normal, but they do assume symmetry. Table 1 4.2 lists some commonly used non-parametric techniques. These are described fully by Siegel and Castellan (1988). Parametric tests are more powerful than non­ parametric tests if the distributional assumptions hold; that is, the former require a smaller sample size than the latter to detect a significant difference of a given size. Moreover, parametric tests are more robust to deviations from Normality than are non-parametric tests to deviations from symmetry. Hypothesis testing versus esti mation

Comparisons have traditionally been made by testing the null hypothesis using an appropriate significance test. However, such tests do not indicate the magnitude of the difference between groups that are being com­ pared, with defined precision, and it is the magnitude that may be of interest (e.g., when assessing the

2 Although visual analogue measurements are subjective, they can be treated as continuous data for the purpose of analysis.

)()

Demonstrating association

""'" W " � ,",>0 H,«,«,'""'w,«" "",«,, ,«»,>0,," ,"" "hHA«,," '" ""'" � � ,"'��'O'MW"

Table 1 4.1

0< 0' 0 ,� 0.05). Confidence intervals can also be calculated for r (Altman et al., 2000). If parametric assumptions are not met by data, an appropriate non-parametric measure of correlation can be calculated (Table 14.2). r = -;========

Multivariate analysis

The analytical techniques that have been described con­ cern the study of relationships between two variables. In some cases it is necessary to assess the relationship

Statistical packages

between a response variable and many explanatory variables. This requires statistical techniques that investigate multiple variables; these are therefore called multivariate techniques. They include cluster analysis, factor analysis, path analysis, discriminant analysis, analysis of principal components and multi­ ple regression analysis. An introduction is provided in the next chapter, but most of these methods are beyond the scope of this book, and are described in detail elsewhere (e.g., Everitt and Dunn, 2001). Statistical packages

There is now a wide range of applications software packages that perform statistical calculations includ­ ing those of the mean, median, standard deviation and standard error, confidence limits, the tests of asso­ ciation, sample-size calculations (briefly mentioned earlier), time series analysis, multivariate analyses and other statistical procedures relevant to epidemiology. Some of these packages are listed in Appendix III. Such packages enable data to be managed and anal­ ysed efficiently and quickly. However, they can be dangerous. They facilitate easy analysis of data and so tend to encourage the collection of masses of data without a clear objective. It is also easy to try many of the different tests that are available, without a know­ ledge of the tests' underlying principles and assump­ tions. These remarks are equally relevant to the use of those pocket calculators that have built-in programs for simple statistical tests. Expert statistical advice therefore should always be sought if there is any doubt about the analytical

technique that should be used in an investigation. This advice should be obtained before the investiga­ tion begins, not after it is completed; otherwise, time may be spent collecting data, only to discover that they cannot be used to solve the problem that is being posed. Further reading Altman, D.G., Machin, D., Bryant, TN. and Gardner, M.J. (Eds) (2000) Statistics with Confidence, 2nd edn. BMJ Books, London. (Estimation of confidence intervals and statistical guidelines)

Armitage, P., Berry, G. and Matthews, J.N.s. (2002) Statistical Methods in Medical Research, 4th edn. Blackwell Science, Malden Bailey, N.T.J. (1 995) Statistical Methods in Biology, 3rd edn. Cambridge University Press, Cambridge. (An introduction to elementary statistics)

Bland, M. (2000) An Introduction to Medical Statistics, 3rd edn. Oxford University Press, Oxford Essex-Sorlie, D. (1995) Medical Biostatistics and Epidemiology. Appleton and Lange, East Norwalk Fleiss, J.L., Levin, B. and Paik, M.C (2003) Statistical Methods for Rates and Proportions, 3rd edn. John Wiley, Hoboken Leech, F.B. and Sellers, K.C (1979) Statistical Epidemiology in Veterinary Science. Charles Griffin and Company, London and High Wycombe Mead, R., Curnow, R.N. and Hasted, A.M. (2003) Statistical Methods in Agriculture and Experimental Biology, 3rd edn. Chapman and Hall, Boca Raton and London Petrie, A. and Watson, P. (1999) Statistics for Veterinary and Animal Science. Blackwell Science, Oxford Siegel, S. and Castellan, N.J. (1988) Nonparametric Statistics for the Behavioral Sciences, 2nd edn. McGraw-Hill, New York

Observational studies

Observational studies are used to identify risk factors, and to estimate the quantitative effects of the various component causes that contribute to the occurrence of disease. The investigations are based on analysis of natural disease occurrence in populations by comparing groups of individualsl with respect to disease occurrence and exposure to hypothesized risk factors. Observational studies differ from experimental studies. In the former the investigator is not free to randomly allocate factors (disease and hypothesized risk factors) to individuals, whereas in the latter the investigator is free to allocate factors to individuals at random. Risk factors may be categorical (e.g., breed and sex) or quantitative, continuous measurements (e.g. weight, age and rainfall). This chapter focusses on categorical data, which are commonly the subject of observational studies. Continuous data can also be analysed using categorical methods by grouping the data into discrete categories (e.g., age intervals). Types of observational study Coho rt, case-control and c ross-sectional studies

There are three main types of observational study: cohort, case-control and cross-sectional. Each classifies animals into those with and without disease, and those

exposed and unexposed to hypothesized risk factors. Therefore, they each generate a 2 x 2 contingency table for each disease/factor relationship (Table 15.1). How­ ever, the methods of generation differ between the types of study. Cohort studies

In a cohort study, a group (cohort) of animals exposed to an hypothesized risk factor, and a group not exposed to the factor are selected and observed to record development of disease in each group. For example, if spaying were considered to be a risk factor for physiological urinary incontinence (PUI) in bitches, a suitable cohort study would comprise a group of spayed ('exposed') puppies and a group of entire ('unexposed') puppies, each of which would be monitored for the development of PUI. Therefore, incidence is measured, and a + b and c + d in Table 15.1 are predetermined.

Table 1 5. 1

studies.

1 Individuals are commonly, but not exclusively, the sampling units

studied.

Diseased

Non-diseased

animals

animals

Hypothesized risk factor present a Hypothesized risk factor absent c Total

in observational studies. Herds, flocks, or other aggregates can also be

The 2 x 2 contingency table constructed i n observational

a+c

Total

b

a+b

d

c+ d

b+d

a + b + c + d= n

I n cohort studies (a + b) and ( c + d) are predetermi ned. In case-control studies (a + c) and ( b + d) are predeterm ined. I n cross-sectional studies only n can be predetermined.

Types of observational study

Case-control studies

In a case-control study, a group of diseased animals (cases) and a group of non-diseased animals (controls) are selected and compared with respect to presence of the hypothesized risk factor. Thus, a case-control study of PUI would involve identification of cases of PUI and comparison of the sexual status (spayed versus entire) of these cases with a control group of bitches that were not incontinent. Therefore a + c and b + d are predetermined. Case-control studies may be conducted with incident (new) cases or existing cases and therefore may utilize incidence or preval­ ence values.

Table 1 5.2

Nomenclature of observational studies.

Cross-sectional

Longitudinal Case-control

Cohort

Synonym :

Synonyms:

Synonyms:

Prevalence

Retrospective Case-referent Case-comparison Case-compeer Case h istory Trohoc

Prospective I ncidence Longitudi nal Fol.low-up

Cohort studies

The cross-sectional study involves the selection of a sample of n individuals from a larger population, and then the determination, for each individual, of the simultaneous presence or absence of disease and hypothesized risk factor; prevalence is therefore recorded. For example, in a cross-sectional study of PUI, a sample of bitches would be selected and classified according to sexual status and whether or not the animals were incontinent. At the beginning of a cross-sectional study, only the total number of animals (n in Table 1 5 . 1 ) is predetermined. The numbers of ani­ mals with and without disease, and possessing or not possessing the risk factor, are not known initially. Nomenclature

A variety of alternative names have been applied to case-control and cohort studies. Both of these studies consider two events - exposure to a hypothesized causal factor or factors and development of disease that are separated by a period of time. Because of this temporal separation of the two events, each of these studies is sometimes termed longitudinal. The case-control study compares diseased animals (cases) with non-diseased animals (controls) and therefore has variously been called a case-comparison, case-referent or case history study. This study selects groups according to presence or absence of disease and looks back to possible causes; it has therefore sometimes been described as a retrospective study (looking back from effect to cause). A cohort study selects groups according to pres­ ence or absence of exposure to hypothesized causal factors, and then looks forward to the development of disease. It has therefore sometimes been called a pro­ spective study (looking forward, from cause to effect). Table 15.2 lists the types of observational study and their synonyms. The groups may be selected as 'exposed' and 'unex­ posed' now, and then observed over a period of time

Prospective

Retrospective

Cross-sectional studies

(concurrent)

(non-concurrent) Select exposed and non-exposed cohorts

Select exposed and non·ex posed cohorts

Fol low the . cohorts

Trace the cohorts

Past

Present

Future

Fig. 1 5 .1 The selection of cohorts in concurrent and non-concurrent cohort studies ('retrospective ' and 'prospective ' used in the temporal sense.) (Modified from L i l ienfeld and L i l ienfeld, 1 980.)

to identify cases; such a cohort study is termed con­ current (Figure 15.1). Alternatively, if reliable records relating to exposure are available (e.g., by tracing animals via adoption records from cat and dog homes/shelters: Spain et al., 2004a,b) then groups may be selected according to presence or absence of pre­ vious exposure, and traced to the present to determine disease status; this constitutes a non-concurrent study. Some investigators use 'retrospective' to refer to any study that records data from the past, and 'prospect­ ive' to refer to any study designed to collect future data. Therefore a non-concurrent cohort (prospective, in the causal sense) study alternatively may be termed a retrospective (in the temporal sense) cohort study. Similarly, a concurrent cohort study also can be called a prospective (in the temporal sense) cohort study (Figure 1 5 . 1 ).

Some studies show characteristics of more than one of the three main types. The range of such 'hybrid' studies, and their nomenclature, are described by Kleinbaum et al. (1982).

Causal inference

The three types of study attempt to identify a cause by applying the first three of Evans' postulates (see

2i>1l

Observational studies

Chapter 3; postulates 1 and 3, rephrased here, using 'prevalence' and 'incidence' in their definitions): 1. the prevalence of a disease should be significantly higher in individuals exposed to the supposed cause than in those who are not (evidence supplied by a cross-sectional study); 2. exposure to the supposed cause should be pres­ ent more commonly in those with than those with­ out the disease, when all other risk factors are held constant (evidence supplied by a case-control study); 3. the incidence of disease should be significantly higher in those exposed to the supposed cause than in those not so exposed (evidence supplied by a cohort study). The credibility of cause is strengthened by fulfilling Evans' other postulates. Thus, Jarrett's (1980) demon­ stration of an association between exposure to bracken and the development of intestinal cancer in cattle is more credible because a carcinogen has been isolated from bracken (Wang et al., 1976) (Evans' postulate 10).

Causal inference is also strengthened if associations are detected in different circumstances (see Chapter 3) or in several studies, enabling results to be generalized more confidently. Thus, an association between spay­ ing and PUI in bitches has been demonstrated in primary-care cases in Scotland and in referred cases in the south-west of England (Holt and Thrusfield, 1993), and demonstrated again in a subsequent national cohort study in the UK (Thrusfield et al., 1998); this strengthens the inference that the association holds in the general dog population. In contrast, a predisposi­ tion to valvular heart disease has been demonstrated in cocker spaniels in North America, but not in Scotland (see Chapter 5), suggesting that the breed predispostion is not universal. Comparison of the types of study

A comparison of cohort, case-control and cross­ sectional studies is given in Table 1 5.3. Case-control studies can be conducted relatively quickly and are a useful means of initially 'trawling'

Table 1 5.3

Comparison of the advantages and d isadvantages of cohort, case-control and cross-sectional studies. (Based on Schlesselmann, 1 982, and C layton and McKeigue, 2001 .J

Cohort studies

Advantages

Disadvantages

1.

1.

2.

Incidence i n exposed and unexposed individuals can be calcu lated Permit flexi b i l ity in choosing variables to be systematica l l y recorded

2. 3. 4. 5.

6. Case-control stud ies

1. 2. 3. 4. 5.

6. 7. 8.

Cross-sectional stud ies

1.

2. 3. 4. 5.

6.

Well suited to the study of rare d i seases or of those with long i ncubation periods Relatively qu ick to mount and conduct Relatively inexpensive Requires comparatively few subjects Existing records occasional ly can be used No risk to subjects Al low study of mu ltiple potential causes of a d i sease S uited to the study of i nteraction between genotype and envi ronmental factors When a random sample of the target population is selected, disease prevalence, and proportions exposed and unexposed in the target population, can be estimated Relatively quick to mount and conduct Relatively inexpensive Current records occasiona l l y can be used N o risk to subjects Al low study of multiple potential causes of d i sease

1. 2. 3. 4. 5.

6.

1. 2. 3. 4. 5.

Exposed and unexposed proportions in target population cannot be estimated Large numbers of subjects are requ ired to study rare diseases Potentially long duration for fol low-up Relatively expensive to conduct Maintaining fol low-up is d ifficult Control of extraneous variables may be i ncomplete Exposed and unexposed proportions i n target populations cannot be estimated Rely o n recal l o r records for information o n past exposures Val idation of i nformation is d ifficult or sometimes i m possible Control of extraneous variables may be incomplete Selection of an appropriate comparison group may be d ifficult Incidence in exposed and unexposed individuals cannot be estimated Unsu ited to the study of rare d i seases Unsu ited to the study of diseases of short duration Control of extraneous variables may be incomplete Incidence in exposed and unexposed individuals cannot be estimated Temporal sequence of cause and effect cannot necessarily be determi ned

Measures of association

for risk factors. Cohort studies, in contrast, may have a long duration (particularly those of diseases with lengthy incubation and latent periods such as cancer) and often focus on a specific risk factor. A logical requirement of demonstration of cause is that an animal is exposed to a causal factor before disease develops (see Chapter 3). The design of cohort studies, which resembles an experiment, ensures that this temporal sequence is detected. However, cross­ sectional and case-control studies may not detect the sequence. For example, if the association between spaying and PUI in female dogs were being investi­ gated using a cross-sectional study (spaying being the hypothesized risk factor), then spayed bitches with PUI may be identified; however, incontinence may have developed before spaying in some of the cases, in which instance spaying could not have been a com­ ponent cause in those animals. For this reason, and the reason that a cohort study measures incidence, the cohort study therefore is a better technique for assess­ ing risk and identifying causes than the other two types of study. Ecological studies

In each of the three types of study just described, it is necessary to know the exposure and disease status of all individuals. Sometimes this information is not available. Characteristics of groups may then be stud­ ied, although an inference may still be required at the level of the individual. Such studies are ecological studies2 . For example, in The Netherlands, the highest human lung cancer mortality rate between 1969 and 1984 was found in the North Brabant region. Most pet bird keepers and bird clubs are also located in this region. Moreover, people who keep birds inhale aller­ gens and dust particles, which impair the function of lung macrophages, resulting in reduced protection of the bronchial epithelium (Voisin et al., 1983). It is therefore tempting to speculate that bird-keeping is a risk factor for lung cancer, although the exposure and disease status of individuals is not known. This inference is logically defective because it is based on the erroneous assumption that group and individual characteristics are always the same; this logical error is termed the ecological fallacy (Selvin, 1958). The cor­ relation between group (i.e., ecological) variables is often considerably different from the individual cor­ relation in the same populations (Robinson, 1950); 2 Some authors use the term

spatial correlation study, when the

relationship between geographical variation in morbidity and putative explanatory variables, measured at the areal level, is assessed (Durr et ai.,

2000).

) (),)

although the lung cancer rate was highest in the region where bird-keeping was predominant, the cases may have occurred in people who did not keep birds. Ecological studies therefore should be interpreted with caution, but are useful preliminary indicators to causal hypotheses that should be tested more thoroughly. Thus, a subsequent case-control study demonstrated an association between bird-keeping and lung cancer (Holst et al., 1988), supporting a causal hypothesis at the level of the individual. Piantadosi et al. (1988) discuss the ecological fallacy in detail, and Kleinbaum et al. (1982) describe ways of strengthening causal inferences from ecological studies. Measures of association

An hypothesis of association between disease and a factor can be tested using the X 2 test (see Chapter 14). However, this test cannot be used to measure the degree of association. This is because X 2 is a function of the proportions in the various cells and of the total sample size, whereas the degree of association is only really a function of the cell proportions; the sample size has a role to play in detecting significance but not in determining the extent of association. It is also desirable to provide a more informative measure of the impact of a factor on disease occurrence. This can be expressed by the absolute difference between dis­ ease occurrence in 'exposed' and 'unexposed' groups, estimated by determining the difference between the two proportions (see 'Attributable risk', below). Alternatively, the ratio of disease occurrence between the two groups can be calculated. Ratios are relative measures, and two are widely used: the relative risk and the odds ratio. Relative risk

The relative risk, RR, is the ratio of the incidence of disease in exposed animals to the incidence in unexposed animals3. Using the notation of Table 1 5 . 1 : incidenceexposed = a/(a + b), incidenceunexposed = c!(c + d ); therefore, RR = {a/(a + b))/{c/(c + d ) ) . A R R greater than one indicates a positive statistical association between factor and disease. Thus, a RR of 3 This is more fully termed the relative risk in exposed animals, RRex

p'

to distinguish it from the less frequently derived population relative risk,

RRpop = {(a + c)/n}/Ic/(c + d)}. (See footnote p. 271.)

Observational studies

two indicates that the incidence of disease in exposed animals is twice that in unexposed animals. A RR less than one indicates a negative statistical association: possession of the factor may be said to have a pro­ tective effect against the disease. A RR of one suggests no association. The RR can be derived either from cumulative incidence, when it is also termed the risk ratio, or from incidence rates, when it is also called the rate ratio. (Some authorities use relative risk as a synonym only for risk ratio.) The RR can only be estimated directly in cohort study. a

Calculation of confidence intervals

The RR is estimated from a sample of the study popu­ lation. Therefore, the significance of the result needs to be assessed. The hypothesis that the RR is significantly greater (or less) than one can be tested (Fleiss et al., 2003). Alternatively, confidence intervals can be estim­ ated. The latter approach is adopted in this chapter because it also indicates the precision of the measure of association (see Chapter 14). However, care needs to be exercised because the relative risk statistic is not Normally distributed. An approximate 95% confidence interval for the relative risk for large samples can be calculated, based on a transformation of the limits for the natural logarithm (loge) of the RR (Katz et al., 1978). Using the data in Table 14.6 relating to PUI; first the sample (point) estimate of the RR is calculated: RR = {a/(a + b)}/{c/(c + d)} = (34/791)/(7/2434) = 14.95. The variance (var) of 10geRR is approximately equal to: {(b/a)/(a + b)} + {(d/c)/(c + d)} = {(757/34)/(34 + 757)} + {(2427/7)/(7 + 2427») = 0.028 + 0.142 = 0.170. The 95% confidence interval is:

Logarithmic-based method

RR exp(-1 .96�var ), RR exp(+1 .96 �var )

= 14.95 exp(-0.8081), 14.95 exp(0.8081 ) = 14.95 x 2.72-0.8081, 14.95 X 2.72°·8081 = 14.95 X 1/(2.72°.8081 ), 14.95 x 2.72°·8081 = 14.95 X 0.45, 14.95 x 2.24 = 6.73, 33.49. Thus, the relative risk is significantly greater than one at the 5% level, suggesting an association between spaying (the risk factor) and PUI. Note that this result is in accord with the result of the X2 test conducted in

Chapter 14, but also gives a measure of the association with defined precision. An alternative method for cal­ culating approximate confidence intervals for the relative risk utilizes the appropriate test statistic: X2 . A 95% confidence interval for the RR can be derived thus:

Test-based method

RRl ±l .96 /X.

(Note that X, not X 2, is used.) Using the data in Table 14.6: the estimated RR = 14.95. The value of X 2 has been derived on page 259, and is 73.35.t Thus X = �73.35 = 8.564, And the 95% confidence interval is: 14.951 -1 .96 / 8.564, 14.951+1.96 / 8.564 = 14.95°.771 , 14.95 1.229 = 8.05, 27.80. Compare this with the logarithmic approximation, 6.73, 33.49, which is less precise. Other confidence intervals can be constructed using appropriate multipliers (Appendix VI). Exact intervals can be computed4, and point and interval estimates based on animal-(person)-years at risk, can also be calculated (Kahn and Sempos, 1989). Such incidence rate estimations are appropriate when the period of observation of individuals varies (e.g., when animals are enlisted over a period of time and when there are many censored observations). Odds ratio

The odds ratio (relative odds), IJI (psi), is another relative measure based on 'odds': the ratio of the probability of an event occurring to the probability of it not occurring (a ratio little used outside betting circles). Thus, the probability of throwing a head with a coin is � (i.e., 0.5), whereas the odds are 'even', 1:1 t This value is computed using a continuity correction. There is debate

as to whether this should be applied, and some authors suggest that

another derivation of X2 - the Mantel-Haenszel X2 - is used in computing confidence intervals - see Sahai and Kurshid

(1995) for a discussion. For

large samples, the differences are trivial.

4 The availability of computers has fostered the development of altern­

ative methods for calculating confidence intervals for many parameters, and for computing

P values, when the exact method proves to be too

lengthy. The main methods involve bootstrap estimation (see Chap­ ter

12)

or Monte Carlo simulation (see Chapter

19). One method is not

uniformly better than the other, each having merit, depending on the problem to be solved. Consideration of these methods is beyond the scope of this text; Efron and Tibshirani

( 1 993)

and the User Manual to

StatXact (see Appendix III) should be consulted for a full discussion.

Measures of association

Table 15.4

Derivation of odds ratios in observational studies.

Cohort study

Probabil ity of d i seasecx o;ed p Probabil ity of no diseaseex pmed

= =

a/(a + b) b/(a + b)

Odds of diseaseex o;ed [a/(a + b)]/[b/(a + b)] . p ( a + b) cancels o u t from the numerator and denominator, leaving a/b. =

'

I

ratios derived in case-control and cross-sectional studies give indirect estimates of the relative risk (Cornfield, 1951). Additionally, with appropriate sampling pro­ tocols, an estimate of the relative risk can be obtained from case-control studies without the assumption of rarity of disease (Rodrigues and Kirkwood, 1990) 5 . Calculation of confidence intervals

Probabi l ity of diseaseunex o;ed c/( c + d) p Probabi l ity of no diseaseunex osed d/( c + d) p Odds of diseaseunex med [c/( c + d)]/[d/( c + d)j . p =

=

=

( c + d) cancels out from the numerator and denominator, leaving c/d.

The disease odds ratio, lfId is the ratio of the odds of diseaseex osed to ' p the odds of d iseaseunex osed: (a/b)/(c/d) ad/be. p =

Case-control study

= a/(a + c) Probabi l ity of expos ured i sea sed Probabi l i ty of no ex posured i sca sed = c/(a + c)

Odd s of exposu red i seased

=

la/(a + c)]/[c/(a + c)] .

(a + c) cancels out from numerator and denominator, leaving a/e.

Proba bil ity of exposu recontrol s Probabi l ity of no exposurecontrol s Odds of expos u recontrols

=

= =

b/(b + d) d/(b + d)

[b/(b + d)]/[d/( b + d)] .

( b + d) cancels out from the numerator and denomi nator, leaving bid. The exposure odds ratio, 0/" , is the ratio of the odds of exposuredi seased to the odds of exposurecont rol s : (a/c)/(b/d) ad/be. =

Cross-sectional study

Both lfId (based on prevalence) and lfIe can be computed (prevalence odds ratio, lfIp )'

=

ad/bc

(O.5/{l - 0.51). Similarly, the probability of throwing a specified number with a six-sided dice is i (0.167), whereas the odds are 1 :5 (O.167/{l - 0.1671). Note that the odds are larger than the probability. In a cohort study, a disease odds ratio, ljId' is estim­ ated; this is the ratio of the odds of disease in exposed individuals to the odds in those unexposed (Table 15.4). This simplifies to ad/be, the cross-product ratio, which therefore is a synonym for the odds ratio. In a case-control study, a different odds ratio, the exposure odds ratio, ljIe ' is determined. It is the ratio of the odds of exposure to the factor in cases to the odds of exposure in controls. Note, however, that this also simplifies to ad/be. A prevalence odds ratio, ljIp , is derived in a cross­ sectional study, thus: ad/be. In a cohort study, when disease is rare, the incidence of disease in exposed animals approximately equals the odds of disease because a is small relative to b; thus a/(a + b) "" a/b. Similarly, e/(e + d) "" e/d. Thus, the values of the odds ratio and relative risk are similar. More­ over, since ljIc' ljId and ljIp are equivalent (ad/be), odds

Logarithmic-based method An approximate 95% confidence interval for the odds ratio can be calculated, based on a transformation of the limits for the natural logarithm (loge) of ljI (Woolf, 1955). The method is exemplified using the data in Table 1 5.5a relating to the association between type of ventilation and respiratory disease (specifically enzootic pneumonia) in pigs. In this example, herds not individuals - are the sampling units. 'Cases' are herds with a high prevalence of pneumonia (a three­ year average >5%), whereas 'controls' are herds with a low prevalence. First, the sample estimate of ljIis calculated: lj/ = ad/be = (91 x 60)/(73 x 25) = 2.99. The variance (var) of logelj/ is approximately equal to:

(l/a + 1/b + l/e + l/d)

= 0.010 99 + 0.013 70 + 0.040 00 + 0.016 67 = 0.081 37. The 95% confidence interval is: lj/ exp(-1.96�var ), lj/ exp(+1 .96�var ) = 2.99 exp(-0.5591), 2.99 exp(O.5591) = 2.99 x 2.72-0.5591 , 2.99 X 2.72°.559 1 = 2.99 x 1 / (2.72°.5591 ), 2.99 x 2.72°.5591 = 2.99 X 0.572, 2.99 x 1.749 = 1 .71, 5.23. The odds ratio is therefore significantly greater than 1 at the 5% level, suggesting an association between

5 Strictly, case-control and cross-sectional studies produce estimates

of the 'relative risk' of

being diseased, whereas cohort studies estimate becoming diseased. The former relative risk is more the prevalence ratio (Kleinbaum et al., 1982). This can

the relative risk of properly termed

also be calculated directly in a cross-sectional study, using the same formulae as those for the point and interval estimates of the relative risk. Cross-sectional studies also allow calculation of a

population

pre­

valence ratio, which is commonly termed the population 'relative risk',

RRpop = I(a + c)/n}/{c/(c + d)}. This adjusts the standard prevalence ratio ('relative risk') for the prevalence of the factor in the population (Martin

et al., 1987). A population odds ratio, lfIpop' can also be calculated in cross­

sectional and case-control studies (if controls are representative of non-diseased animals in the study population), and is interpreted in the

pop' lfIpop = Id/(a + c)/{c(b + d)} (Martin et ai., 1987).

same way as RR

272

Observational studies

Table 1 5 .5

The relationsh ip between type of venti lation system and porci ne enzootic pneumon ia. (Data from Wi I leberg, 1 980b.)

(a) Crude relationships Cases*

(No. of herds)

91 (a) 25 (cl

73 (b) 60 (d)

Fan ventilation No fan ventilation Total *

**

Controls**

(No. of herds)

116

Total

1 64 85 2 49

1 33

Herds with a h igh prevalence of porcine enzootic pneumonia. Herds with a low prevalence of porcine enzootic pneumonia.

(b) Relationships according to herd size

Herd size �200

201-300

+

Fan ventilation No fan ventilation

2 4

301-400 +

+

7 27

15 8

401-500

30 18

13 7

>500

+

19 10

7 2

+

5 4

54 4

12

'+'

= high prevalence of porcine enzootic pneumonia (disease 'present'); '- ' = low prevalence of porcine enzootic pneumonia (d isease 'absent' ) . lJf; = 1 .93 n; = 40 w; = 0.70 v; = 0. 9 3 w 2 = 0 49 w> v; = '0 .46

lJf; = 1 . 1 3 n; = 7 1 w; = 3 .38 v; = 0.28 w 2 = 1 1 42 w> V; = 3·.20

fan ventilation and pneumonia, based on these crude data. A more precise method of estimating confidence intervals is described by Cornfield (1956), but in large studies the difference between this and Woolf ' s method is trivial. The test-based formula for an approximate 95% confidence interval is simply: Test-based method

o/l±1.96/X.

Exact confidence intervals can be calculated (Mehta 1985); the method requires an appropriate com­ puter program. An odds ratio cannot be calculated when a contin­ gency table cell contains the value zero. This problem can be overcome by the addition of 1/2 to the values in each cell of the table before calculating the odds ratio and its associated confidence interval (Fleiss et al., 2003). However, if a study involves 2 x 2 tables with cell totals of zero, or with cell totals so small that adding 1/2 will substantially affect the calculation, then its precision is likely to be too low to contribute much to knowledge. Alternatively, if a cell has a zero value, the X 2 test can be applied, or a confidence

et al.,

lJf; = 0.98 n; = 49 w; = 2 . 7 1 v; = 0. 3 7 w 2 = 7 34 w> V; = ·2.72

lJf; = 2 .80 n; = 1 8 w; = 0.56 v; = 0.45 w/ = 0. 3 1 w/ v; = 0. 1 4

rJI; = 1 . 1 3 n; = 71 w; = 0.68 v;= 1 .35 w/ = 0.46 w/ v; = 0.62

interval can be calculated for the difference between the two proportions (see Chapter 14). Attri butable risk

The terms 'attributable risk' and 'attributable propor­ tion' have been used to denote a number of different concepts, often with several inconsistently used syn­ onyms (Last, 2001). The first describes absolute differ­ ences; whereas the second expresses these differences in relative terms. Each can relate either to animals exposed to the risk factor or to the total population. Attributable risk (exposed)

Table 14.6 shows that although the incidence of urin­ ary incontinence in spayed (exposed) dogs, a/(a + b), is greater than the incidence in entire (unexposed) dogs, (cic + d ), the spayed dogs are still susceptible to a 'background' risk, corresponding to (cic + d). Put another way, if some of the spayed dogs had not been neutered, then they may still, as entire dogs, have developed urinary incontinence. The extent of the risk associated with spaying is the attributable risk (risk

Measures of association

or attributable rate) in exposed animals, (delta): the difference between the incidence of disease in exposed animals and the incidence in unexposed animals: difference

Dexp

Dexp = !a/(a + b)} - k/(c + d)}.

Thus, in this example: Dexp = (34/791) - (7/2434) = 0.043 - 0.003 = 0.040. This represents an incidence of incontinence in spayed dogs, attributable to spaying, of 4.0 per 100 during the period of observation. The attributable risk therefore indicates the extent to which the incidence of disease in exposed animals would be reduced if they had not been exposed to the risk factor, assuming that the risk factor is causal.

This attributable risk can be expressed in terms of the relative risk: Dexp = !a/(a + b)} - k/(c + d)} = [l a/(a + b)}/k/(c + d)} - 11 x k/(c + d ) } .

Since !a/(a + b)}/k/(c + d)} = RR, then Dexp = (RR - 1) x !(c/c + d)) .

Note that the incidence in unexposed animals is required to calculate Dexp' An attributable risk, based on prevalence values, can be estimated in cross-sectional studies because the prevalence in unexposed animals is known. However, this is not known in a case-control study, and so Dexp cannot be determined in this type of study, unless information from other sources is available on the baseline incidence. It is clear that ratios (a/(a + b)}/c/{(c + d)} of 0.02/0.01 and 0.0002/0.0001 give the same relative risk, even though they represent vastly different incidence ratios. The attributable risk, however, includes the baseline incidence rate, and therefore gives an indication of the magnitude of the effect of a causal factor in the popula­ tion. Thus, the attributable risk gives a better indica­ tion than the relative risk of the effect of a preventive campaign that removes the factor (MacMahon and Trichopoulos, 1996). However, the use of 'attributable' in the former term is dangerous because it implies a causal relationship, whereas the parameter is based only on statistical associations. Its practical application in reducing disease incidence therefore depends on strong evidence of a causal relationship between risk factor and disease, which may need to be determined by other means (see Chapter 3). The main advantage of the relative risk is the empirical finding that the relative risk for a particu­ lar disease/factor relationship is fairly consistent in a wide range of populations (Elwood, 1998) and, in con­ trast to the attributable risk, is therefore independent

of the background incidence. This property of con­ sistency makes the relative risk more valuable than the attributable risk in evaluating whether a relation­ ship is likely to be causal. Moreover, the relative risk, or an approximation of it, can be derived from any of the main types of study. An approximate confidence interval for Dexp can be calculated using the formula for the difference between two unrelated proportions (see Chapter 14). Rothman and Greenland (1998) give a formula based on incidence rates. (These authors also argue a dis­ tinction between attributable risk and attributable rate, depending on whether cumulative incidence or incidence rate, respectively, are used.) Population attributable risk

The

population attributable rate),

attributable

risk

(population

is the difference between the incidence of disease in the total population and the incidence of disease in the unexposed group: Dpop'

Dpop = ! (a + c)/n) - k/(c + d)} = { (a + b)/n) x Dex ' p

This gives a direct indication of the amount of disease in the total population attributable to the risk factor. Using the data in Table 14.6: Dpop

(41/3225) - (7/2434) 0.013 - 0.003 = 0.010.

=

=

Thus, the incidence of incontinence in the total popu­ lation during the period of observation, attributable to spaying, is 1 per 100, and, if bitches were not spayed, the incidence in the population could be expected to be reduced by 1 per 100. The population attributable risk can only be calcu­ lated when disease morbidity in the total population is known. Again, a population attributable 'risk', based on prevalence values, can be estimated directly in a cross-sectional study. Kahn and Sempos (1989) describe methods for calculating a confidence interval for Dpop. Attributable p ropo rtion Attributable proportion (exposed)

The attributable proportion (exposed), Aexp, (Elwood, 1998), also termed the aetiological fraction (exposed) (Last, 2001), attributable fraction (exposed) (Martin et al., 1987) and attributable risk (exposed) (Kahn and Sempos, 1989), is the proportion of incidence in

, ·1

Observational studies

exposed animals attributable to exposure to a risk factor. \xp = (RR - l )/RR. Using the data in Table 1 4.6: \xp = (14.95 - 1)/14.95, = 0.93.

That is, 93% of cases of incontinence in spayed bitches are attributable to spaying, assuming that spaying is causal. Alternatively: Aexp = (incidenceex osed - incidenceunexposed ) / p (incidenceexposed) i.e., Dexposed / (incidenceexposed) =

{a/(a + b) - c/(c + d) l!{a/(a + b)} .

It is estimated directly in a cohort study, and can be estimated indirectly in case-control studies, using the odds ratio approximation to the relative risk: Aexp = ( Ifl - 1 )/ 1fI· Population attributable proportion

The population attributable proportion, \.,op (Elwood, 1998), also termed the population aetiologlcal fraction (Schlesselman, 1982), aetiological fraction (Last, 2001), attributable fraction (Ouelett et al., 1979), poplation attributable fraction (Martin et al., 1987), attributable risk (Lilienfeld and Lilienfeld, 1980), attributable risk percent (Cole and MacMahon, 1971), and population attributable risk (Kahn and Sempos, 1989) is the pro­ portion of the incidence in the population attributable to exposure to a risk factor. Therefore, it represents the proportion of disease occurrence that would be eliminated if the group exposed to a causal factor has its incidence reduced to the level of the unexposed group. A o = { (RR - l )/RR} x i, pp

where i is the proportion of diseased individuals exposed to the causal factor, a/(a + c). Using the figures in Table 14.6: RR = 14.95

i = 34/41 = 0.829.

Thus: Apop = {(14.95 - 1 )/14.95} x 0.829 = 0.77.

Thus, if spaying is causal, 77% of cases of PUI in the population are attributable to spaying. The population attributable proportion, like the population attributable risk, therefore is an indication

of the impact that removal of a causal factor would have on overall reduction in incidence in the popula­ tion6 . In terms of causal model 1 (see Chapter 3), the sum of the population attributable proportions of all sufficient causes is 1 (100%). Other formulae for calculating Apop are: Apop = (incidencepop - incidenceunexposed)/ (incidencepop); i.e., Dpo/(incidencepop) = {(a + c)/n - c/(c + d)l/{ (a + c)/nl; Apop = {p(RR - 1 ) l/ {p(RR - 1) + I }, where p = proportion of population exposed, •

• •

(a + b)/n; Apop = Dpo/ { (a + c)/nl; Apop = (RR o - l )/Rrpop ' pp

The popUlation attributable proportion can only be calculated directly when disease morbidity in the total population is known. However, it can also be estimated indirectly in case-control studies (if controls are representative of the healthy population): A op = 1 - [{c(b + d)l!{d(a + c)ll. p value of Apop' based on prevalence values,

Again, a can be estimated directly in cross-sectional studies. The derivation of confidence intervals for \xp and Apop is described by Kahn and Sempos (1989). Forrow et al. (1992) and Bucher et al. (1994) discuss the influence of the type of parameter quoted (absolute versus relative) on clinical decisions. Interaction

Interaction was introduced in Chapter 5 as occurring between two or more factors when the frequency of disease is either in excess of or less than that expected from the combined effects of each factor. If there is a plausible biological mechanism for the interaction, then synergism is said to occur when the frequency is in excess of the anticipated value, and antagonism when the frequency is less than the anticipated value. Two models of interaction were also introduced in Chapter 5: additive and multiplicative. The choice of model depends on the measure of disease frequency. Generally, the additive model is most appropriate in indicating the impact of interaction on incidence (Kleinbaum et ai., 1982f. Therefore, an additive model will now be described (details of both types of model h For example, it has been applied to assess the impact of endemic

helminth infections on disease morbidity, and therefore the extent to which helminth control will improve community health (Booth,

1998).

7 For a discussion of the appropriateness of additive and multiplica­

tive models, see Thompson (1991).

I nteraction

Table 1 5 .6

Nu mber of cases of the fel ine urological syndrome and controls, and estimated relative risk val ues for combinations of categories with i n the factors, sex, d iet and activity. (From Wi l l eberg, 1 976.) No. of cats

Categories Sex

Entire male

Castrated male

dry cat food

Level of

Leve/ of outdoor activity

Low Low H igh H igh Low Low H igh H igh

H igh Low H igh Low H igh Low H igh Low

Total no. ofmale cats

Estimated relative risk

(RRt)

Cases

Controls

2 4 2 5

12 7 11 4 12

14 28

5 2

3 .43 (a) 4.36 (b) 6.00 (d) 5 . 00 7.20 33 .60*** 1 68.00***

58

1 2 .2**

3

5

59

** Significant at the 1 % leve l ; *** significant at the 0.1 % level, by the X2 method. t Odds ratio approximation, relative to u nexposed group = entire cats with h igh levels of outdoor activity and receiving low levels of dry cat food.

j RRm = 1 + I,(RRi - 1 )

are given by Kleinbaum et al. (1982) and Schlesselman (1982» . The model is based on additivity of excess risks. The additive model

Consider two factors, x and y. If Poo is the incidence rate when neither factor is present, PlO is the incidence rate when x alone is present, Pal is the incidence rate when y alone is present, and PII is the incidence rate when both are present, then: PIO - POD = risk attributable to x, POl - Poo = risk attributable to y. If the combined effect of x and y equals the sum of their individual effects, then: (PII - Poo) = (PIO - Poo) + (POl - POD), and there is no interaction. Lack of interaction can be expressed in terms of the excess relative risk, by dividing the formula above by POD : (PI,!POO - 1) = (PIO/POO - 1) + (Po,!Poo - 1). The relative risk when both factors are present is denoted by RR xy = PI ,!POO; the relative risks when x or y is present alone are denoted by RRx = Pl O/POO and RRy = Po,!Pow respectively. Thus: (RRxy - 1) = (RRx - 1) + (RRy - 1 ), that is: RRxlf = 1 + (RRx - 1) + (RRy - 1). If more than two factors, j say, are being considered, then the combined relative risk, RRm, for these is given by:

i= l

where RR1, , RRj denote the individual relative risks. Examples of positive interaction, based on an addi­ tive model, are given in Table 15.7, using the raw data in Table 15.6 relating to the feline urological syndrome (Willeberg, 1976). Hypothesized causal factors in males are feeding high levels of dry cat food, castration, and low levels of outdoor activity. The background risk, (RR = 1 ), there­ fore is represented by entire male cats consuming low levels of dry cat food, and with high levels of outdoor activity. Consider the two factors: low levels of outdoor activity and high levels of dry cat food intake. The estimated relative risk associated with low levels of outdoor activity and low levels of dry cat food intake in entire males is 3.43 (a in Table 15.6). The relative risk associated with high levels of dry cat food and high levels of outdoor activity is 4.36 (b in Table 15.6). Therefore, applying the additive model for these two factors (Table 1 5.7): •

RRm = 1 + (3.43 - 1) + (4.36 - 1) = 6.79

(c in Table 15.7).

The estimated combined relative risk for these two factors is 6.00 (d in Tables 15.6 and 15.7). Thus, there is no evidence for interaction between high levels of dry cat food and low levels of outdoor activity because the estimated combined relative risk (6.00) is similar to the expected combined relative risk, assuming no interaction (6.79). Similarly, there is no evidence of interaction between castration and low levels of outdoor activity. However, there is evidence

Observational studies

Table 1 5.7 Comparison of estimated and expected relative risk values of the fel i ne urological syndrome for male cats for m ultiple excess risk category combinations, based on an additive interaction model. (Adapted from Wi l l eberg, 1 976.) Categories

Sexual status

Entire Castrated Castrated Castrated

Estimated

dry cat food

Leve/ of

Leve/ of outdoor activity

H igh Low H igh H igh

Low Low H igh Low

of positive interaction between castration and high levels of dry cat food, and between castration, high levels of dry cat food and low levels of outdoor activ­ ity: in each case the estimated combined relative risk is greater than the expected combined relative risk, using the additive model. A plausible biological mechanism for the inter­ action should be posited; that is, synergism should be explained. Thus, castration and high levels of dry cat food intake (usually associated with overfeeding) may both result in inactivity, thereby reducing blood flow to the kidneys, impairing kidney function, and therefore possibly promoting changes in the urine that are conducive to the formation of uroliths; this con­ stitutes a possible common causal pathway. Estimation of confidence intervals for interaction is discussed by Hosmer and Lemeshow (1992). Bias

Observational studies are subject to bias (see Chap­ ter 9). Although many types of bias can occur in observational studies (Sackett, 1979), three are particu­ larly pertinent to observational studies: 1. 2. 3.

selection bias; misclassification; confounding.

Selection bias

Selection bias results from systematic differences between characteristics of the study population and the target population from which it was drawn. Most observational studies use data gathered from conve­ nient populations such as veterinary clinics, abattoirs and particular farms. Willeberg' s investigation of the feline urological syndrome in Denmark (Willeberg, 1977), for instance, utilized data collected at a veterin­ ary school's clinic. Ideally, a sample should be selected from the target population (all cats in Denmark in this

relative

risk

(RR)

6.00 (d) 7.20 3 3 .60 1 68.00

Expected relative risk based on additive model (RRm)

6.79 (c) 7.43 8.36 1 0.67

example), but this is rarely possible. It was stated in Chapter 13 that the inferences from investigations that might be biased by selection need to be made with care if they are to be extrapolated to the target population. Consideration should be given to the likelihood of the study population being biased with respect to the dis­ ease and factors that are being investigated. Selection bias is unlikely if: •

exposure to a factor does not increase the likeli­ hood of an animal being present in the study population; the likelihood of inclusion of cases and controls in the study population is the same.

For example, Darke et al. (1985) investigated the association between the presence of an entire tail (the hypothesized causal factor) and tail injuries (the dis­ ease) in a veterinary clinic population to determine whether docking reduces the risk of tail damage. It is improbable that docking or otherwise affects atten­ dance at a veterinary clinic and so selection bias was unlikely in this study. Misclassification

Misclassification is a type of measurement bias; it occurs when either diseased animals are classified as non-diseased, or animals without a particular disease are classified as possessing it. The likelihood of mis­ classification depends on the frequency of disease, the frequency of exposure to the hypothesized causal fac­ tor, and the sensitivity and specificity of the diagnostic criteria used in the study (Table 9.4 and Figure 9.5). For example, Thrusfield et al. (1985) studied the asso­ ciation between breed, sex and degenerative heart valve disease in dogs. Animals were classified as being diseased if they had either audible cardiac murmurs or signs of congestive cardiac failure. However, murmurs and cardiac failure can be produced by lesions other than heart valve incompetence - cardiomyopathy and anaemia are examples. Therefore, in order to prevent dogs with the latter two lesions being incorrectly

Bias

2.0

r-------,

Sensitivity of test

1 .8

.�

'"

1 .6

III

2.8 ....-----....., 2.5

--

.90 ' - ' - .70 - -- .50

o

.�

2.2

II>

't) 't) o ... c

( 1 .5 )

� 1 .4 �

Sensitivity of test

(2.67)

-- .90 - . - . . 70 - .50

1 .9

� 1 .6

III C. C.

«

« 1 .2

1 .3 1 .0

_ _ __ _ _ _

1 .0 .50 (a)

.55

.60 Specificity of test

Specificity of test

Fig. 1 5.2 (a) Cohort study: bias in the estimation of the relative risk as a function of sensitivity and specificity. Disease incidence (cumulative) in exposed and unexposed cohorts is 0.1 0 and 0.05, respectively. True relative risk (exposed and unexposed) equals 2 . 0 . ( b ) Case-control study: bias in the estimation of the odds ratio as a function of sensitivity and specificity. Exposure in cases and controls is 40% and 20%, respectively. The true odds ratio equals 2.67. (From Copeland et al., 1 977.)

classified as having heart valve incompetence (in which case they would constitute 'false positives'), their case records were scrutinized in detail to ascertain the exact nature of their murmurs. Similarly, early degenerative heart valve disease may not produce audible murmurs, and clinicians may miss the mur­ murs, in which circumstance animals would be clas­ sified incorrectly as disease-free (i.e., 'false negatives'). Two types of misclassification can occur: non­ differential and differential. The former occurs if the magnitude and direction of misclassification are sim­ ilar in the two groups that are being compared (i.e., either cases and controls, or exposed and unexposed individuals). Non-differential misclassification pro­ duces a shift in the estimated relative risk and odds ratio towards zero (Copeland et al., 1977) depicted in Figures I5.2a and I5.2b; respectively. Figure I5.2a illustrates that specificity is more important than sensitivity in determining bias in the estimate of relative risk. Even when sensitivity and specificity are seemingly acceptable (90% and 96% respectively, exemplified in Figure I5.2a), the relative risk can be severely biased. However, sensitivity plays a more important part as a source of bias in estimation of the odds ratio (Figure I5.2b). Differential misclassification occurs when the magnitude or direction of misclassification is different between the two groups that are being compared. In this case, the odds ratio and relative risk may be biased in either direction (see Copeland et al., 1977, for numerical examples). Therefore, misclassification can not only weaken an apparent association but also strengthen it.

If a simple, valid (i.e., highly specific and sensitive) test is not available, there can be difficulty in defining a case in the absence of a rigorous definition. For ex­ ample, in an investigation of the relationship between enzootic bovine leucosis (EBL) and human leukaemia (Donham et al., 1980), cattle were defined as being exposed to EBL virus when post-mortem examination revealed alimentary lymphosarcoma, even though this lesion may develop without exposure to the virus, and exposure to the virus may not produce alimentary tumours. Similarly, it may be difficult to define and quantify a hypothesized causal factor to which an animal is exposed. For example, if 'inadequate feeding' were the factor, then the investigator may have to rely on an opinion based on owners' descriptions of diet, rather than using the more rigorous results of an examination by a nutritionist. Confounding

Confounding was introduced in Chapter 3, where its effect on the inferring of causal associations was exemplified. In reiteration, a confounding variable (confounder) is any factor that is either positively or negatively correlated with both the disease and hypothesized causal factors that are being considered. For example, size of herd is a confounding variable in relation to porcine respiratory disease (see Figure 3.4b). If fan ventilation were being considered as the factor under study, then the results would be confounded (biased, confused, rendered unrepresentative) if the herds that were fan ventilated and that had respiratory

): : ;

Observational studies

disease comprised all large herds (which are likely to develop the disease), and the herds that were not fan ventilated and were non-diseased comprised all small herds (which are much less likely to develop the dis­ ease). The uneven proportion of large and small herds in each group therefore will confound the association between fan ventilation and disease, therefore distort­ ing the estimation of the odds ratio and relative risk. Confounding is particularly important in case­ control studies because animals are chosen according to presence and absence of disease: therefore cases may have a whole range of factors in common, some of which may be causal, and some of which may be statistically significant but non-causal because of an association with a confounder. Confounding is not an 'all-or-none' event, but occurs to varying degrees, and can be accompanied by interaction, from which it should be distinguished. A pictorial representation of confounding is given by Rothman (1975). Identification of confounding and interaction are discussed by Miettinen (1972), Ejigou and McHugh (1977), Breslow and Day (1980), Kleinbaum et al. (1982), Schlesselman (1982) and Rothman and Greenland (1998), and described briefly below (see The Mantel-Haenszel procedure'). These three causes of bias (selection bias, misclassi­ fication and confounding) should not be considered in isolation but as an interconnected complex that can distort results. Controlling bias Selection bias

It is often not possible to control selection bias; this results from inherent characteristics of the study popu­ lation, and a less biased study population may not be available. Control can be attempted during either the design or analysis of the investigation. The former essentially involves avoiding the bias by selecting animals from a population that will not produce the bias. This may be impractical and obviously depends on the investigator being aware of the potential bias. Control during analysis requires knowledge of the probability of selection in the study population and the target population. Kleinbaum et al. (1982) provide formulae for this correction. Misclassification

The control of non-differential and differential mis­ classification is described by Barron (1977) and Green­ land and Kleinbaum (1983), respectively. Essentially control is effected by algebraic manipulation during analysis, although this is never as satisfactory as using

a highly sensitive and specific test to determine dis­ eased and non-diseased cases. Confounding

There are two simple methods of dealing with confounding: 1 . by adjusting for the confounding variable in the analysis, for example, by using adjusted rates specific to the confounder (see Chapter 4), or by producing a summary odds ratio for the combined odds ratios of each confounder (Mantel and Haenszel, 1959); 2. by 'matching' the two groups during the design of the study. Additionally, more complex multivariate methods may be employed (see below). The control of con­ founding is discussed mainly in the context of case­ control studies in this chapter. Breslow and Day (1987) discuss control in cohort studies. The Mantel-Haenszel procedure

This technique produces a summary odds ratio, which is the weighted average of individual odds ratios derived by stratifying data with respect to potential confounders. This approach is exemplified using the data in Table 15.5. The crude estimate of the odds ratio has already been calculated (2.99). The 95% confidence interval is 1 .71, 5.23, suggesting an association between fan ventilation and pneumonia. However, herd size is also known to be associated with the prevalence of pneumonia and type of ventilation (Aalund et al., 1976). Thus, herd size could be con­ founding the association between fan ventilation and pneumonia that was identified in the crude data (Table 1 5.5a). The first step in adjusting for this potential confounding is construction of a series of sub-tables, according to herd size (Table 15.5b). The Mantel-Haenszel summary odds ratio, IflI Ilh' is given by: I h = II. /bi di· Thus, for the 'herd size =200' stratum: Wi = (7 x 4)/40 = 0.70 and V = (2 + 4)/(2 x 4) + (7 + 27)/(7 x 27) = 0.75 + 0.180 = 0.93, and so on. I(w 12v.1 ) = 0.46 + 3.20 + 2.72 + 0.14 + 0.62 = 7.14. (I w)2 1 = (0.70 + 3.38 + 2.71 + 0.56 + 0.68)2 = 8.032 = 64.48. Thus var logetjlmh = 7.14/64.48, = 0.1107. 1

Therefore: tjI exp(-1. 96 Fa-;- ), tjI exp(+1 . 96 �var ) = 1.26 exp(-0.6521), 1 .26 exp(O.6521) = 1 .26 x 0.521, 1.26 x 1 .920 = 0.66, 2.42. The adjusted odds ratio, 1 .26, is much less than the crude odds ratio, 2.99, indicating that confounding may be occurring. The calculation of a summary, adjusted odds ratio implies that it adequately describes the data; that is, that the odds ratios in the different strata are similar (homogeneous). If there are major discrepancies in the stratum-specific values, either in the same or opposite direction (i.e., some values being greater than one, and others clearly less than one), then the Mantel-Haenszel procedure should not be used. The summary statistic may disguise important real variation, suggesting that interaction is present; that is, the effect of the hypo­ thesized causal factor is modified by the potential con­ founders. This may indicate a biological mechanism for the interaction (i.e., synergism; see the example above relating to the feline urological syndrome) and so should be identified, quantified, reported and explained. Some means of distinguishing between confounding and interaction is therefore needed, and this is fulfilled by testing for homogeneity of the odds ratios across the strata. A simple method9, which

can be conducted on a pocket calculator, computes Woolf's statistic (Woolf, 1955):

±

]

[

l loge(tjI;> - lo�e(tjI) 1 2 , var l lOge(I/l) I i=l where, following the notation in Table 15.5: tjli = odds ratio in the ith stratum, tjI = summary odds ratio = tjl111 i1' var{log/tjI;> 1 vi. Thus, for the first stratum (herd size :s; 200): l loge1

]

= 0.196 + 0.042 + 0.055 + 1 .417 + 0.009 = 1 .719. Woolf 's statistic has a X 2 distribution, with k - 1 degrees of freedom, where k = the number of strata. There are five strata, and so, consulting row 4 of Appendix IX, the value of 1.719 is less than the tabu­ lated value for P = 0.05 (9.488); thus, there is insufficient evidence, at the 5% level of significancel O, that the stratum-specific odds ratios are not homogeneous, and so it is concluded that the difference between the crude and adjusted odds ratios is the result of the confound­ ing effect of herd size, rather than interaction. The sub-tables may therefore be collapsed legitimately to produce a summary adjusted odds ratio. Note that the confidence interval for the adjusted odds ratio (0.66, 2.42) includes one, indicating that there is not a significant association between fan

8 Effect modification is therefore also sometimes used to describe this interaction between factors (Miettinen,

1974).

� The method was devised in the context of the 'logit method' for estim­

ating the summary odds ratio (which is not described in this book; see Sahai and Kurshid

(1995) for details), but generally performs acceptably

with other methods of estimation. 10 Tests for homogeneity have low power, and so some authorities

advocate conservative interpretation; say, at the 10% level of significance.

l lJ ( l

Observational studies

ventilation and pneumonia when the confounding effect of herd size has been removed. A widely used alternative test for homogeneity, which is too cumbersome to compute on a pocket calculator, is the Breslow-Day test (Breslow and Day, 1980). Fortunately, it can be undertaken by some stat­ istical packages (e.g., WINEPISCOPE: Appendix III). The Breslow-Day statistic also has a X2 distribution, with k - 1 degrees of freedom. Using appropriate software, the Breslow-Day statistic has a value of 1 .02 - somewhat lower than Woolf' s statistic. Con­ sulting Appendix IX, the same conclusion is reached: P > 0.05, and the summary odds ratio may therefore be quoted. In summary, assessment of confounding therefore includes these steps: •

calculate the crude odds ratio; calculate the adjusted odds ratio; decide whether the difference between the crude and the adjusted values is 'big' (this is somewhat arbitrary); if the answer is 'yes' , then there is con­ founding and the adjusted odds ratio should be used, if there is no interaction; assess if the stratum-specific odds ratios are homogeneously distributed across the strata (e.g., using either Woolf' s statistic or the Breslow-Day statistic); if not, there is interaction, and the sub­ tables should not be collapsed.

The Mantel-Haenszel procedure is applicable to estimation of summary odds ratios for all three types of study, and there is also a modification for summary relative risk estimation in cohort studies based on animal-(person)-years at risk (Kahn and Sempos, 1989). Matching Matching is the process of making the groups that are being compared comparable with respect to a potential confounder. It can be undertaken in case-control and cohort studies, and can be per­ formed in two ways: frequency matching, in which the groups to be sampled are divided so as to contain the same proportion of the potentially confounding variable; for example, if there are four times as many males as females in the case group, then the control group also should be selected to contain four times as many males as females; this technique therefore is a form of stratification (see Chapter 13); 2. individual matching, a more precise form of matching in which each case is matched with a control with respect to the variable; for example, a 6-year-old dog with bladder cancer is paired with a 6-year-old dog without bladder cancer (match­ ing for age).

1.

Matching is useful when potential confounders are complex and difficult to measure or define (e.g., farm environments). Additionally, it can ensure compar­ ability in terms of the information that is collected. However, it is cumbersome to match for many possible confounding variables. It is usual to match for the main possible ones: age, sex and breed (i.e., common determinants: see Chapter 5). As a general rule, if the confounding variable is unevenly distributed in the population (e.g., age in relation to chronic nephritis), then it is better to match cases or controls when the study is designed, rather than correct for them in the analysis (all young control animals would, in a sense, be wasted when considering chronic nephritis). Unnecessary matching ('overmatching' ) should be avoided (Miettinen, 1970). If the effect of a factor is in doubt, then it is best not to match but to control it in subsequent analysis; when a factor is matched, it cannot be studied separately.

Matching is used to prevent confounding in cohort studies. However, in case-control studies, the main value of matching is the enhanced efficiency in con­ trolling confounding in subsequent stratified analysis (Rothman and Greenland, 1998). (Matching can in itself be a source of confounding in case-control stud­ ies, notably when the matched factor is correlated with the exposure factor but not with disease.) Matched studies should be analysed as such. The simplest matched study involves 1 :1 matching, where one matched control is chosen for each case (Table 1 5.8). Matching results in the two groups being related; thus, McNemar's change test (see Chapter 14), rather than the X2 test, can be used to assess the significance of observed differences between exposure status in cases and controls. The formula for the odds ratio uses just discordant pairs: If! = sit.

The variance (var) of logelf! is approximately equal to (1/5 + l/t), and an approximate 95% confidence inter­ val for large samples is again: If! exp(-1 .96�var ), If! exp(+ 1.96�var ) Calculation of exact intervals is described by Schlesselman (1982). The analysis of studies where the matching ratio is not 1 :1, and where further stratification is also prac­ tised during analysis, is more complex (Elwood, 1998). Table 1 5.8

of pairs.

Format for a 1 : 1 matched case-control study: n umbers

Controls exposed

Cases exposed Cases unexposed

Controls unexposed 5

u

What sample size should be selected?

What sample size should be selected?

Appropriate sample sizes can be determined for cohort and case-control studies. The principles relating to sample size determination, outlined in Chapter 14, are followed. The examples below are conservatively based on two-tailed tests.

;; g

P2 = 0.03 (because the relative risk is set at three), q2 = 0.97. From Appendix XV, Ma/ 2 = 1 .96, Mf3

= 0.84.

Therefore: Cohort studies

Four values should be specified to determine optimum sample size in a cohort study: 1. the desired level of significance ( a: the probability of a Type I error - claiming that exposure to a factor is associated with a disease when, in fact, it is not); 2. the power of the test (1 - /3: the probability of claiming correctly that exposure to a factor is associated with disease, where /3 is the probability of a Type II error); 3. the anticipated incidence of diseasell in unex­ posed animals in the target population; 4. a hypothesized relative risk that is considered important enough, from the point of view of the health of the animal population. The formula, for an unmatched study in which exposed and unexposed cohorts of equal size, and the hypothesis is conservatively two-tailed, is:

K = (1.96 + 0.84)2 = 7.84.

Thus: (0.01 x 0.99 + 0.03 x 0.97) x 7.84 (0.01 - 0.03)2 = 0.306/0.0004 = 765.

n=

------

Therefore, a total of 1530 animals is needed for the study. If a disease is rare, a cohort study requires a con­ siderable number of animals in the exposed and unexposed groups to detect a significant difference, especially when the relative risk is small. If the cohort sizes are different, a matched study is conducted, or a confounding factor is to be addressed, modifications of this formula are used (Breslow and Day, 1987; Elwood, 1998). Case-control studies

where: n = number required in each cohort; PI = anticipated incidence in unexposed animals; ql = 1 - PI ; P2 = minimum incidence to be detected in exposed animals; q2 = 1 - P2; K = (Ma/2 - Mli where Ma/ 2 and Mf3 are the respec­ tive multipliers associated with a and /3.

For example, if a relative risk of three or more is to be detected, the anticipated incidence in unexposed animals during the period of the study is one per 100, and significance level and test power are set at 0.05 and 0.80 ( /3 = 0.20), respectively, then:

Four values should be specified to determine optimum sample size in a case-control study: 1 . the desired level of significance; 2. the power of the test; 3. the proportion of controls exposed to the risk factor; 4. a hypothesized odds ratio that is considered important enough, from the point of view of the health of the animal population. The formula used to determine cohort sample sizes is used, but: PI = proportion of cases exposed to the risk factor; P2 = proportion of controls exposed to the risk factor. The value of PI is estimated from P2' given the specified odds ratio:

PI = 0.01, q l = 0.99, 11 Cumulative incidence must be specified. There is no simple method

for sample-size calculation using incidence rates (i.e., based on animal­ years at risk).

For example, if an odds ratio of four or more is to be detected, the anticipated proportion of controls exposed to the risk factor is 0.05 (5%), and significance

)

Observational studies

and test power are set at 0.05 and 0.80, respectively, (two-tailed hypothesis) first estimate PI : PI =

0.05 x 4

1 + 0.05(4 - 1 )

= 0.2/1.15 = 0.174.

Again, K = 7.84. Thus: n=

(0.174 x 0.826 + 0.05 x 0.95) x 7.84 (0.174 - 0.05)2

in case-control studies, and n = number of animals studied in each group. For example, suppose that a case-control study was conducted to investigate the association between urinary incontinence and spaying in bitches, and that only 50 dogs were studied in each group. If 40% of control dogs were spayed, then P2 = 0.40. If a twofold increase in risk in spayed bitches is to be detected, then lJI= 2, and: P2 X lJI

P1 =

-------

I + P2( lJI- 1 )

--

--

0.40 x 2 1 + 0.40(2 - 1)

= 1 .499/0.015 = 100.

Therefore, a total of 200 animals is needed for the study. If exposure to the risk factor is rare in the target population, a case-control study requires a consider­ able number of animals in the case and control groups to detect a significant difference, especially when the odds ratio is small. If the case and control group sizes are different, a matched study is conducted, or a confounder is to be addressed when the study is designed, modifications of this formula are used (Breslow and Day, 1987; Elwood, 1998). Matching criteria and stratum sizes are discussed by Greenland et al. (1981). Tables of the smallest and largest detectable relative risks and odds ratios, for different values of specified parameters, are given by Walter (1977). Sample size estimations that include cost functions are described by Pike and Casagrande (1979). Calculating the power of a study

The number of animals available for inclusion in a study may be limited (e.g., by financial constraints, availability or time). Additionally, a study may not detect a significant association between a risk factor and disease. In such circumstances, the investigation may have had insufficient power, and it may be useful to know the value of the study' s power in detecting various levels of increased risk. First, the value of Mf3 appropriate to the study is calculated. For a case-control study with groups of equal size, and a two-tailed test:

where PI ' q1 ' P2 and q2 follow the same notation as that used in the formula for calculation of sample sizes

= 0.80 / 1 .40 = 0.57.

Thus: qI

= 1 - 0.57 = 0.43;

q2 = 1 - 0.40 = 0.60;

n = 50.

If the level of significance is 0.05, Ma/2 = 1 .96, and: (0.57 - 0.40) 2 x 50 - 1 .96 (0.57 x 0.43) + (0.40 x 0.60)

-------

=

1 .455 0.481

_

1 .96

= 1 . 73 - 1 .96 = -0.23.

Appendix XV is now consulted. Note, though, that the value of Mf3 is negativeI 2 in this example, but, for brevity, the appendix only tabulates {3 for positive values of M{3" However, the appendix can still be used because the value of {3 for a negative Mf3 is one minus the value of {3 for a positiveM{3" Thus, when Mf3 is negat­ ive, using the appendix as if Mf3 is positive directly provides the power (because power = 1 - {3). The value of {3 corresponding to Mf3 = 0.23 is 0.4090, and this is therefore the power of the study. Thus, if the odds ratio in the target population were two, a study comprising 50 cases and 50 controls would only have a 41 % chance of finding that the sample estimate will be significantly ( a = 0.05) greater than one.

12 Negative values of MfJ indicate a power of less than

positive values point to a value greater than 50%.

50%, whereas

Calculating the power of a study

Association between progesti n treatment and pyometra in n u l l iparous dogs i n F inland: odds ratio (ljr) and its 95% confidence i nterval . (From N iskanen and Thrusfield, 1 998.)

Table 1 5 .9

Cases

Controls

Odds ratio tft

95% confjdence interval for tft

6 925

47 9865

1 .36

0.47, 3 .20

Progesti n treated U ntreated p= 0.457 (Fisher's two-tai led test) a = 0.05: '1'= 2 ; power = 0.41 ; l i ke l i hood = 0 . 1 9 '1'= 3; power = 0.83; l i keli hood = 0.04

x P1 ) - (N1 x P1 ) - ( M a/2 x N1 X P1 (N2 x M p = ��--�--���===�����X P1 N2 X

Consider the results of a case-control study of the relationship between progestin treatment and canine pyometra (Table 15.9). A significant association at the 5% level was not detected (P > 0.05), and the 95% confidence interval for the odds ratio there­ fore included one. Post-study power calculation (as described above) revealed that the power of the study to detect an odds ratio of two and three was 0.41 and 0.83, respectively ( a = 0.05). However, this does not incorporate the information that has been gleaned about the likely value of the odds ratio, which the sample estimate of 1 .36 reveals. It may therefore be argued that there is little value in computing the power of the study to detect an odds ratio of three when the study suggests that the value is somewhat lower. An alternative approach involves calculation of the upper confidence limit that just 'touches' the value of interest, and therefore the likelihood of the odds ratio exceeding this value. The following formula is used : loge(U/cp) za = var1/2

where:

where:

Schlesselman (1982) gives an appropriate formula for determining power when case and control groups are of unequal size. A similar calculation of power can be made for cohort studies based on cumulative incidence, with: P1 = anticipated incidence in unexposed animals; P2 = minimum incidence to be detected in exposed animals. The formula can also be applied for power calcula­ tions in clinical trials (see Chapter 16) when outcome is measured as a proportion. Elwood (1998) gives an appropriate formula for determining power when exposed and unexposed cohorts are of unequal size. If incidence rates are used in calculating the relative risk, then the power, with a two-tailed hypothesis, is calculated thus (Thrusfield et al., 1998):

RR

RR

) 1

incidence rate in the unexposed cohort; animal time at risk in the unexposed cohort; N2 = animal time at risk in the exposed cohort; RR = relative risk to be detected;

P1 = N1 =

and Ma/2 and Mp follow the usual notation. Lipsey (1990) discusses power calculations for continuous response variables. Calculati ng uppe r co nfide n ce limits

Some authors suggest that calculation of power after a study has been completed is uninformative because it does not utilize information acquired during the study (notably, an estimate of the relative risk/odds ratio, and its variance), and can be misleading (Smith and Bates, 1992; Goodman and Berlin, 1994).

A

estimate of the standardized Normal deviate; the value of the odds ratio of interest; 1jt = study estimate of the odds ratio; var = variance of the Natural logarithm of this estimate. For example, considering the data in Table 15.9: 1jt = 1 .36; var = 1/6 + 1/47 + 1/925 + 1/9865 = 0.1891. If the odds ratio of interest is two, U = 2, and: -loge(2 /---' 1 .36) za = ---'='-''-0.1891 1/2 -0.3857 0.4349 = -0.8869. za = =

U

A

;'1\ ..).

Observational studies

Appendix XV is then consulted. The negative sign is ignored 1 3, and the nearest tabulated value of za is 0.89, with a related P value of 0.1867. This corresponds to a confidence interval of {l - (2 x 0.1867)}% (because the tabulated probabilities are one-tailed); that is, a 62.66% confidence interval. Therefore, the upper 62.66% con­ fidence limit just touches an odds ratio of two. The interval is symmetric, and so the likelihood of the odds ratio being greater than two is 0 - 0.6266)/2 = 0.1867. (Note that, for negative values of z a' the likeli­ hood can therefore be read directly from the tabulated P value.) If the procedure is repeated for U = 3, the likelihood is 0.035l. Thus, although the power of the study to detect an odds ratio of two or greater is 0.41 (i.e., approaching 50%), the likelihood of the odds ratio actually being two or more is only 0.19 ('19% ' ). More strikingly, the power to detect an odds ratio of at least three is impress­ ive (0.83), but the likelihood of the odds ratio actually being that high is very low (0.04). The same formula can be applied in cohort studies, with the relative risk replacing the odds ratio. Multivariate techniques

In case-control studies, if matching is practised to adjust for confounding, there may be many 2 x 2 con­ tingency tables, for example for different combinations of age, sex, breed and management practices. The number of animals in each cell may then be small (even zero), resulting in inestimable or large confidence intervals that are statistically insignificant. Similarly, if the odds ratio varies considerably between each contingency table, calculation of a summary adjusted odds ratio is inappropriate. These problems can be overcome by using multivariate techniques, which can simultaneously consider the individual and joint effects of many factors, the number of which can be substantial (Dohoo et al., 1996). These techniques (which are essentially mathematical models) also provide 'smoothed' estimates of the effects of factors by depressing variation induced by unimportant vari­ ables. Common methods use a logistic model for dis­ crete and continuous variables and a loglinear model for discrete variables and stratified continuous data (Schiesselman, 1982). The former model is applicable to cohort and case-control studies, and is easily inter­ pretable in terms of the relative risk and odds ratio. It is, however, more complex than the analytical 13 If the value of za is positive, one minus the tabulated probability is

used: negative values yield likelihoods less than

0.5,

whereas positive

values give likelihoods greater than 0.5, but Appendix XV only tabulates

P for negative values.

methods described above, and therefore requires more intense study. In practice, appropriate computer programs are usually needed to 'fit' the model to data. It is presented formally below, with an example. Detailed descriptions of model building, including identification of interaction and confounding, are given in texts cited at the end of this chapter. The logisti c mode l

The logistic model derives its name from its use of nat­ ural logarithms (loge)' It is based on a mathematical function that can be used to describe several biological phenomena including growth curves (see Figure 7.4) and dose-response relationships in biological assays. It may be thought that a linear regression model (see Chapter 8) can represent the relationship between the probability of disease and the presence or absence of one or more risk factors, either alone or in combina­ tion. However, such a model may predict values that are outside the permitted range of 0 to 1 . Also, when fitting a linear regression model, the variance of the response variable is assumed to be a constant, inde­ pendent of the values of the explanatory variables. This is not the case with a binary response variable presence or absence of disease in this context - where the variance is proportional to PO - P), where P is the true, but unknown, probability of disease. These problems are overcome by using a logistic transformationl4. Let P be the probability of disease occurrence (0 < P < 1). The logistic transformation of P is defined to be loge/P/O - P)), where P/O - P) is the odds of developing disease. Define the transformed variable to be y, say, so that y = loge/P/O - P)}. This transformation can take values ranging from 'minus infinity' when P = 0, to 'plus infinity' when P = 1 (i.e., it is unrestricted). Linear regression techniques may then be applied to this transformed variable. The function loge/P/O - P)} is known as the logit of P. Once a value of y has been predicted, the corresponding values for P = exp(y)/{l + exp(y)}. (Note that this takes values in the range 0 to 1 .) Now consider the simple 2 x 2 contingency table (Table 15.1). Suppose, in a cohort study, that a propor­ tion, p, of animals was exposed at the beginning of the study. Denote by Po the probability of an exposed animal developing disease, and by PI the correspond­ ing probability for an unexposed animal. Let Qo and Q1 be 1 - Po and 1 - PI ' respectively; and q = 1 - p. The expected proportions of animals falling into each of

14 Other transformations that have been suggested are the probit

transformation (Finney,

formation (Collett, 2003).

1971)

and the complementary log-log trans­

Multivariate

Table 1 5. 1 0

The expected proportions of animals fal l i ng i nto each of the four cells of the 2 x 2 contingency table constructed i n observational studies, given t h e probabil ities Po ( PI ) o f exposed (unexposed) animals developing disease, and the proportion, p, of animals exposed at the beginning of the study.

Animals exposed to the risk factor Animals not exposed to the risk factor Total

Total

Table 1 5. 1 1

Microorgan isms i ncriminated in kennel cough. (Modified from Thrusfield, 1 992.) Major microorganisms

Minor microorganisms

Bordetella bronchiseptica

Bacillus spp. Canine adenovi ruses Type 1 (CAV-1 ) Type 2 (CAV-2) Canine d i stemper virus (CDV)

Can ine parainfluenza virus (CPIV)

Diseased

Non-diseased

animals

animals

p Po

pQo

p

Corynebacterium pyogenes

qP1

q Ql

q

p Po + q P1

pQO + q Ql

Mycoplasma spp. Pasteurella spp. Staphylococcus spp. Streptococcus spp.

the four cells of the contingency table are given in Table 15.10.

The odds ratio lff = (PI X Qo)/(Po x QI )' The logarithm of the odds ratio, f3, may be expressed as: f3 = logelff = 10git(Po) - logit(PI ), the difference between the two logits. This formulation is in the context of cohort studies; however, the same model can be applied to case­ control studies, in which the interpretation of the parameters f3; is essentially the same.

('exposed'), and 'I' indicating its presence ('unexposed'). This type of variable is called a 'dummy' or 'indicator' variable because it has no numerical significance. The derivation of the logistic regression model in this context is eased by the use of slightly different notation. Thus, let P(x) be the probability of a dog developing kennel cough if its vaccinal status is x. Then: P(1 ) = PI , P(O) = Po ' Write: P(x)Qo r(x) = . Po Q(x) Then loger(x) = 10ge{P(x)/Q(x)} - loge(PoIQo) and 10git{P(x)} = 10git(Po) + loge{r(x)}. Let a = 10git(Po)' Then 10git{P(x)} = a+ loge{r(x) }. When x = 0, 10git{P(x) } = 10git{P(O) } = a, by definition. Thus, loge{r(O)} = O. Let f3 = 10ge {r(1 ) } . Then 10git{P(x)} may b e written in the linear form a + f3x, where x is a dummy variable taking the values o (exposed) and 1 (unexposed). Thus: 10git{P(x) } = a + f3x, and a simple linear logistic model has been derived. There is one explanatory variable, which takes the values 0 (exposed; i.e., unvaccinated) or 1 (unexposed; i.e., vaccinated). --

An example of expansion of the logistic regression model: a case-control study of vaccinal efficacy against canine infectious tracheobronchitis (kennel cough)

Canine kennel cough is a multifactorial disease in which several infectious agents have been incrimin­ ated (Table 15.1 1). Vaccines are available for protection against Bordetella bronchiseptica, CPIV, CAY-I, CAV-2 and COY. However, isolation of specific causal agents is rarely justified and frequently impractical in the field, and so direct assessment of the efficacy of the individual vaccines is impossible. However, an indir­ ect assessment can be made by comparing the prob­ ability of disease in dogs vaccinated with various combinations of vaccine with the probability in un­ vaccinated dogs. Thus, several explanatory variables (the vaccines) are being considered simultaneously. A suitable approach would be to conduct a case­ control study of cases using data collected, by questionnaire, from general practices (Thrusfield et al., 1989a). In this instance, the unvaccinated state con­ stitutes a risk factor for developing kennel cough, and vaccinal efficacy therefore is defined in relation to a reduction in estimated relative risk, (approximated by \fie because this is a case-control study1 5 ). Vaccinal status, x, is a dichotomous variable which needs to be coded '0' indicating absence of vaccination

1 5 For a discussion of transformation of odds ratios to relative risks in

logistic regression, see Beaudeau and Fourichon

(1998); and, for calcula­ (1985).

tion of the population attributable proportion, see Bruzzi et al.

in!..

Observational studies

The two parameters, a and {3, in the model and the two risks correspond perfectly such that: PI = P(1) = exp(a+ {3 )/1II+ exp( a+ f3)); and: Po = exp( a)/II+ exp(a» ) . In this example, {3 will b e less than zero. A negat­ ive value of {3 indicates that dogs that have not been vaccinated have a higher risk of developing kennel cough than those that have been vaccinated. This formulation extends naturally to the situation where there are two vaccines. Define the dichotomous 'dummy' variable xi to be 1 or ° according to a dog's vaccinal status against vaccine i, where i may take the value 1 or 2, corresponding to the two possible vaccines. Thus, Xl = 1 indicates that the dog was vac­ cinated with vaccine 1; Xl = ° indicates that the dog was not vaccinated with vaccine 1; x2 = 1 indicates that the dog was vaccinated with vaccine 2; x2 = ° indicates that the dog was not vaccinated with vaccine 2; (xI X2) ' indicates the dog's vaccinal status with vaccines 1 and 2. Define P(xjlx2) as the disease probability corre­ sponding to vaccinal status (XI ,X2), and r (xl ,x2) as the odds ratio of P(XI ,X2) relative to the exposed (unvaccin­ ated) category X l = x2 = 0. (This represents the inverse of the usual ratio in observational studies, where the relative risk and odds ratio are relative to the unexposed category because exposure is usually in terms of presence, rather than absence, of a factor. Recall that exposure is defined as absence of vaccination. ) These odds ratios and, equivalently, the probabilities, may be expressed using the model: loge {r (xl ,x2» ) = ({3IXI )+ ({32X2)+ (yx1X2), or: logit{P(x1 , x2» ) = a+ ({31X1 ) + ({32X2) + (yx1X2) . (Equation 1 ) In this example, there are four parameters, a, {31 {32 ' and y, to describe four probabilities, P(O,O), P(O,l), P(1,O) and P(1,I) (summarized as P(X1,X2» , and there­ fore the model is termed 'saturated' The model makes no assumptions about the association between disease status and exposure status. The log odds ratios for the individual exposures are given by: {31 = loge{ r(1,O» ) ; {32 = 10ge{ r (O,1 » ); y = 10gJ { r( 1 ,I»)/{r(1,0) x r (O,l » ) ] = 10git{P(1,I») - logit{P(1,O») - logit{ P(O,I» ) + 10git{P(O,0) ) . The parameter, y, i s a n interaction parameter, and the function, exp( y), of Y is an indication of any statistical interaction between factors. In this model,

interaction is multiplicative and represents the multi­ plicative factor by which the odds ratio for those animals vaccinated with both vaccines differs from the product of the odds ratios for those receiving only one of the individual vaccines. If y > 0, there is 'positive' interaction and the reduction in risk of developing kennel cough for dogs that have received both vac­ cines is not as great as that predicted by simply multi­ plying the effects, as measured by the corresponding odds ratios, of giving each vaccine separately (and the converse if y < 0). If y = ° (no interaction), then the reduction in the risk of developing kennel cough for dogs that have received both vaccines is that predicted simply by multiplying the effects of giving each vaccine separately. It is possible to test the hypothesis that y = ° for a given data set and, if this hypothesis is not rejected, to fit the reduced model, which excludes the interaction parameter: (Equation 2) In this circumstance, {31 now represents the loge lI' for vaccine 1 relative to not receiving vaccine 1, whether or not the dog has been vaccinated with vaccine 2. This is a different interpretation than that from the saturated model (Equation 1 ) . In the saturated model, {31 repres­ ents the loge lI'for vaccine 1 at level ° (not vaccinated) of vaccine 2 whereas, in the reduced model, {31 represents the logell' for vaccine 1 independent of the level of vaccine 2. Testing the hypothesis {31 = ° in the reduced model is equivalent to testing the hypothesis that vaccine 1 has no effect on risk, against the alternative hypothesis that there is an effect, but one that does not depend on vaccine 2. This approach can be easily generalized to incor­ porate the effects of more than two vaccines. Thus, for five vaccines, the extension to the reduced model (Equation 2) is given by: logit{P(Xl ,X2,X3,x4 xS» ) = a+ ({31XI )+ ({32X2)+ ({33X3) ' + ({3 X4)+ ({3sxs )· 4 If a better fit is provided by a model that includes some interaction terms, it is important to assess the significance of the interaction. The results of the case-control study are presented in Table 15.12. The background risk <equivalent to a = logit(Po» is represented by dogs vaccinated against CDV because all dogs in the study were vaccinated against this virus. Efficacy of CDV vaccine therefore was not considered. The model was fitted to these data using an appro­ priate statistical package (GUM: Generalised Linear Interactive Modelling: see Appendix III), the best fit being provided by one that included some interaction terms. The estimated values of the parameters for various vaccine combinations in the model, and their

Multivariate techniques Table 1 5. 1 2

Estimates and their associated standard errors of the log

odds ratio* in favour of a kennel cough case for each of five vacci nes and thei r assoc iated i nteractions relative to vaccination only with can i ne d i stemper virus vacc i ne. ( F rom Thrusfield et al., 1 989a.) Vaccine

Estimated

Standard

Jog odds

error of

ratio (Iogel{!)

logel{!

B. branchiseptica

-0.3

CPIV

-2 .0

0.53

CAV-l ( i nactivated)

-0.7

0.21

CAV-l ('l ive')

-2.8

0.84

CAV-2

-0.2

0.26

1 .3

0.42

B. branchiseptica + CPIV

0.48

B. branchiseptica + CAV-l 0.8

0.55

-2 . 2

0.78

CPIV + CAV-l (i nactivated)

2 .7

0.69

CPIV + CAV-l ('I ive')

3.8

0.99

-1 .5

0.56

1 .1

0 . 57

(i nactivated) B. branchiseptica + CAV-l ( ' l i ve')

B. bronchiseptica + CAC-2 CPIV + CAV-2 *

A red uction is i ndi cated by a negative value, and an increase by a

positive value.

Table 15. 1 3 The relationsh i p between 'dum my' variables and vaccinal status. (From Thrusfield et al., 1 989a.) 'Dummy'

Value of 'dummy'

variable

variable

Xl x2 Xl

1 0

Vaccinal status

B. bronchiseptica given B. branchiseptica not given CPIV given

CPIV not given

1

CAV-l (i nactivated) given

CAV-l (i nactivated) not given

CAV-l ('l ive') not given

CAV-l ('l ive') given

x4 x,

CAV-2 given 0

CAV-2 not given

associated standard errors, are given in The model that was fitted is thus:

Table 15.12.

logit{P(x1,x2,xyx4'xs) ) - 2.0x2 - 0.7x3 - 2.8x4 - 0.2xs + 1 .3x1x2 - 0.8x1X3 - 2.2x 1 X4 + 2.7x2X3 + 3.8X2X4 - 1 . Sx l xS + 1 . 1 x2xs'

= -0.3X 1

where Xl ' . . . , Xs are defined in Table 15.13. The model may be used to predict the effect of various vaccine combinations. For example, the loge IfI for a dog vaccinated against CDV, B . bronchiseptica and CAV-2 (for which Xl 1, x2 X3 x4 = 0, Xs = 1 ) i s calculated from the results in Table 15.12 thus: - 0.3 - 0.2 - 1 .5 = -2.0. This computation includes the main effects of the individual vaccines (the first two numbers) and the interaction (the third number). Table 15.14 presents the results for the usual com­ binations of vaccines. Interactions are present, for example that between B. bronchiseptica and CPIV vac­ cines. This could be explained biologically by the poten­ tiating effect of prior inapparent infection with B. bronchiseptica o n CPIV infection (Wagener et al., 1 984). This could result in more CPIV infections being manifest clinically in dogs with both infections, and would therefore explain why B . bordetella vaccine could have a protective effect against CPIV-induced kennel cough. Equally, however, it could simply have resulted from combined vaccination with these two vaccines occurring in dogs that had an increased risk of infection (e.g., in dogs that were vaccinated electively against these two major microorganisms because they were being kennelled), in which cir­ cumstance the interaction is interpreted predictively. The log odds ratio can be converted to the odds ratio by taking the antiloge. Thus, for the combination of CDV, CAV-l ('live') and B. bronchiseptica vaccines, the loge IfI is -S.3, and antiloge -S.3 O.OOS. The associated standard error of the loge IfI is 1 .04. An approximate 9S% confidence interval for logelflcan be constructed using the Normal approximation: =

=

=

=

Table 1 5.1 4 Estimates and their assoc iated standard errors of the log odds ratio* in favou r of a kennel cough case for common com binations of vaccine, relative to vaccination with canine distemper vi rus vaccine only. (From Thrusfield et al., 1 989a.) Vaccine combination

Standard error of loge 'I'

CDV + CAV-l (inactivated) + B. branchiseptica

-1 .8

0.33

CDV + CAV-l (inactivated) + CPIV

- 0. 1

0.50

0.1

0.61

CDV + CAV-l (i nactivated) + B. branchiseptica + CPIV

*

Estimated log odds ratio (loge '1')

CDV + CAV-l ('l i ve') + B. branchiseptica

-5.3

1 .04

CDV+ CAV-l ('live') + CPIV

-1.0

0 . 27

CDV + CAV-l (' l ive') + B. bronchiseptica + CPIV

-2 . 3

0.45

CDV + CAV-2 + B. branchiseptica

-2.0

0.32

CDV + CAV-2 + CPIV

-1.2

0.24

CDV + CAV-2 + B. branchiseptica + CPIV

-1 .7

0.85

A reduction is i n d icated by a negative value, and an increase by a positive value.

21W

Observational studies -5.3± 0.96 X 1.04) =-5.3±2.04 = -7.34, -3.26.

Thus, the 95% confidence interval for the odds ratio = e-7.43, e-3.26, = 0.00065, 0.038. This interval clearly excludes one and so the reduction in risk of kennel cough associated with this combination of vaccines is statistically significant at the 5% level. This multi­ variate model can therefore be used to identify which combinations of vaccines predict the greatest reduc­ tions in the risk of kennel cough in the field. Comprehensive discussions of the application of these methods to observational studies are presented by Breslow and Day 0980, 1 987), Kleinbaum et al. ( 982) , Schlesselman (982) and Hosmer and Lemeshow (2000). Some examples of observational studies, which include both simple and multivariate analyses, are listed in Appendix XXII.

F u rther Read i ng Breslow, N.E. and Day, N.E. (1980) Statistical Methods in Cancer Research, VoU: The Analysis of Case-Control Studies.

IARC Scientific Publications No. 32. International Agency on Cancer Research, Lyon Breslow, N.E. and Day, N.E. (1987) Statistical Methods in Cancer Research, Vol.2: The Design and Analysis of Cohort Studies. IARC Scientific Publications No. 82. International

Agency on Cancer Research, Lyon Collett, D. (2003) Modelling Binary Data, 2nd edn. Chapman and Hall, London (Describes the application of the logistic model to observational studies)

Elwood, J.M. (1998) Critical Appraisal of Epidemiological Studies and Clinical Trials, 2nd edn. Oxford University Press, Oxford Fleiss, J.L., Levin, B. and Paik, M.C. (2003) Statistical Methods for Rates and Proportions, 3rd edn. John Wiley, Hoboken Frankena, I. and Graat, E.A.M. (2001) Multivariate ana­ lysis: logistiC regression. In: Application of Quantitative Methods in Veterinary Epidemiology, revised reprint. Eds Noordhuizen, J.P.T.M., Frankena, K., Thrusfield, M.V. and Graat, E.AM., pp. 131-161. Wageningen Pers, Wageningen. (A concise introduction to the logistic model) Green, MD., Freedman, D.M. and Gordis, L. (2000) Reference guide on epidemiology. In: Reference Manual on Scientific Evidence, 2nd edn, pp. 333-400. Federal Judicial Center, Washington. (A general guide to analytical methods, with emphasis on interpretation)

Hosmer, D.W. and Lemeshow, S. (2000) Applied Logistic Regression, 2nd edn. John Wiley, New York Kelsey, J.L., Whittemore, AS., Evans, AS. and Thompson, W.D. (1996) Methods in Observational Epidemiology, 2nd edn. Oxford University Press, New York and Oxford Kleinbaum, D.G., Kupper, L.L. and Morgenstern, H. (1982) Epidemiologic Research. Principles and Quantitative Measures.

Lifetime Learning Publications, Belmont Newman, S.c. (2001) Biostatistical Methods in Epidemiology. John Wiley, New York Rothman, K.J. and Greenland, S. (Eds) (1998) Modern Epidemiology, 2nd edn. Lippincott-Raven, Philadelphia Sahai, H. and Kurshid, A (1995) Statistics in Epidemiology: Methods, Techniques, and Applications. CRC Press, Boca Raton. (A comprehensive discussion of the variety of methods for deriving parameters in observational studies) J.J. (1982) Case-Control Studies: Design, Conduct, Analysis. Oxford University Press, New York and

Schlesselman, Oxford

Clinical trials

The effects of some treatments are so marked that they are obvious; for instance, the intravenous administra­ tion of calcium to cases of acute bovine hypocalcaemia. However, this is not true for many prophylactic and therapeutic procedures, where, for example, the advantages of a new drug over an established one may be small. Moreover, the observations of individual veterinarians provide insufficient evidence for deter­ mining efficacy1 . In the past, treatment was often based on beliefs that had never been scientifically assessed; and anecdotal or unattested cures entered the veterinary and medical literature. Indeed, it has been estimated that only about 20% of human medical procedures have been evaluated properly (Konner, 1993), and many veterinary procedures have also been poorly evaluated (Shott, 1985; Smith, 1988; Bording, 1990; 2 Elbers and Schukken, 1995) . Conclusive evidence of efficacy is provided by a clinical trial. Clinical trials date back to the 1 8th century, when they provided clues to the cause of disease3 . The provi­ sion of citrus fruits to English sailors prevented scurvy, 1 A distinction is sometimes made between effectiveness and efficacy (Last, 2001). The former is the extent to which a procedure does what it is intended to do when applied in the day-to-day routine of medical or veterinary practice. The latter is the ex tent to which a procedure produces beneficial results under ideal conditions. A procedure may be efficacious but relatively ineffective if it is not taken up widely (e.g., if the owner's compliance with the advice of the veterinarian is low). 2 See Wynne (1998) and Verdier et al. (2003) for a discussion of assess­ ment of veterinary homeopathic remedies. 3 The principle of making medical inferences from comparisons is much older. The earliest recorded ex ample is probably the study of the diet of captive Jewish children in Babylon in the 6th century Be (docu­ mented in the Old Testament: Daniel 1: 3-16). Nebuchadnezzar, the Chaldaean ruler of Babylon, instructed Ashpenaz, his chief eunuch, to take some of the captive children into his court. They were offered the king's meat but refused it, eating vegetables instead. After ten days 'they

looked healthier and were better nourished than all the young men who had lived on the food assigned them by the king'.

indicating that the cause (subsequently shown to be vitamin C deficiency) was nutritional (Lind, 1 753). Similarly, at the beginning of the 20th century, improve­ ment in the diet of inmates of some American orphan­ ages and asylums cured and prevented pellagra, and suggested a nutritional cause of the disease, which hitherto had been considered to be infectious (Goldberger et ai. , 1923).

Definition of a clinical trial A clinical trial is a systematic study in the species, or in particular categories of the species, for which a procedure is intended (the target species) in order to establish the procedure's prophylactic or therapeutic effects. In veterinary medicine, effects may include improvements in production as well as amelioration of clinical disease. The procedure may be a surgical technique, modification of management (e.g., diet), or prophylactic or therapeutic administration of a drug. If the latter is being assessed, a clinical trial would also include studies of its pattern of absorption, metabolism, distribution within the body and excre­ tion of active substances. With these aims in mind, the assessment of drugs can be classified chronologically into four categories, according to the purpose of the assessment (Friedman et ai., 1996): 1.

2.

pharmacological and toxicity trials, usually con­ ducted on either the target species or laboratory animals to study the safety of a drug; initial trials of therapeutic effect and safety, usually conducted on the target species on a small scale in a controlled environment (e.g., on research establishments), and often with the object

""!(!

3.

4.

Clinical trials of selecting the potentially most attractive drugs from those that are available; clinical evaluation of efficacy, undertaken on a larger scale in the field, that is, under operational conditions, where management and environment can affect the result of the trial; post-authorization surveillance of a drug after it has been licensed, to monitor adverse drug reactions.

This chapter focusses on the third category of trial: assessment of efficacy in the field, in which circum­ stance the term field trial is commonly used. Hitherto, some authors have distinguished between a field trial and a clinical trial on the grounds that the former possesses two characteristics: 1. 2.

it i s conducted under operational conditions; it is frequently prophylactic, and therefore relies on natural challenge to the treatment that is being assessed (e.g., assessment of the efficacy of a bacterial pneumonia vaccine would rely on vaccin­ ated animals being naturally exposed to infection with the relevant bacterium during the period of the trial).

However, these characteristics only represent related circumstances under which clinical trials may be conducted (2 is a logical consequence of 1 ), and so a distinction between clinical and field trials is not considered necessary on these grounds. Some authors (e.g., Rothman and Greenland, 1998) draw the distinction more forcibly on the grounds that a clinical trial is undertaken on patients that are ill, and is therefore always therapeutic (this may include pre­ vention of sequelae, though; see Chapter 22: Secondary and tertiary prevention); whereas a field trial is invari­ ably conducted on clinically healthy individuals to determine prophylactic effect (primary prevention). Such a strong distinction is also not made in this chapter, where in addition, for brevity, all types of procedure are described as 'treatment' .

Randomized controlled clinical trials

The clinical condition of sick animals can be compared before and after treatment. This is sometimes termed an open trial (Toma et al., 1999). However, interpreta­ tion of such an uncontrolled trial may be difficult because any observed changes could result either from the treatment or from natural progression of the dis­ ease. An essential feature of a well designed clinical trial therefore is a comparison of a group receiving the treatment with a control group not receiving it; this is a controlled clinical trial. The control group may be selected at the same time as the group receiving the treatment (a concurrent

control group) or generated using historical data (a historical control group) . Early clinical trials, such as Lister' s assessment of antiseptic surgery (Lister, 1 870), utilized historical controls, but this approach is open to criticism because of the various factors, unrelated to treatment, that can produce observed differences over a period of time (e.g., improvements in husbandry, changes in diagnostic criteria, disease classification and selection of animals, alterations in virulence of infectious agents, and reduction in the severity of dis­ ease). The net result of these problems is that studies with historical controls tend to exaggerate the value of a new treatment (Pocock, 1983). Concurrent control groups are therefore usually advocated4• The control group may receive another (standard) treatment with which the first treatment under trial is being compared (a 'positive' control group), no treat­ ment (sometimes called a 'negative' control group), or a placebo (an inert substance that is visually similar to the treatment under trial, and therefore cannot be dis­ tinguished from the treatment by those administering and those receiving the treatment and placebo)5. Bias (see Chapter 9) can occur in a trial if there is preferential assignment of subjects to treatment or con­ trol groups, differential management of the groups, or differential assessment of the groups. For example, a veterinarian may allocate animals only with a good prognosis to the treatment group. A central tenet of a controlled clinical trial is that subjects are assigned to treatment and control groups randomly (see Chapter 1 3) so that the likelihood of bias due to preferential allocation is reduced. This process of randomization should also balance the distribution of other variables that may be outcome-related (e.g., age), and guar­ antees the validity of the statistical tests used in the analysis of the trial (Altman, 1991b). Randomized controlled clinical trials therefore adopt the experimental approach (see Chapter 2) and closely resemble cohort studies (see Chapter 15)6.

4 A notable early ex ample of the use of concurrent controls was Pasteur's trial of an anthrax vaccine in sheep (Descour, 1922). 5 The first placebo-controlled clinical trial was probably undertaken by the English physician, John Haygarth, at the end of the 1 8th century (Haygarth, 1800). At that time, a popular treatment for many diseases was the application of metal rods, called 'Perkins' tractors', to the body to relieve symptoms by the supposed electromagnetic influence of the metal. Haygarth made wooden imitation tractors, and found that they were as efficacious as the metal ones. In so doing, he demonstrated the 'placebo effect': the expectation that a treatment will have an effect is sufficient to produce an improvement. A placebo was originally a sub­ stance with no known therapeutic effect which was administered in the hope that the power of suggestion, alone, would alleviate symptoms (Latin: placebo = I shall be pleasing). 6 In the UK, randomized controlled trials were introduced in the mid-1940s by Bradford Hill: the first to test the efficacy of pertussis vaccine, and the second to test the efficacy of streptomycin in the treat­ ment of pulmonary tuberculosis (Doll, 1992).

Design, conduct and analysis Confirmatory and exploratory trials

Trials are also classified as confirmatory or explorat­ ory (EAEMP, 2001). The former include randomized controlled clinical trials and controlled trials to deter­ mine appropriate dosage levels of drugs, both of which require strict protocols (discussed later in this chapter). These are often preceded by exploratory trials, the initial nature of which allows a less stringent protocol, which may be modified as analyses are undertaken; however, exploratory trials cannot be the sole basis of proof of efficacy. A trial that has both exploratory and confirmatory aspects is a composite trial.

to which an active substance reaches the tissues, and its tissue concentration) relative to a reference substance. This is the basis for concluding that preparations are therapeutically equivalent. Equivalence trials that assess if the effects of two treatments are the same may be more specifically termed 'full equivalence trials'. A special case of an equivalence trial is the non­ inferiority trial, in which the goal is to demonstrate that a therapy is no worse than an established one. This is common in initial trials of therapeutic effect, where it is often desirable to demonstrate that a new drug is no less effective than (i.e., is non-inferior to) an established preparation, although it could also be equivalent or better.

Community trials

A community trial is a trial in which the experimental unit (see below) is an entire community. Community trials have been undertaken in human medicine; for example, the fluoridation of the public water supply to prevent dental caries (Lennon, 2003)? Multicentre trials

Pharmacological and toxicity trials, initial trials of therapeutic effect and safety, and exploratory trials are usually conducted either in a single laboratory or at a single field site. Confirmatory field trials, however, are often conducted at several sites, following a standard protocol. Such multicentre trials are conducted for two reasons: they may be the only means o f accruing sufficient animals within a reasonable period of time; they allow a widely representative cross-section of the population of animals to be exposed to the therapy, increasing the validity of the trial (see below: The experimental population).

l.

2.

Superiority, equivalence, and non-inferiority trials

Superiority trials are designed to detect a difference between a treated and a control group. Efficacy is established most convincingly in such trials. Some­ times, however, two treatments are compared without the goal of demonstrating superiority (e.g., comparing an inexpensive new drug with an established costly drug, with the objective of replacing the latter by the former). This may involve demonstrating that the effects of each treatment are the same (equivalence trials). A particular category of equivalence study is the bioequivalence study. This assesses the phar­ macological kinetics of a new substance (e.g., the extent 7

The application of a therapy to a whole community without its con­ sent does, of course, raise ethical issues (Cross, 2003).

Design, conduct and analysis

The trial protocol The goal and design of a clinical trial should be documented in a trial protocol. This is required by regulatory organizations, which assess the value and validity of the proposed trial, and also provides back­ ground information to veterinarians and owners who are asked to participate in the trial. The main com­ ponents of a protocol are listed in Table 16.1 8•

The pri mary hypothesis The first step in writing a protocol for a clinical trial is determination of its major objective, so that a primary hypothesis can be formulated. Thus, a primary hypo­ thesis could be 'evening primrose oil has a beneficial effect against canine atopy' (Scarff and Lloyd, 1992). Several principal criteria of response might be assessed, but it is helpful if one particular response variable can be identified as the main criterion for testing the primary hypothesis; this is the primary end point. The following topics must be addressed in determining this end point: •

which end points are the most clinically and economically important? which of these can be measured in a reasonable manner? what practical constraints (e.g., budgetary limits) exist?

Thus, the primary end point in the evening primrose oil trial might be the level of pruritus. Other end points

8 A similar protocol is the basis of the standard for reporting veter­ inary (Begg et al., 1 996) and medical (Altman, 1 996) clinical trials in scientific journals.

2'l2

Clinical trials

Table 1 6.1 Components of a protocol for a c l i n ical trial. (Modified from Noord h u izen et al., 1 99 3 . ) General information Title of trial Names and addresses of i nvestigators Name and address of sponsor(s) Identity of tria l site(s) j ustification and objectives Reason for execution of the trial Pri mary hypothesis to be tested; Primary end point Secondary hypotheses to be tested Desig n Response variables: Nature of response variables (level of measurement) Scoring system (for o rd i n a l va riables) Definition of efficacy (magnitude of the d i fference to be detected between treatment and control groups) Du ratio n : Date o f beg i n n i n g Date of end D u ration of d i sease under study Period for recruitment of cases Duration of treatment Drug withdrawal period (for food-prod ucing a n i mals) Decision rules for term i nating a trial Experimental population:* The experimental u n it Composition (e.g., age, sex, breed) I n c l u s ion/excl u sion criteria Post-ad m i ssion withdrawal criteria Defi n ition of cases/d iagnostic criteria Case identification Selection of controls Sample size determ i nation Owners' i n formed consent Therapeutic or prophylactic proced u re : Dosage Product formu lation and identification Pl acebo/standard treatment form u l ation and identification Method of admin istration Operators' safety Defi n ition of stage at which ad m i n i stration stops B l i nd i ng tech n i q u e Compli ance mon itoring Type of trial : Randomization Stratification variables I m p lementation of a l l ocation process Data collection: Data to be col lected Frequency of data collection Method for record i ng adverse drug reactions Identification of experimental u n its Tra i n i ng/standardization of data col lection and record ing Confidential ity Commun ication between participants Data analysis: Tec h n i q ue for ' u n b l i nd i ng' Description of statistical methods Interpretation of significance levels/confidence i ntervals Approach to withdrawals and a n i m a l s 'lost to follow up' * Some authorities refer to the experimental pop u l ation as the study pop u l ation. The latter term i s not used, to avoid confusion with study population defined as the population from which a sample of a n i m a l s i s drawn (see Chapter 1 3) .

could include the levels o f oedema and erythema; these constitute secondary end points. The response variables that are used to measure the end points (the primary and secondary end point vari­ ables) should adequately represent the effect that is being studied in the trial, and therefore address the primary hypothesis (construct validity and content validity: see Chapter 9). Thus, there is a relation­ ship between plasma essential fatty acid levels and the inflammatory response (Horrobin, 1 990), and so changes in plasma phospholipid levels could be mon­ itored, but these are less clinically relevant than the actual clinical signs which may, therefore, be more appropriate response variables for ensuring construct validity. However, clinical signs are often measured subjectively on an ordinal or visual analogue scale (see Chapter 9), whereas fatty acid levels can be mea­ sured on the ratio scale. Thus, a compromise between strength of measurement and relevance (construct validity) may be necessary. If complex or subjective measures are used, their reliability should be assessed (see Chapter 9). In exploratory trials, it may be desirable to use more than one primary end point variable, to cover the potential range of effects of a therapy, one of which may then be subsequently selected for a confirmatory trial. Defining efficacy

The primary end point defines the outcome that is assessed, and therefore the nature of the trial's response variables (Table 16.2), and efficacy is deter­ mined in terms of differences between treatment and control groups. The differences may be measured either absolutely or relatively (e.g., by the relative risk9). Additionally, a useful measure of vaccinal efficacy is the attributable proportion (exposed), \xp' (see Chapter 1 5), in which unvaccinated animals are defined as 'exposed' to the risk factor. Table 16.3 shows the results of a clinical trial of the efficacy of a Bacteroides nodosus vaccine against foot-rot in sheep. In this trial, prevalence figures are used instead of incidence figures; thus: exp =

A

(prevalenceexposed -

prevalenceunexposed)/(prevalenceexposed)

= (94/422 - 21/31 7)/(94/422) = 0.157/0.223 = 0.704. 9 Caution should be exercised in using the odds ratio in clinical trials. Recall (Chapter 15) that the odds ratio overestimates the relative risk, and this overestimation can be considerable if disease (outcome) is not rare. In clinical trials, the outcome of interest (e.g., recovery rate) may not be rare, in which circumstance the odds ratio will substantially overestimate the effect of treatment.

Design, conduct and analysis Table 1 6.2

�(U

Response variables assessed in c l i nical trial s .

Efficacy

Response variable Definition

Level of measurement

Examples

Nominal

Morta l ity

D ifference between two proportions

Chapter 1 4

I ncidence

Relative risk

Chapter 15

Difference between two med ians

Chapter 1 4 Chapter 14

Description ofmethod and sample size determination

Prevalence Scores of cI i n ical severity

Ordinal

Condition scores I nterval

liveweight gain

Difference between means

and ratio

M i l k cel l counts

(if the variables are

and the visual

Visual analogue assessment

Normal ly d i stributed)

analogue scale

of c l i n ical severity

Table 1 6.3

Efficacy of a B acteroides nodosus vaccine against

foot-rot (84 days after vaccination). (Raw data derived from H i ndmarsh et at., 1 989.)

Foot rot absent

Foot rot present

Total

Non-vacc i n ated sheep

94

328

422

Vaccinated sheep

21

296

317

Therefore, 70.4% of foot-rot in unvaccinated sheep is attributable to not being vaccinated; this is altern­ atively the percentage of disease prevented by the vaccine in vaccinated animals. There is not always a fixed standard for acceptable therapeutic effect or efficacy. In the European Union, for example, the therapeutic effect of a veterinary medi­ cinal product is generally understood by the relevant regulatory body to be the effect 'promised by the manufacturer' (Beechinor, 1993). European regulatory guidelines have attempted to define efficacy of ectoparasitic preparations (CVMP, 1993): % efficacy =

C-T

--

C

x

1 00,

where:

C = mean number of ectoparasites/animal in the

control group; 1 0 T = mean number of ectoparasites/animal in the treated group.

An approximate confidence interval can be calcu­ lated for this parameter by computing a confidence 1

0 The mean may be the arithmetic mean, geometric mean, or other appropriate transformation (see Chapters 12 and 17); noting, however, that transformations have less meaning to clinicians than the original scales.

interval for the difference between the two means,

C and T (as described in Chapter 14), and then divid­ ing each limit by C. (Note that this approximate approach ascribes no sampling variation to C in the denominator.) Target levels of efficacy include 'approximately 1 00%' for flea and louse infestations; '80-100% (prefer­ ably more than 90%)' for infestations with Diptera; and 'more than 90%' for tick infestations. Note, however, that the value of a therapeutic effect lies ultimately in its clinical and economic impact.

The experimental u n it The experimental unit is the smallest independent unit to which the treatment is randomly allocated. It may be elementary units (usually individual animals) or aggregates such as pens or herds. Most companion­ animal and human clinical trials involve allocation to individuals. Some trials in livestock, in contrast, may involve allocation of treatments to groups (e.g., Gill, 1 987). In contrast, the experimental unit may be the udder quarter when locally administered intramam­ mary preparations are being assessed; the elementary unit is then the quarter, not the animal. The experimental unit may be a group because events at the individual level cannot be measured, even though they are of interest. For instance, in trials of in-feed compounds likely to affect weight gain in poultry and pigs, either the amount eaten by, or the weight increase of, individuals within a house or pen is not recorded. This often arises because it is not practical to identify individual animals at weighing. Consequently, liveweight gain per house or pen is the response variable. Moreover, when animals are penned together, external factors (e.g., farm hygiene) may affect the group, and such 'group effects' can­ not be separated from individual treatment effects;

'q·1

Clinical trials

therefore the group must be identified as the experi­ mental unit (Donner, 1993; Speare et al., 1995). Thus, the efficacy of in-feed antibiotic medication in reducing the incidence of streptococcal meningitis in pigs could be assessed by dividing a herd into pens containing a specified number of animals ( Johnston et al., 1 992). The treatment is then randomly allocated to the pens, and medicated and 'placebo' diets supplied to pigs in the respective treatment and control pens. In this circumstance, each pen only contributes the value 1 in sample size determination for the trial because variability can only be legitimately assessed between pens, rather than between individuals. A particular problem arises with trials involving some infectious diseases. If the treatment could reduce excretion of infectious agents (e.g., vaccination in poultry houses or anthelmintic trials on farms), then treated and control animals should not be kept together because any reduction in infection 'pressure' will benefit treated and control animals; similarly, control animals constitute a source of infection to treated ani­ mals. This can lead to similar results in both categories (Thurber et al., 1 977), therefore reducing the likelihood of detecting beneficial therapeutic effects. The practice of mixing animals in each group is therefore un­ acceptable when herd immunity or group immunity is being assessed. In these circumstances, an appropriate independent unit must be identified. Thus, separate houses could be used on an intensive poultry enter­ prise, or separate tanks on a fish farm. Dairy farms, in contrast, usually have a continuous production policy with mixing of animals, and so the herd may become the experimental unit.

The ex peri mental population The population in which a trial is conducted is the experimental population. This should be representat­ ive of the target population (see also Chapter 13). Differences between experimental and target popula­ tions may result in the trial not being generaliz­ able (externally valid); that is, unbiased inferences regarding the target population cannot be made. For example, findings from a trial of an anaesthetic drug conducted only on thoroughbred horses may not be relevant to the general horse population because of dif­ ferences in level of fitness between thoroughbreds and other types of horse (Short, 1987). External validity (which is faciltated by conducting trials 'in the field') contrasts with internal validity, which indicates that observed differences between treatment and control groups in the experimental population can be legitim­ ately attributed to the treatment. Internal validity is obtained by good trial design (e.g., randomization). The evaluation of external validity usually requires

much more information than assessment of internal validity. Prophylactic trials require selection of an experi­ mental population that is at high risk of developing disease so that natural challenge can be anticipated during the period of the trial. Previous knowledge of disease on potential trial sites may be sufficient to identify candidate populations ( Johnston et al., 1992). However, the period of natural challenge may vary, reflecting complex patterns of infection. Many infec­ tions are seasonal (Figure 8.14); others may be poorly predictable (Clemens et al., 1993).

Ad m i ssion and excl usion criteria Criteria for inclusion of animals in a trial (admission criteria, eligibility criteria) must be defined. These should be listed in the protocol, and include: •

a precise definition of the condition on which the treatment is being assessed; the criteria for diagnosis of the condition.

For example, in the trial of the efficacy of evening prim­ rose oil in the treatment of canine atopy, chronically pruritic dogs were included only if they conformed to a documented set of diagnostic criteria (Willemse, 1986) and reacted positively to the relevant intradermal skin tests. Similarly, specific types of mastitis may need to be defined in bovine mastitis trials; other admission criteria could include parity and stage of lactation. Exclusion criteria are the corollaries of admission criteria. Thus, dogs with positive reactions to flea aller­ gens were excluded from the trial of evening primrose oil. Cows might be excluded from a mastitis trial if they had been previously treated for mastitis during the relevant lactation, if they had multiple mammary infections, or if they also had other diseases that could affect treatment. Trials of non-steroidal anti-inflamma­ tory drugs would require exclusion from the treatment group of animals to which corticosteroids were being administered. However, too many exclusion criteria should be avoided; otherwise external validity may be compromised. It may be prudent to accommodate factors either in the trial design by stratification, or during the analysis. The objectives and general outline of a trial should be explained to owners of animals that are included in the trial, and then their willingness to participate documented. This is informed consent.

Bl i nd i ng Blinding (masking) is a means of reducing bias. In this technique, those responsible for measurements or

Design, conduct and analysis Table 1 6.4

Sum mary of types of bl i nd i n g to assignment of treatment.

Type of blinding

Knowledge o fassignment of treatment Owner

Investigator

None

Yes

Yes

Si ngle

No

Yes

Double (fu l l )

No

No

clinical assessment are kept unaware o f the treatment assigned to each group. The classification of blinding into single or double (full) is based on whether the owner or attendant (patient in human medicine) or investigator is 'blinded' (Table 16.4). The investigator' can be more than one category of person; for example, participating veterinary practitioners and the principal investigators that analyse the results (the term 'treble­ blinding' has been advocated in this situation). Blinding should be employed wherever possible, and is facilitated by the use of a placebo in the control group. However, there may be circumstances in which blinding is not feasible; for example, if two radically different treatments are being compared (e.g., com­ paring infiltration of local anaesthetic with bloodless castrators to reduce pain associated with castration and tail-docking of lambs: Kent et al., 2004), or if formulation of visually identical 'trial' and 'standard' drugs is impracticable. Such unblinded studies are sometimes termed open-label trials (Everitt, 1 995). Open-label trials can be avoided by partial blind­ ing through denying personnel involved in clinical assessment access to details of treatment. If full blinding is infeasible, those that are blinded (sponsor, investigator, or owner) should be clearly documented, as should any intentional or unintentional breaking of blinding.

Random izat ion Simple randomization

Simple randomization is the most basic type of randomization. When there are only two treatments, tossing a coin is an elementary method. However, it is usually more rigorous to randomize in advance using random numbers (Appendix X), allocating units identified by odd numbers to one group, and evenly numbered units to the other. Randomization should be applied after eligible units have been identified. When comparing a new treatment with an estab­ lished one, and there is evidence that the new treat­ ment is superior, it can be allocated to twice the number of units as the established one (Peto, 1 978).

This can increase the benefit to participating animals. For example, if a new treatment was expected to reduce mortality by 50%, 2:1 randomization would be expected to produce an equal number of deaths in the two groups. This randomization ratio can be obtained by using twice as many random numbers for allocation of the new treatment as those used to allocate the established one. There is no advantage in increas­ ing the ratio further, because of the resultant loss of statistical power which can only be counteracted by increasing the total sample size. Block randomization

Simple randomization can produce grossly uneven totals in each group if a small trial is undertaken. This problem can be overcome using block (restricted) randomization. This limits randomization to blocks of units, and ensures that within a block equal numbers are allocated to each treatment. For example, if randomization is restricted to units of four animals, receiving either treatment A or treatment B, the num­ bers 1 - 6 are attached to the six possible treatment allocations in a block: AABB, ABBA, ABAB, BBAA, BAAB and BABA. One of these numbers is then selected from a random number table for the next block of four individuals entering the trial, and given its treatment allocation. Stratification

Some factors (e.g., age, parity or severity of disease) may be known to affect the outcome of a trial and may bias results if they are unevenly distributed between the treatment and control groups. This can be taken into account during initial randomization by stratify­ ing (Le., matching) both groups according to these confounding factors. The experimental units are then allocated to treatment and control groups within the strata, using simple or block randomization. The most extreme case is individual matching (see Chapter 15), with subjects in the matched pairs being randomly allocated to the treatment and control groups. Stratification leads to related samples and therefore decreases the number of units that are required to detect a specified difference between treatment and control groups (see Chapter 14). These and other methods of randomization are described in detail by Zelen (1974) . Alternatives t o randomization

Some alternatives to randomization include allocation according to date of entry (e.g., treatment on odd days, placebo on even days), clinic record number, wishes of the owner, and preceding results. An example of the

)'JI,

Clinical trials

last method is the 'play-the-winner' approach (Zelen, 1969): if a treatment is followed by success, the next unit receives the same treatment; if it is followed by failure, the next unit receives the alternative treatment. This limits the number of animals receiving an inferior treatment. All of these techniques have disadvantages and should never be considered as acceptable altern­ atives to randomization (Bulpitt, 1 983).

Trial designs There are four main trial designs: 1. 2. 3. 4.

parallel-group (standard); cross-over; sequential; factorial.

Parallel-group-design (standard) trials

The parallel-group (standard) design is commonly used in confirmatory trials. Experimental units are randomized to a single treatment group using either simple or block randomization, and each group re­ ceives a single treatment. A specified number of units enter the trial and are followed for a predetermined period of time, after which the treatment is stopped. The basic design can be refined by stratification. The analytical techniques employed in a parallel trial involving two unstratified groups are listed in Table 1 6.2. Estimation of parameters with associated confidence intervals is preferred to hypothesis testing, for the reasons given in Chapter 14. Confidence intervals should also be quoted for negative, as well as positive, results. Details of complex multivariate methods for strati­ fied analyses are described by Meinert and Tonascia (1986) and Kleinbaum et al. (1982), but these are seldom used in veterinary product development.

Cross-oyer-design trials

In a cross-over trial, subjects are exposed to more than one treatment consecutively, each treatment regimen being selected randomly (Hills and Armitage, 1 979). Experimental units therefore serve as their own con­ trols, and treatment and control groups are therefore matched. This design is useful when treatments are intended to alleviate a condition, rather than effect a cure, so that after the first treatment is withdrawn the subject is in a position to receive a second. Examples are comparisons of anti-inflammatory drugs in arth­ ritis, and hypoglycaemics in diabetes. Moreover, a com­ parison on the same individuals is likely to be more precise than a comparison between subjects because

the responses are paired (see Chapter 14). The cross­ over trial is therefore valuable if the number of experi­ mental units is limited. However, analysis of results is complex if a treatment effect carries over into the next treatment period. If treatment effects do not carry over into sub­ sequent treatment periods, the techniques described in Chapter 14 for the analysis of related samples can be used. However, the absence of a carry-over effect may be difficult to prove. If there is any doubt, conclusions should be based only on the first period, using ana­ lyses of independent samples. Alternatively, more complex methods that identify interactions between treatment effect and period of treatment can be applied (Hills and Armitage, 1979). Sequential-design trials

A sequential trial is one whose conduct at any stage depends on the results so far obtained (Armitage, 1 975). Two treatments are usually compared, and experimental units (usually individuals) enter the trial in pairs; one individual being given one treatment, and one the other. Results are then analysed sequentially according to the outcome in the pairs, and boundaries are drawn to define levels at which specified differ­ ences are obtained at the desired level of statistical significance. The trial may be terminated when these levels are reached. If the desired level is not reached, the investigator may decide to increase the sample size indefinitely until the former is reached; this is an openll trial. Alternatively, the trial may be terminated if a specified difference is not reached by a certain stage; this is a closed trial. Sequential trials facilitate early detection of bene­ ficial treatment effects and can require fewer experi­ mental units. However, they may be difficult to plan because their duration is initially unknown. They are also unsuited to trials in which treatment response times are long because responses need to be analysed quickly so that a decision can be taken to enlist more subjects, if necessary. A key feature of sequential trials therefore is that significance tests are conducted repeatedly on accu­ mulating data. This tends to increase the overall significance level (Armitage et al., 1969). For example, if five interim analyses, rather than one, are conducted, the chance of at least one analysis showing a treatment difference at the 5% level (a 0.05) increases to 0.23 (i.e., 1 - [1- a]5); if 20 interim analyses are undertaken, it increases to 0.64 (1 - [1 a]20). The overall Type 1 error therefore increases if, for any single interim =

-

11 This should not be confused with open, uncontrolled trials (men­ tioned earlier in this chapter) in which the same animals are compared before, and after, treatment.

Design, conduct and analysis Table 1 6.5

Nominal significance level req u i red for repeated

sign ificance test i ng with an overa l l sign ificance level,

a=

0.05

or 0.01 , and various val ues of N, the maxi m u m n u m ber of tests. (From Pocock, 1 9 77.) N

a=

0. 05

a=

0.01

2

0.0294

0.0056

3

0.0221

0.0041

4

0.01 82

0.0033

5

0.01 58

0.0028

6

0.0 1 42

0.0025

7

0 .0 1 3 0

0.0023

8

0.0 1 20

0.0021

9

0.01 1 2

0.00 1 9 0.001 8

10

0.01 06

15

0.0086

0.001 5

20

0.0075

0 . 00 1 3

interaction, enables groups to be combined to increase the power to detect the effects of treatment A and treatment B. The approach can be extended to any number of factors, and with each factor having a differ­ ent number of levels.

What sample s ize should be selected ? Superiority trials

The number of experimental units in treatment and control groups in a superiority trial should be deter­ mined using the techniques outlined in previous chap­ ters (Table 1 6 .2). In summary, the following parameters should be considered: 1.

analysis, a= 0.05 is used as the trial's stopping criterion. If data are analysed frequently enough, a value of P < 0.05 is likely, regardless of whether there is a treat­ ment difference. This problem can be overcome by choosing a more stringent nominal significance level for each repeated test, so that the overall significance level is kept at a reasonable value such as 0.05 or 0.01 (Pocock, 1 983) . Table 1 6.5 can be used for this purpose under two­ tailed conditions. For example, if the overall signific­ ance level is set at a = 0.05, and if a maximum of three analyses is anticipated, P < 0.022 is used as the stop­ ping rule for a treatment difference at each analysis; similarly, if a maximum of five analyses is anticipated, P < 0.016 is used. Suitable values for one-sided tests are given by Demets and Ware (1980). Sample-size calculations should therefore be modified if more than one significance test is planned (Wittes, 2002). Sequential trials are considered in detail by Armitage (1 975) and Ellenberg et al. (2002). Factorial-design trials

If two factors, A and B, are to be investigated at a levels and b levels, respectively, this gives rise to ab experi­ mental conditions, corresponding to all possible com­ binations of the levels of the two factors; this is a complete a x b factorial-design study (Zar, 1 996). Thus, in a 2 x 2 factorial design where one factor is the absence or presence of treatment A (a = 2) and the other factor is the absence or presence of treatment B (b = 2), animals are randomly allocated to one of the four com­ binations of two treatments thus: A alone, B alone, A and B together, and neither A nor B. This is a powerful method of testing the effect of two factors in the same study, using the same experimental units. It can be used to explore any interactions that might occur between the two treatments and, in the absence of

2.

3. 4.

the acceptable level of type I error, a (the probab­ ility of erroneously inferring a difference between treatment and control group); test power, 1 f3 (the probability of correctly infer­ ring a difference between treatment and control group) where f3 = the probability of type II error (the probability of erroneously missing a true difference between treatment and control group); the magnitude of the treatment effect (i.e., the dif­ ference between proportions, medians or means); the choice of alternative hypothesis: 'one-tailed' or 'two-tailed'. -

There is no rule for defining parameters 1-3. Type I error is traditionally set at 0.05, but a value as low as 0.01 can be justified if a trial is unique and its findings are unlikely to be repeated in the future. Power can vary considerably (values between 0.50 and 0.95 have been quoted in human clinical trials; 0.80 is common when a = 0.05, and 0.96 when a = 0.01 : see Chapter 14). The magnitude of the treatment effect depends on its clinical and economic relevance. (In clinical trials in which treatment and control groups are matched, the formulae for sample size determination listed in previous chapters will tend to overestimate the number of units required.) If a placebo or no treatment has been administered to the control group, and there is therefore intuitive evidence that the treatment can cause only an improvement in comparison with the control group, a one-tailed test (see Chapter 14) is justifiable, and the sample size can be determined accordingly. However, the use of placebos or 'negative' control groups is now ethically debatable; consequently many contempor­ ary clinical trials use a 'positive' control group and it is therefore prudent to assume two-tailed conditions (i.e., the treatment under test may be either better, or worse, than the standard treatment). Additionally, the magnitude of the difference between treatment and 'positive' control groups may be small; thus large

H )I)

Clinical trials

sample sizes may be specified. These may be unattain­ able in practice. However, a knowledge of sample size determination is necessary to appreciate the inferential limitations that may be imposed by the number of experimental units included in a trial. Wittes (2002) presents a general discussion of sample­ size calculation in clinical trials, and Machin et al. (997) tabulate sample sizes. Sample size determina­ tion for cross-over trials is discussed by Senn (993). Sample size determination for sequential trials is dis­ cussed by Armitage (975); the estimated sample size for a given Type I and Type II error is smaller than for a non-sequential trial. General guidelines are provided by Shuster (992). Hallstrom and Trobaugh (985) provide formulae that incorporate diagnostic sensitivity and specificity (see Chapters 9 and 17). Equivalence and non-inferiority trials

Determination of sample size to demonstrate equi­ valence focusses on the maximum difference that is tolerated - termed the margin of clinical equivalence (M). This is the largest difference that is clinically acceptable, larger differences having unwelcome con­ sequences; for example, a difference in mean blood glucose levels induced by a new hypoglycaemic, relat­ ive to an established drug, such that signs of diabetes recur. The common context is therefore of demonstrat­ ing non-inferiority. Thus, for a dichotomous response variable, the sample-size formula to demonstrate a difference between two proportions (Chapter 14) is applied, but PI - P2 is now the margin of clinical tolerance, rather than the difference to be detected. Moreover, the values of a and /3 are reversed because attention now focusses on the power of the comparison to detect any difference that may be present. For example, a new foot-rot vaccine may be com­ pared with the one listed in Table 16.3, which prevents disease in 296 of 317 sheep (93%). In determining equivalence of the two vaccines, it may be considered acceptable not to detect a difference as trivial as 5% or less in favour of the established vaccine (in which cir­ cumstance the vaccines are deemed to be equivalent), but desirable to detect a difference greater than 5% (in which circumstance they are identified as not being equivalent); thus M = 5%. Note that this is a one-tailed situation, because if non-equivalence is demonstrated it is only in the direction of the new vaccine being inferior to the established one - not either inferior or superior. Assume that the two vaccines are equivalent, with the proportion of disease in vaccinated sheep 0.07 (i.e., 100% - 93%: the estimate for the established vaccine). Thus, PI = 0.07. If M 5%, P2 0.07 + 0.05 = 0.12, and (PI + P2)/2 = (0.07 + 0.12)/2 0.095 p. Set /3 at 0.05 (that =

=

=

=

=

is, power = 0.95), and set aat O.20; thus, from Appendix Mf3 = 1.64, and Ma = 0.84 (because the hypothesis is one-tailed). The number of animals required in each vaccinated group, is then derived thus:

XV,

n,

n=

[Ma �2p(1 - p) + Mf3 �PI (1 - PI ) + P2 (1 - P2 ) ] 2 (P2 - PI?

(O.84�0.19 x 0.905 + 1.64�0.07 x 0.93 + 0.12 x 0.88) 2 (0.12 - 0.07) 2 = [(0.3483 + 0.6776)2]/0.0025 = 421. Therefore, a trial comprising 421 animals vaccinated with the established vaccine, and 421 animals vacci­ nated with the new vaccine, will detect any difference between the performance of the two vaccines as small as an absolute difference in disease occurrence of 5%, but no smaller, with probability 0.95. Alternatively, the requirement may be to show that a new vaccine is neither inferior nor superior to an estab­ lished one (i.e., assessment of full equivalence). In this circumstance, Mf3 is obtained from Appendix XV using a /3 value obtained by setting 1 - 2/3 equal to the overall power required for the two one-sided tests that need to be conducted. For example, if the overall power is to be 0.95, then Mf3 should be based on /3 being 0.025 (i.e., Mf3 = 1.96). The same approach can be adopted for continuous and ordinal variables, using the relevant formulae for sample-size determination for differences between two means or two groups of ordinally ranked data (see Chapter 14). Losses to 'follow-up'

The outcome of a trial may not be recorded in some experimental units because they are lost to 'follow-up'. For example, owners may move house or refuse to con­ tinue with the trial. The extent of this loss to follow-up needs to be assessed, and is frequently based on the experience of the investigator. The sample size then needs to be increased by multiplying the sample size by 1/0 - d), where d is the anticipated proportion of experimental units lost. For example, if d 10/100, the sample size would need to be multiplied by 1.11 0/0.9) to compensate. Losses to follow-up cannot be included in subsequent analyses. =

Compl iance

The success of a trial depends on participants acting in accordance with the instructions of the trial's

Design, conduct and analysis

designers; that is, complying with treatment. For example, they may decide to switch from the treatment under trial to an alternative treatment. Poor com­ pliance will decrease the statistical power of the trial because the observed difference in outcome between treatment and control groups will be reduced, but it will not produce spurious differences between groups. Reasons for poor compliance include: unclear instructions; forgetfulness; inconvenience of participation; cost of participation; preference for alternative procedures; disappointment with results; side-effects. Participants cannot be forced to comply, and so regular contact should be maintained with them so that they can be encouraged to comply, and the degree of compliance should be regularly assessed. For example, if a treatment is formulated as a tablet, the number of tablets remaining can be counted regularly by the veterinarian. Assessment may be difficult (e.g., with in-feed medication) but should, nevertheless, be attempted. Other methods of improving compliance include: enrolling motivated participants; assessing the willingness of participants to comply; providing incentives (e.g., free treatment); supplying simple, unambiguous instructions; limiting duration of the trial. If non-compliance is substantial, the required sample size should again be modified in the same way as adjustment for loss to follow-up. If both losses to follow-up and non-compliance are anticipated, a composite value for d is required.

The goal of a superiority trial is to detect a difference between treated animals and controls. Evidence of a difference is provided, at the 5% level of significance, if the probability of a Type I error is less than 5% (exact values of P should always be quoted). The 95% confidence interval for the difference between the treatment effect will then exclude the null value (zero for differences; but 1 for ratio measures such as the relative risk and odds ratio, and ratios of geometric means). This is illustrated in Figure 16.1a. A 95% confidence interval with a lower bound clearly above the null value, and with a related value of P substan­ tially lower than 0.05, provides strong evidence for superiority of the treated group over the control group. A 95% confidence interval with the lower limit touching the null value (P = 0.05) provides adequate evidence of superiority at the 5% level of significance. In contrast, if the 95% confidence interval includes the null value (P > 0.05), there is insufficient evidence to demonstrate superiority.

Term i nati ng a trial

Equivalence and non-inferiority trials

• •

I nterpretation of resu Its

In Chapter 14, the use of statistical hypothesis testing as an approach to interpreting data was dis­ cussed. Increasingly, however, this is being replaced by estimation - in particular, by calculating confidence intervals (introduced in Chapter 12). Significance testing and confidence interval estimation are two ways of interpreting the same data. However, an advantage of confidence intervals is that they encourage the investigator to express results in terms of the size of any treatment effect or difference. The following dis­ cussion will therefore place particular emphasis on the interpretation of confidence intervals.

The number of experimental units entering a trial and the duration of treatment are specified during the design of a trial; therefore a trial will usually last as long as it takes to enlist the units and for the last unit to complete the trial. However, it may be necessary to terminate a trial (particularly a long-term one) pre­ maturely if there are serious adverse side-effects in the treatment group, and such a decision rule should be written into the trial's protocol. In sequential trials, another decision rule may be that a trial will be termin­ ated when the specified difference is detected to the predetermined level of significance (see above). Decision rules, and the advantages of early and late termination of trials, are discussed in detail by Bulpitt (1983).

Superiority trials

A full equivalence trial is intended to confirm the absence of a clinically relevant difference between treatments. This is best explored using confidence intervals. First, the margin of clinical equivalence, M, is selected. This margin should be chosen before a trial is undertaken to prevent bias, and therefore has been specified in the sample-size calculation undertaken before the study was conducted (see above). Two treat­ ments (say, control and new treatment) are considered equivalent if the 95% confidence interval12 lies entirely within the interval -M to +M (Figure 16.1b). A non-inferiority trial aims to demonstrate that a new therapy is no less effective than (i.e., is 12 In bioequivalence studies involving drug kinetics, 90% intervals are the accepted standard.

;00 (a)

Clinical trials

p= 0.002 p= 0.05

p= 0.2

I1-1-----.---

-------.e--

Superio rity shown more strongly

Su perio rity shown

--+1---

Control better

.... .. ---- Superio rity not shown

Treatment d ifference

(b)

New agent better

Equivalence shown E q u ivalence shown

-----

E q u ivalence shown

-

Equivalence not shown

t--....--i-- E q u ivalence not shown

-

-M

Treatment d ifference

(c)

----r---

--

;.-

-

-M I

-

Control better

Fig. 1 6.1

+M

o

Control better

New agent better

Non-i nferiority shown

not shown

o

Goals of meta-an alysi s

New agent better

Significance levels and confidence i nterval s in c l i n ical

trials. Null value for treatment d ifference between treated a n i mals •

Meta-analysis is the statistical analysis of data pooled from several studies to integrate findings13. The tech­ nique has its origins in educational research (Glass, 1976) and has been widely applied in the social sciences, where key texts have been published (Wolf, 1986; Hunter and Schmidt, 1989). More recently, it has been used in economics (van den Bergh et al., 1997) and biology (e.g., to investigate parasite-induced behavioural changes: Poulin, 1994). In human and veterinary medicine, meta-analysis has been applied in several areas (Stangle and Berry, 2000), including the evaluation of diagnostic tests (e.g., Greiner et al., 1997), observational studies (e.g., Willeberg, 1993; Fourichon et al., 2000), cost-benefit analysis of diagnostic tech­ niques and treatments, and assessment of the mag­ nitude of health problems (e.g., Chesney, 2001; Dohoo et al., 2003; Trotz-Williams and Trees, 2003). However, it has been used most extensively in the area of clinical trials (e.g., Srinand et al., 1995; Peters et al., 2000) and, for that reason, is discussed in this chapter.

....>l. ---- N o n - i nferiority

Treatment difference

and controls = O .

Meta-analysis

: Point estimate of treatment d ifference; : 9 5 % --

i nterval est i mate of treatment d i fference. (a) Superiority trials;

(b) equ ivalence trials; (e) non-i nferiority trials.

The aims of meta-analysis (Sacks et al., 1987; Dickersin and Berlin, 1992; Marubini and Valsecchi, 1995) are to: increase statistical power for primary end points; resolve uncertainty if there are conflicting results; improve estimates of therapeutic effect, and their precision14; answer questions not posed at the beginning of individual trials; give a 'state-of-the-art' literature review; facilitate analysis of subgroups when the power of individual analyses is low; guide researchers in planning new trials; offer rigorous support for generalization of a treat­ ment (i.e., external validity); balance 'overflow of enthusiasm' which might accompany introduction of a new procedure following a single beneficial report. Correctly conducted meta-analyses therefore offer strong evidence for efficacy of treatment (Table 16.6). •

non-inferior to) an established preparation, although it could also be equivalent or better. Thus, concern lies with a difference only in one direction. The new pre­ paration therefore is considered not to be inferior to the established (control) preparation only if the confidence interval lies entirely to the right of -M (Figure 1 6.1c). For example, a new foot-rot vaccine may be compared with an established one, with M set at a difference of 5% in the proportion of disease in sheep between the two groups in favour of the established vaccine (i.e., 5% less disease in sheep vaccinated with the estab­ lished preparation than in sheep given the new vac­ cine). If the 95% confidence interval for the difference was -7%, -3%, then it would cross the -M boundary (i.e., does not fall entirely to the right of -5%), and so it could not be concluded that the new vaccine was non-inferior to the established one. Sometimes, the goal of a comparison may switch from a non-inferiority trial to a superiority trial, or vice versa. Results then have to be interpreted cautiously (EAEMP, 2000).

13 The term is derived from the Greek preposition, /lE7:a- (meta-) = 'alongside', 'among', 'in connection with'. A subsidiary meaning is 'after. Meta-analysis is therefore either one that is done alongside/in conjunction with the normal analysis, or one that is done after the normal analysis, that is, at a later stage in the process. An alternative term 'overviews' of research - has also been suggested (Peto, 1 987). 14 This includes not only revealing beneficial effects that are not identified in isolated studies, but also identification of 'false-positive' effects in individual studies: meta-analysis is designed to produce accurate results - not necessarily positive ones.

Meta-analysis

WI

moves downwards.

analysis of similarity in design, execution and ana­ lysis, and exploration of differences between trials; aggregation of data, testing various combinations and interpretations; drawing of careful conclusions. Note that the conventional, qualitiative, review article has traditionally been accepted as the means of summarizing research data - usually by listing the individual results of several studies - and lacks objective rigorous analysis. A properly designed meta­ analysis, in contrast, goes further, and uses quantita­ tive analytical procedures to combine results from several sources, where possible, to produce an overall conclusion.

Table 1 6.7 Advantages and disadvantages of meta-analysis. (Based on Mei nert, 1 989.)

Sou rces of data

H ierarchy of strength of evidence concern i ng efficacy of

Table 1 6.6

treatment. (From Maru b i n i and Val secch i , 1 99 5 . ) 1 . Anecdotal case reports 2. Case series without contro l s 3 . Series with l iterature controls 4 . Analysis using computer databases 5. Case-control observational studies 6 . Series based o n h i storical control groups 7. Single randomized contro l l ed c l i n ical trials 8. Meta-analyses of randomized controlled c l i n ical trials The table l i sts the types of study used in med i c i ne, suggested by Green and Byar ( 1 984). The table can be considered as an e ight-tiered pyra m i d . In the context of c l i n ical trials, the base on which conclusions about efficacy can be bu i l t becomes broader as one

Advantages: Focusses attention on trials as an evaluation tool I ncreases the i m pact of trials on c l i n ical practice Encourages good trial design and reporting Disadvantages: Cu rrent fash ion for meta-analysis may discourage large definitive trials Tendency to unwittingly m i x d i fferent trials and ignore d i fferences Potenti al for tension between meta-analyst and cond uctors of origi nal trials

The statistical procedures used are also applicable to the analysis of multicentre trials. However, there are disadvantages, as well as advan­ tages, to the technique (Table 1 6.7). Perhaps the major disadvantage is the seductive notion that combination of several small trials is a substitute for a well designed large one15. In this section, the main issues associated with meta­ analysis are outlined. For details of specific statistical procedures, the reader is directed to the standard texts mentioned above, and to the excellent reviews by Abramson (1991) and Dickersin and Berlin (1992).

Data for meta-analyses are usually obtained from pub­ lished material, most of which is presented in refereed journals. This has the advantage of guaranteeing (at least theoretically) minimum standards with respect to the design, conduct and analysis of the component studies. However, there is a tendency for positive findings (beneficial treatment effects) to be more read­ ily accepted for publication than results that either do not show significant effects or reveal only minor effects (Easterbrook et al., 1 991); this constitutes publication bias. This is a complex matter, though, and unpub­ lished results can show larger effects than published ones (Detsky et al., 1987). Assessment of the quality of all potential data is therefore desirable, so that useful material does not escape the analyst. Various methods have been recommended for hand­ ling publication bias. A simple approach (Rosenthal, 1 979) calculates an overall P value from the P values of the component studies, and then calculates a 'fail-safe N': the number of statistically non-significant studies that, if added, would increase the P value to a critical threshold level (say, 0.05). Comparability of sources

Components of meta-analys i s

There are both qualitative and quantitative com­ ponents to meta-analysis, listed in a scheme for meta-analysis of clinical trials (Naylor, 1 989): selection of trials according to inclusion and exclusion criteria; evaluation of the quality of the trials; abstraction of key trial characteristics and data; •

• •

15 This may appear particularly attractive in the current academic cli­ mate where financial support is in short supply, and there is pressure to generate publications.

A key feature of component trials is the variability (heterogeneity) in their results. The latter may actually be contradictory, but this is generally due to differ­ ences in the design, conduct or analysis of the studies (Horwitz, 1987). Additionally, different trials may be measuring different response variables on different scales (e.g., median values or visual analogue measure­ ments). Differences between old and recent studies may be ascribed to underlying health trends unrelated to the therapy in question - somewhat akin to the use of historical controls. If a meta-analysis intends to address general policy or efficacy of a class of drugs, then incorporation of trials with obvious differences can

.102

Clinical trials

be condoned. However, a specific question will require selection of a relatively homogeneous set of trials. Differences between the different studies that are inc�uded in an analysis prevent interpretation of pooled estimates as being precise16, and 99% confidence limits may therefore be more prudent than the conventional 95% limits. Data analys i s

Analytical techniques treat each incorporated clinical trial as a stratum. The single treatment effects are estimated within each trial, and are then combined to produce a suitable summary, weighted treatment effect. Methods of weighting, and addressing variabil­ i�y in study results, vary. However, the tendency to sImply pool the results of the trials and compute an a�erage . effect is avoided. This could be dangerously misleadmg; for example, a mean mortality rate com­ puted from a series of separate mortality rates does not address differences in sample size between trials, and therefore the different precision of each trial's estimate. A �ommon a�proach for categorical data is to provide a weIghted estimate, for example, of the odds ratio or relative risk. Standard methods include the Mantel­ Haenszel procedure (see Chapter 15); Westwood et ai. (2003) give an example relating to the effects of mon­ �n�in treatment on lameness in dairy cattle. More soph­ Isticated procedures allow pooling of parameters that have been adjusted for confounding (Greenland, 1987). Continuous explanatory variables require different procedures. A commonly used measure is the effect size. This is the difference between the mean values of the treatment and control groups divided by the stand­ ard d�viation in the control group (or in both groups co.mbmed) (Glass et ai., 1981). This can be interpreted wIth reference to tables of probabilities associated with the upper tail of the Normal distribution (Appendix XV). For example, an effect size of 2.9 means that 99.8% of controls have values below the mean value of treated �ndividuals. Consulting Appendix XV, this percentage �s obtained by identifying the one-tailed probability, P, m the body of the table for which the effect size equals The percentage then equals (1 - P) x 100. Thus, if the effect size = 2.9, P = 0.0019, and (1 - P) x 100 = (1 0.0019) x 100 = 99.81 %. Similarly, for an effect size of 1 .0, the corresponding percentage is 84% ({1 - 0.1587) x 100). Effect size has no units, and so allows the combination of results expressed in different units. However, it should be interpreted with caution because it depends not only on differences in the effect itself, but also on dif­ ferences in standard deviations. The use of effect size is therefore particularly dubious if sample sizes are small. z.

10 The confidence limit is strictly a limit on the expected results, based on what was done in the studies, rather than on future trials.

Heterogeneity

The heterogeneity between studies must always be addressed. Commonly, tests for homogeneity are based on X2 or F statistics for categorical (Schlesselman, 1982) and continuous data (Fleiss, 1986), respectively. These are usually interpreted liberally at the 10% level because of the relatively low power of such tests (Breslow and Day, 1980). A sensitivity analysis (see Chapter 19) can also be conducted to determine if exclusion of one or more trials materially affects the �eterogeneity. If the heterogeneity is larger than can be mferred from the results of significance tests, a sum­ mary measure is questionable, and the reason for the heterogeneity should be explored17. Note. however, that a high P value does not unequivocally indicate that the results are homogeneous, and the data should be explored by other means, such as graphical repres­ entation. Examples include a vertical two-tiered plot of results (e.g., odds ratios, relative risks18 or effect size) with their 95% and 70% confidence intervals, for ease of comparison around the point estimates (Pocock and Hughes, 1990). A 'funnel display' plots results against a measure of precision (e.g., sample size or the reci­ procal of the variance); if all studies are estimating a similar value, the spread of results should become narrow as precision increases, producing a funnel shape (Greenland, 1987). Fixed-effects and random-effects models

Most of the analytical procedures that have been employed in meta-analyses are based on a fixed­ effects model, which assumes that all clinical trials included in the meta-analysis are estimating the same treatment effect. They therefore ignore any variability between different studies when producing a sum­ mary estimate. An alternative approach, based on a random-effects model (e.g., DerSimonian and Laird, 1986), assumes that treatment effects may be different, and each study represents a random sample of a (theoretically infinite) number of studies. The variabil­ ity between studies is then an integral part of the ana­ lysis (Bailey, 1987), and the variations in the observed treatment effects can then result from two sources: (1) the sa�pling variation in each study (the within-study vanance), and (2) the variation of the true study effects about their mean (the between-study variance). The net result of such an analysis is that the interval estimate of treatment effect is generally widened relative to the fixed­ �ffect estimate, particularly if there is clear heterogene­ Ity between studies (Dickersin and Berlin, 1992). 17 For example, different dosage levels (analogous to different expo­ sure levels in observational studies: e.g., Frumkin and Berlin' 1988) may induce heterogeneity. 18 Odds ratios and relative risks are best plotted on a logarithmic scale.

Meta-analysis

Year

Number of individuals

1 990

1 52

2

1 990

1 90

3

1991

274

4

1 992

281

5

1 992

1 49

6

1 993

267

7

1 993

80

8

1 994

259

9

1 994

66

10

1 994

196

11

1 994

240

12

1 995

40

13

1 995

84

14

1 996

237

15

1 996

1 19

Study

Pooled results of random-effects model

2634

Odds ratio

Odds ratio

0.1

0.2

2

0.5

5

10

0.1 1 52

, ,

897 1 046 1313 1 393 1 652 1718 1914

.,

2 1 54 2 1 94

2634

Favou r s control

: , e: , , • , , --+, , ---:., : ---:-, , "t+, , � : -:.., , .:.....: ,

T*, , , , , , , , ,

Favours control

Favours treatment

(a)

Fig. 1 6.2

10

, ++, ,

2515

, , , , , r+, , ,

5

:-++,

2278

, , , •

2

0.5

616

0.2 •

342

Favours treatment

ll! l

(b)

A typical meta-analysis. (a) I ndividual results and pooled results u s i ng a random-effects model; (b) results of sequential analyses of

accumulating data .

: Point estimate of the odds ratio; - : 95% i nterval estimate of the odds ratio. (Based on Hematology/Oncology Clinics of

North America, 1 4, loa n n i d i s, I . P.A. et al. Meta-analysis in hematology and oncology, 973-991 . © 2000, with permission from E l sevier.)

In reality, whether or not the studies are all estimat­ ing the same treatment effect is not known. The results of tests for homogeneity therefore usually form the basis for deciding on the appropriate model. If the result of a test is non-significant, the fixed-effects model is generally employed; whereas significant results prompt a random-effects model. However, some statisticians argue that it is prudent always to employ a random-effects model, because some vari­ ation between studies is inevitable. Although the random-effects model may be attract­ ive, it needs to be interpreted with caution (Marubini and Valsecchi, 1 995). First, the degree of heterogeneity may be such that a random-effects model may greatly modify the inferences made from a fixed-effects model. This will tend to nullify the summary statistic for both models, and there is then a need to investigate the variability further. Secondly, specific statistical distributions of the random-effects model cannot be justified either empirically or by clinical reasoning. Finally, the random-effects model cannot be interpreted meaningfully at the level of the target population; it is merely the mean of a distribution that generates effects. The random-effects model therefore 'exchanges a questionable homogeneity assumption for a ficti­ tious distribution of effects' (Greenland, 1 987).

Debate continues over the relative merits of the fixed-effects and random-effects approaches. Some of the biases can be reduced by excluding poorly designed trials and including all relevant results (e.g., results from germane unpublished studies). With this goal in mind, Meinert ( 1 989) has suggested that meta­ analyses should be planned prospectively, with the component trials enlisted into a meta-analysis when they start, rather than being retrospectively identified. This should promote good individual trial design, and therefore consistent quality. Moreover, cumula­ tive meta-analyses may allow both fixed-effects and random-effects models to demonstrate efficacy in the presence of heterogeneity of estimates19. Presentation of results

Any pooled results, and the results of each study, should be reported as point estimates with 95% confidence intervals, and presented graphically next to one another. Figure 1 6.2 is an example. The results of the individual studies show considerable variability, with 19 There is, of course, danger of an increase in Type I error such as that which can occur in sequential trials. Yusuf et al. ( 1 99 1 ) suggest methods

of significance-level adjustment in this circumstance.

.l04

Clinical trials

some results (Figure 1 6.2a: Studies 3, 4, 5, 7, 8, 9, 1 1 and 13) providing no evidence of a treatment effect (the upper 95% confidence limits for the odds ratios being greater than one). This variability is masked in the analysis of the accumulating data (Figure 1 6 .2b), which consistently demonstrates a beneficial effect. The pooled results of the random-effects model and the final analysis of accumulating data, in this exam­ ple, generate similar point and interval estimates of the odds ratio, demonstrating a significant treatment effect. Meta-analysis is more advanced in human than in veterinary medicine, but is still a contentious issue. Responses to a meta-analysis of over 3000 random­ ized controlled clinical trials of preventive care in human pregnancy and childbirth (Chalmers et ai., 1989) ranged from describing it as 'arguably the most important publication in obstetrics since William Smellie wrote his A Treatise on the Theory and Practice of Midwifery in 1 752' to describing its authors as 'an obstetrical Baader-Meinhof gang' (quoted by Abramson, 1 991). However, meta-analysis is a power­ ful technique, which is likely to be applied more in veterinary science, and veterinarians should profit from the experience of their medical counterparts. Fu rther read i n g Bulpitt, c.J. (1983) Randomised Controlled Clinical Trials. Martinus Nijhoff Publishers, The Hague Chalmers, 1. and Altman, D.C. (Eds) (1995) Systematic Reviews. BMJ Publishing Croup, London. (A concise intro­ duction to medical meta-analysis) Code of Practice for the Conduct of Clinical Trials on Veterinary Medicinal Products in the European Community. Federation

Europeenne de la Sante Animale (FEDESA), 1 993. Rue Defacqz, 1 /Bte 8, B-I050, Brussels Conduct of Clinical Trials of Veterinary Medicinal Products

(1990) Committee of Veterinary Medicinal Products, Commission of the European Communities, Brussels. Document III/3775/90 Dent, N. and Visanji, R (Eds) (2001) Veterinary Clinical Trials from Concept to Completion. CRC Press, Boca Raton Duncan, J.L., Abbott, E.M., Arundel, J.H., Eysker, M., Klei, T.R, Krecek, RC., Lyons, E.T., Reinemeyer, C. and Slocombe, J.OD. (2002) World association for the advancement of veterinary parasitology (WAAVP): second edition of guide­ lines for evaluating the efficacy of equine anthelmintics. Veterinary Parasitology, 103, 1-18 Elbers, A.RW. and Schukken, Y.H. (1995) Critical features of veterinary field trials. Veterinary Record, 136, 1 87-192

Friedman, L.M., Furburg, C. and DeMets, D.L. (1996) Fundamentals of Clinical Trials, 3rd edn. Mosby, St Louis Guidelines for Clinical Trials (1 988) Questionnaire l OSS/A. International Dairy Federation, Brussels. (Guidelines with specific reference to mastitis) Guidelines for the Conduct of Bioequivalence Studies for Veter­ inary Medicinal Products (2001) The European Agency for

the Evaluation of Medicinal Products, EMEA/CVMP016/ oo-corr-FINAL Hunt, M. (1997) How Science Takes Stock: The Story of Meta­ Analysis. Russell Sage Foundation, New York. (A general description of the application of meta-analysis, with examples from numerous scientific disciplines) Meinert, c.L. and Tonascia, S. (1 986) Clinical Trials: Design, Conduct, and Analysis. Oxford University Press, New

York Moher, D., Cook, D.J., Eastwood, S., Olkin, 1., Rennie, D. and Stroup, D.F. (1999) Improving the quality of reports of meta-analyses of randomised controlled trials: the QUOROM statement. The Lancet, 354, 1896-1900. (Recom­ mended guidelines for reporting meta-analyses of clinical trials)

Moher, D., Schultz, K.F. and Altman, D.C. (2001 ) The CON­ SORT statement: revised recommendations for improving the quality of reports of parallel-group randomised trials. The Lancet, 35 7, 1 191-1 1 94; Journal of the American Medical Association, 28 5, 1 987-1991; Annals of Internal Medicine, 134, 657-662. (Recommended guidelines for reporting clinical trials)

Noordhuizen, J.P.T.M., Frankena, K., Ploeger, H. and Nell, T. (Eds) (1993) Field Trial and Error. Proceedings of the inter­ national seminar with workshops on the design, conduct and interpretation of field trials, Berg en Dal, Netherlands, 27 and 28 April 1 993. Epidecon, Wageningen Note for Guidance on Statistical Principles for Clinical Trials

(1998) The European Agency for the Evaluation of Medicinal Products, CPMP /ICH/363/96 Note for Guidance on Statistical Principles for Veterinary Clinical Trials (2001) The European Agency for the Evaluation of

Medicinal Products EMEA/CVMP /816/00 -Consultation Perino, L.J. and Apley, MD. (1998) Clinical trial design in feedlots. Veterinary Clinics of North America, Food Animal Practice, 14, 343-365 Pocock, S.J. (1983) Clinical Trials: A Practical Approach. John Wiley, Chichester and New York Proceedings of the First European Symposium on the Demonstra­ tion of Efficacy of Veterinary Medicinal Products, Toulouse,

1 9-22 May 1 992 Schukken, Y.H. and Deluyker, H. (1995) Design of field trials for the evaluation of antibacterial products for therapy of bovine mastitis. Journal of Veterinary Pharmacology and Therapeutics, 18, 274-283 Senn, S. (1993) Cross-over Trials in Clinical Research. John Wiley, Chichester and New York Spriet, A. and Dupin-Spriet, T. (1997) Good Practice of Clinical Drug Trials, 2nd edn. Karger, Basel

Diagnostic testing 00000000« ««00 000 0000000000

The range of diagnostic techniques that are currently available for the diagnosis of infectious and non­ infectious diseases is wide, and includes clinical and pathological examination; microbiological, biochem­ ical and immunological investigation; and diagnostic imaging (e.g., radiography and ultrasound). These tech­ niques may be used either to diagnose disease in the individual animal, or to investigate disease in popula­ tions. This chapter focusses primarily on the assessment and performance of diagnostic tests when applied to populationsl. Diagnosis of infectious diseases using serological methods is addressed first. This is followed by a more general discussion of diagnostic testing. Serological epidem iology Serological epidemiology is the investigation of dis­ ease and infection in populations by the measurement of variables present in serum. A range of constituents of serum can be measured, including minerals, trace elements, enzymes and hormones. One of the main constituents that is frequently measured is the specific antibody activity of immunoglobulins, and it is invest­ igation of antibodies that is commonly understood to comprise serology. Alternative terms for antibody measurement are 'titration' and 'assay'. Antibodies provide evidence of current and previous exposure to infectious agents; their assay is commonly employed in veterinary medicine as a relatively efficient and cheap means of detecting this exposure in both indi­ vidual animals and populations. The statistical methods employed to analyse anti­ body levels are equally applicable to other serological

tests, such as those that detect enzymes and minerals, in which case, however, results can be compared with normal reference ranges. These commonly include: (1) the mean ± 2 standard deviations for Normally dis­ tributed data, selected from a normal (i.e., reference) population, and (2) the middle 95% of values (i.e., from the 2.5th to 97.5th percentile: see Chapter 12) from a reference population for data that are not Normally distributed (Hutchison et al., 1991). Although values for reference levels are available in published tables (e.g., Kaneko et al., 1997), each laboratory should estab­ lish its own norms. If the values are Normally dis­ tributed, or can be transformed to Normality, then a one-sample t-test (see Table 14.1) can be applied to compare a sample's values with those of a reference population; otherwise one-sample non-parametric methods may be appropriate (see Table 1 4.2). The serological diagnosis of disease based on the detection of circulating antibodies is one of the tech­ niques available for the identification of current and previous exposure to infectious agents. This and other methods are listed in Table 1 7. 1 . A range of tests to Table 1 7. 1

Methods of d iagnosing i nfectious d i sease.

Evidence of current infection Isolation of agent Identification of agent's genes (molec u l a r epidemiology) CI i n ical signs Pathognomonic (characteristic) changes B iochemical changes Demonstration of an i mm u ne response: detection of antigens and antibodies (serological epidemiology) Evidence of past infection C l i n ical h i story

1 A detailed discussion of diagnostic testing applied to the individual in clinical practice is presented by Sackett et al. ( 1 991).

Pathognomo n i c changes Demonstration of an i m mune response: detection of antibodies

itll)

Diagnostic testing

detect antigen/ antibody reactions has been developed over the last 1 00 years, and more are being added to the range. Descriptions of these techniques are found in standard immunology texts (e.g., Hudson and Hay, 1989; Paraf and Peltre, 1 991; Roitt, 1 994; Tizard, 2000), and a basic knowledge of them is assumed. Emphasis is now generally shifting towards the detection of anti­ gens, rather than antibodies, in current infections.

Assaying antibodies

Table 1 7.2 Antibody titres expressed as rec iprocal d i l utions (X) and coded titres (log2X ) .

Reciprocal dilution (X) o

1 ( u nd i l uted serum) 2 4

2

8

3

16

4

32

5

64

6

Methods of expressi ng amou nts of anti body The concentration of antibody is expressed as a titre. This is the highest dilution of serum that produces a test reaction. Thus, if the highest dilution that pro­ duces a test reaction is 1 in 32, then the titre is 1/32. Alternatively, the reciprocal, 32, can be quoted, indic­ ating that the undiluted serum contains 32 times the antibody for the reaction. Animals with detectable antibody titres are seropositive; animals with no detectable antibodies are seronegative. Animals pre­ viously seronegative and now seropositive have seroconverted. However, classification of an animal as seropositive often is based on the titre being above a certain threshold level (cut-off point) (see below: 'Evaluation of diagnostic tests') . For example, animals with titres >1/32 may be classed at positive, whereas animals with titres �1/32 may be classified as negative. Logarithmic transformation of titres

Serum is usually diluted in a geometric series, that is, with a constant ratio between successive dilutions. The commonest ratio is 2. Thus, serum is diluted 1/2, 1/4, 1/8, 1/16, 1/32 and so on. This suggests that the titres should be measured on a logarithmic scale. There are two reasons for this measurement: 1.

2.

the frequency distribution of titres often is approx­ imately lognormal (see Figure 12.5); statistical tests that assume Normality may therefore be applied; geometric dilution series are equally spaced on a logarithmic scale; thus serum may be diluted geometrically 1 /2, 1 /4, 1 /8, 1/16 and so on, cor­ responding to log transformation to base 2, the respective logs to base 2 of the reciprocals of the dilutions being I, 2, 3, 4, and so on; the dilution can be coded as the value of these logarithms to base 2

(Table 17.2). In some cases, high concentrations of serum that react non-specifically are avoided by initially diluting by log1Q! and then continuing in log2 dilutions, thus: 1/10, 1/20, 1/40, 1/80.

Mean titres

H several coded (i.e., log2 transformed) titres are recorded, their arithmetic mean can be calculated. This is simply the sum of the coded titres divided by the number of titres. For example, if five titres are 1/2, 1/4, 1 /2, 1/8, and 1/4, then the coded titres are 1, 2, 1, 3, and 2, respectively. The arithmetic mean therefore is o + 2 + 1 + 3 + 2)/5 1 .8. The geometric mean titre (GMT) is the antilog2 of the arithmetic mean. This can be obtained from a pocket calculator with an'xY' function key on it. For instance, if the arithmetic mean of several coded titres 1 is 1 .8, then log2 GMT 1 .8; thus GMT 2 .8 3.5. H an initial logl O dilution has been carried out, sub­ sequently followed by log2 dilutions, values are divided by 1 0 before taking logarithms to base 2. For example, dilutions of 1/10, 1 /20, 1/40, 1/80 would be coded as 0, I, 2, 3 0/10 is coded 0 because it is equivalent to undiluted serum), giving a mean of 1 .5. Then: GMT/ 1 0 21 .5 2.8. Thus, GMT 28. The logarithm of zero cannot be expressed because it is 'minus infinity' . Therefore, when calculating means of coded titres, seronegative animals have to be excluded because their reciprocal titres are zero and therefore cannot be coded; mean titres can be calculated only for seropositive animals. Thus, when comparing coded antibody titres in populations, two parameters must be considered before inferences are made: the rel­ ative proportion of seropositive animals, irrespective of titre, and the GMTs of the seropositive populations. For instance, it might be found that in two dairy herds approximately 20% of cows in each herd were sero­ positive to Leptospira, serovar pomona, but that the GMT in one herd was 40 while in the other it was 640. Such circumstances might indicate a recent epidemic in the second herd and merely the persistence of anti­ bodies in convalescent animals in the first. Conversely, a serological survey of workers in two different abat­ toirs might reveal similar GMTs of complement fixing antibodies to Coxiella burnetti in each group of sero­ positive workers, but at one abattoir 30% of workers =

=

=

=

=

=

=

Assaying antibodies had titres, while at the other only 3% were seropositive. Such results would indicate a much greater probability of infection at the first abattoir, although the GMTs of the groups were similar.

Quantal assay A quantal assay measures an 'all-or-none' response; for example, agglutination or no agglutination, infected or non-infected. Two systems frequently are used: 1. 2.

single serial dilution assay; multiple serial dilution assay.

The first is the commoner. Both techniques utilize geometric (logarithmic) dilutions, the range of dilution depending on the sensitivity of the test. Sensitivity here refers to the ability of the system to detect amounts of antibody and antigen: the more sensitive the test, the smaller the amount of antibody and antigen it will detect. This is sometimes more fully termed analytical sensitivity, to avoid confusion with sensitivity as a validity parameter of a diagnostic test - more fully termed diagnostic sensitivity (Stites et al., 1 997). Single serial dilution assay

In a single serial dilution assay, each dilution is tested once. For instance, in a virus haemagglutination­ inhibition test, the highest dilution that prevents agglutination of erythrocytes on a test plate is the anti­ body's haemagglutination-inhibition titre. This is a relatively 'weak' form of measurement. If the titre is 1/32 it implies that 1/33 would not produce the effect. However, since 1/64 is the next highest dilution that is tested, the actual titre could lie between 1/63 and 1/32. Thus, this type of titration, which tests only dilution intervals, actually divides the dilutions into blocks. The blocking is more marked when titres are expressed as 'less than' or 'greater than' (e.g. 1/256). The data therefore are essentially ordinal (see Chapter 9).

Table 1 7.3 Serum

;i

Multiple serial dilution assay

In a multiple serial dilution assay, each dilution is tested several (preferably at least five) times. The object is to achieve a 'strong' measure. The end point is the dilution of a substance at which a specified number of members of a test group show a defined effect, such as death or disease. The most frequently used and statistically useful end point is 50% (Gad dum, 1933). Thus, in pharmacology, the toxicity of a drug can be expressed as an LOso (lethal doseso): the amount of drug that will kill 50% of test animals. An amount of drug therefore can be expressed in terms of the number of LOsos that it contains. Fifty per cent end-point titrations can also be used to estimate antibody concentrations, in which case antibody titres are expressed in terms of the dilution of serum that prevents an effect in 50% of members of a test group, the effect being produced by the infectious agent responsible for induction of the antibodies that are being titrated. For example, the dilution of serum that prevents infection of 50% of cell culture mono­ layers with a standard concentration of virus can be estimated: an 'effective doseso' (EOso). Several methods of calculating 50% end points are available, including the Reed-Muench and Spearman-Karber methods, and moving averages. The Reed-Muench method is not recommended because precision cannot be assessed, there is no validity test, and the method is less effi­ cient than some of the alternatives (Finney, 1 978). The second method (Spearman, 1908; Karber, 1931 ), which involves relatively simple calculations, is described below. Example of a Spearman-Karber titration The anti­ body titre to a virus is required. The defined measured response is a cytopathic effect (CPE) in cell culture monolayers. The test serum is diluted (usually in twofold geometric increments). One-tenth of 1 ml of each dilution is inoculated into groups of five cell cul­ ture monolayers, each of which has been inoculated with a fixed, potentially lethal, dose of the virus. Table 1 7.3 depicts the results. The 50% end point is the

Example of a 50% end-point titration (Spearman-Karber method). Log, 0 dilution

dilution

Mono{ayers showing

Intact mono/a yers

Proportion 'positive'

1-P

cytopathic effect

(intact) P

1 /1

0.0

5

1 .00

0.00

1 /2

-0.3

5

1 .00

0.00

1 /4

-0.6

5

1 .00

0.00

1 /8

- 0 .9

4

0.80

0.20

1 /1 6

- 1 .2

4

0.80

- 1 .5

3

2

DAD

0.20

1 /3 2 1 /64

- 1 .8

4

1

0.20

0.80

1 /1 28

-2.1

5

0 . 00

1 .00

0.60

1 1 )()

Diagnostic testing

dilution of serum that prevents a CPE in 50% of the monolayers in a group, that is, in two and a half monolayers (note that this is clearly a statistical estimation). According to the Spearman-Karber formula: log EDso = L - dCI,P - 0.5) where: L = log highest dilution at which all monolayers survive intact; d = log of the dilution factor (i.e., the difference between the log dilution intervals); IP = sum of the proportion of 'positive' tests (i.e., intact monolayers), from the highest dilution showing a positive result to the highest dilu­ tion showing all results positive (i.e., P = 1 ) . From Table 1 7.3: L = - 0.6 d = log1 02 = 0.3 IP = 0.20 + 0.40 + 0.80 + 0.80 + 1 .00 = 3.2. Thus: 10gl OEDso = -0.6 - {0.3(3.2 - 0.5») = - 0.6 - (0.3 x 2.7) = - 0.6 - 0.8 = -1 .4. Therefore, EDso

antilog (- 1 .4) = l /antilog 1 .4 = 1/25. 1 .

=

Thus 0.1 ml of serum contains 25.1 EDsos, and 1 ml contains 251 EDsos. The estimated standard error (e.s.e.) is calculated using:

e.s.e. (logl OEDso) = d I {P(1 - P»)/(n - 1) where n = number of animals in each group. Substituting the values from Table 1 7.3: loglOe.s.e. = 0.3�{ (0.2 x 0.8) + (0.4 x 0.6)

= 0.3 (O.1 6

+

(0.8

x

0.2) + (0.8

x

0.2)}/(5 - 1)

+ 0.24 + 0. 1 6 + 0.1 6)/4

= 0.13. Multiple serial dilution assays are now less common than previously because they are more expensive and slower than single serial dilution assays, and titrations conducted on single dilutions - notably the enzyme­ linked immunosorbent assay (ELISA). However, they still have a role in measuring vaccinal potency.

Serological estimations and com parisons in populations

A ntibody prevalence The presence of detectable antibody indicates that an animal or its dam has been exposed to the antigen that stimulates the antibody's production. In the absence of further challenge, the antibody level will decline. The rate of decline, usually measured in terms of the anti­ body's half-life (the time taken for its level to halve), varies between antibodies. Titres to some antibodies persist because the antibodies have a long half-life or there is persistent infection or repeated challenge. The possession of a long half-life explains why some vaccines can produce lifelong immunity after a single course. The half-life of vaccinal antibodies therefore is an important aspect of vaccinal efficacy (see also Chapter 1 6) and of passively acquired immunity in young animals. The half-life of antibodies following natural infection, however, is rarely estimated. If the amount of antibody in an animal population is to be estimated, without particular regard to the frequency distribution of antibody titres, animals are categorized as either 'positive' or 'negative', and the prevalence of antibodies in the population (i.e., sero­ prevalence), with its associated confidence interval, can be calculated using the methods described in Chapter 13. A titre cut-off point, below which animals are considered to be negative, and above which animals are categorized as positive, is often defined (see below). The prevalence of detectable antibody depends on the rate of infection, the rate of antibody loss and the time at which these rates have been effective. A high prevalence therefore may reflect not a high rate of infection but a low rate of antibody loss; recall (Chapter 4) that prevalence, P, is related to incidence, I, and duration, D:

p o d x D. It follows that not only the prevalence of detectable antibody in a population but also the titre in the individual is related to the half-life of the antibody. If the frequency distribution of antibodies is required, then, if the scale of measurement is 'strong' (e.g., an EDso) the mean and standard deviation can ' be quoted and confidence intervals can be calculated (see Chapter 1 2). The much more common single-serial dilution assays, which define a titre as the highest dilution producing a test reaction, produce ordinal data; this is particularly evident when a large proportion of the titres are expressed as 'less than' or 'greater than' a particular dilution. If there are not any 'less than' or 'greater than' titres, and there is a reasonable spread of

Serological estimations and comparisons in populations titres, then the log titres can be regarded as crude approximations to Normally distributed measure­ ments, and the mean, standard deviation and confidence intervals can again be quoted. However, if these assumptions are not met, the median and semi-interquartile range should be quoted. Confidence intervals for the median can also be calculated (see Chapter 12).

Rate of seroconversion If a population is susceptible to infection a t birth, the duration of antibodies following infection is lifelong, and mortality due to infection is negligible, a simple mathematical model can be used to describe the age distribution of antibodies for various rates of sero­ conversion (Lilienfeld and Lilienfeld, 1 980). If P = probability of becoming infected in one year (i.e., rate of seroconversion); = age in years; = probability of not having become infected by age (i.e., in years); = proportion of population that have become infected by age (i.e., seroprevalence at age then:

y

y

Plf

0 - p)Y

y

y

y),

Py = I - 0 - p)Y. It is also possible to estimate the rate of serocon­ version from age-specific seroprevalence values by inversion of the formula: 10gO -

p) = {logO - Py)}/y.

Therefore:

o - p) = antilog[ {logO - Py) }/y], and:

p = 1 - antilog[ {logO - P) Vy]. A series o f age-specific seroprevalence values can therefore produce estimates of rates of seroconversion, and changes in these can provide information on the patterns and effects of infection in a herd. Table 1 7.4 lists the age-specific seroprevalence values for anti­ bodies against bovine leucosis virus in a random sample of beef cattle. There is a slow increase in seroprevalence with age, up to and including 10 years. This infection produces chronic latent infections with persistent antibodies, and so the rate of seroconversion can be calculated. Thus, for one-year-old animals = 1):

(y

p = 1 - antilog[ {logO - 0.15) VI ] = 1 - antilog(- 0.0706/1 ) 1 - 0.850 = 0. 1 50;

=

for two-year-old animals

(y = 2):

)()'l

Table 1 7.4 Age-specific seroprevalence and an nual mean seroconversion rates for bovine leukosis virus reactors in a sample of Lou i s iana beef cattle, 1 982-1 984. (Mod i fied from Hugh-Jones and H ubbert, 1 988.)

Age (years)

Number of cattle tested

Seroprevalence

67

0. 1 5

0. 1 50

2

191

0.21

0.1 1 1

3

1 05

0.23

0.083

4

1 43

0.39

5

1 67

0.40

0.1 1 6 0.097

6

1 37

0.47

0 . 1 00

7

98

0.53

0 . 1 02

(PyJ

Annual mean seroconversion rates (p)

8

92

0.55

0.095

9

32

0.63

0. 1 05

10

53

0.60

0.088

> 1 0*

19

0.37

0.036

* Average age used i n calcu l ating p= 1 2 .5 .

p = 1 - antilog[{logO - 0.21 ) }/2] = 1 - antilog(-0.1024/2) = 1 - 0.889 = 0.111;

and s o on. There is a steady estimated rate of seroconversion in animals up to 10 years of age, suggesting that the disease is having little impact on the herd: if diseased animals were being culled, a reduction in estimated seroconversion rates (because of the removal of seropositive animals) could be expected from about 6 years of age. The relatively high seroconversion rate in animals 1 2-23 months of age could (speculatively) be due to the curiosity of young heifers or persistent passive immunity. The low seroprevalence and sero­ conversion rate in animals greater than 10 suggests that preferential culling of affected animals is only taking place at that age. Houe and Meyling ( 99 1 ) and Houe et al. ( 995) further exemplify calculation of rate of seroconversion in relation to bovine virus diarrhoea virus infection. More complex models, which can be applied to infections in which antibodies decline during life, are reviewed by Muench ( 959).

Com parison of antibody level s Comparison of two different populations

If a comparison of two different populations in terms of presence and absence of antibody (i.e., 'positive' or 'negative' animals) is required, then the X2 test can be used; alternatively, confidence intervals for dif­ ferences between two proportions for independent samples can be calculated (see Chapter 14).

l !)

Diagnostic testing

Table 1 7.5

Serum anti body titres (SNso: serum neutral izing doseso') of dogs, for two types of rabies vaccine, before and 60 days after vaccination.

( F rom Merry and Kolar, 1 984.) Pre-vaccination titre

Dog number

Vaccine

Titre 60 days after vaccination

Reciprocal

K i l led vaccine

A653

3

0.48

214

2.33

A6 1 6

3

0.48

1 82

2.26

2Cl 0

2

0.30

280

2 .45

2B39

2

0.30

267

2 .43

2 B4 7

2

0.30

1 98

2 . 30

2.4

0.372

228

2.354

Xl =

1 1 .77;

nl

=

5; I

XI

2

= 2 7 . 73 3 9 ; Xl = 2 . 3 54; 51

=

0.083.

K i l led vaccine

A603

3

0.48

10

1 .00

porc i n e cel l

A654

2

0.30

51

1 .7 1

l i ne origin

A6 1 8

2

0.30

9

0.95

2C1 6

2

0.30

16

1 . 20

2C3

2

0.30

38

1 . 58

2.2

0 . 3 66

25

1 .288

Mea n : I

10gl O

fel i ne cell origin

Mea n : I

Reciprocal

Xl

=

6.44;

n2

= 5; I

x/ = 8.763; x2 =1 .288; 52 = 0 . 3 4 2 .

I f the frequency distributions o f antibodies in two populations are to be compared, then, if the scale of measurement is 'strong', a parametric test can be used. Moreover, since antibodies are usually lognormally distributed, standard tests that assume Normality can be used. An EDso' calculated in multiple serial dilution assays, is a 'strong' measurement. The following example uses the data in Table 1 7.5 relating to vaccination titres in two groups of five dogs, one group vaccinated with killed rabies virus of porcine origin, and the other with vaccine of feline origin. The comparison is between the titres in each group, 60 days after vaccination. Log titres are used; this transformation allows the assump­ tion of Normality. Student's t-test for independent samples less than 30 can be used (see Chapter 14), assuming unknown variance. Using the same notation as that in Chapter 14,

nl 5, i\ 2.354, 51 = 0.083, n2 = 5, x2 = 1.288, 52 = 0.342. =

the numerator is the greater of the two. This ratio is then compared with the appropriate percentage points of an F-distribution (Appendix XXIII) with a pair of degrees of freedom, the first being one less than the sample size used in calculating the variance in the numerator, and the second being one less than the sample size used in calculating the variance in the denominator. In this particular case:

5 l/51 2 = 1 7.0 with (4,4) degrees of freedom. The 1 % point of the corresponding F distribution is 15.98. The sample value of 1 7.0 is greater than this value. The sample value therefore is significant at the 1 % level and there is strong evidence to suggest that the variances of the 10gl O of 60-day antibody titres differ between groups. The test statistic in this situation is now: t = (Xl

=

The hypothesis to be tested is that there is no dif­ ference in 60-day antibody titres between the dogs vaccinated with killed rabies virus of porcine origin and dogs vaccinated with vaccine of feline origin. Let f11 and f12 be the mean 60-day titres in the two groups, and let 0 = f11 - f12 . The hypothesis then may be written as 0 = O. 2 2 First it is necessary to check that 51 and 5 2 are estim­ ates of a common population variance. This is done by calculating the ratio of the two variances, where

- x2 - 8)/ �(5/ /nl ) + (5/ /n2)

with approximate degrees of freedom, v, given by:

V = (VI + v2)2/ ! v1 2/(nl - 1 ) + vl/(n2 - I ) } where:

and:

V2 = 5 22/n 2 to take account of unequal variances (Snedecor and Cochran, 1 989).

Interpreting serological tests For this example:

Table 1 7.6

(2.354 - 1.288 - 0) / �(o.0832 /5) + (0.3422 /5) = 1.066/ �0.001 38 + 0.023 39 = 6.773.

Haemagglutinins (H) and neuraminidases (N)

Thus:

V = (0.001 37 + 0.023 41)2 /(0.000 000 466 + 0.000 37) = 4.47. Rounding down to the nearest whole number, when using the t-table (Appendix V) there are only degrees of freedom because the variances differ significantly. From Appendix V, the value for 4 degrees of free­ dom is which is less than Therefore, the two groups of dogs have significantly different mean titres at the level. Note that the result is also significant at the level and the level. An alternative approach is estimation of confidence intervals for the difference between the means of two independent samples, noting that the variances (and therefore the standard deviations) differ (see Chapter Single-serial dilution assays present a more difficult choice of statistical test because the titres are ordinal. Again, if there are not any 'less than' or 'greater than' titres, and there is a reasonable spread of titres, then the log titres can be regarded as crude approximations to Normally distributed measurements, and a t-test for independent samples can be used; otherwise the non­ parametric Wilcoxon-Mann-Whitney test should be applied; alternatively, confidence intervals can be cal­ culated for the difference between two medians for independent samples (see Chapter

4

5%

6.773.

5%

2%

The classification of some influenza A viruses. (Ma i n l y

from M u rphy a n d Webster, 1 990; Zambon, 1 998.)

t=

2.776,

;I

1%

14).

14).

Comparison of different estimates on the same population

Strains

Hl Nl

PR!8/34

HI N I

Sw/Ia/1 5/30

H2 N 2

S i n g/l/57

H 3 N2

H K/l /68

H3 N2

Sw/Taiwan/70

H3 N 8

Eq/M i a m i/l /63

H3 N 8

NEq-2/Suffol k!89

H3 N8

NEq-2/Newma rket2/93

H3 N8

NEq-2/Newma rket2/95

H4 N 6

Dk!Cz/56

H5 N 3

Tern/S.A./61

H6 N 2

Ty/Mass/3 740/65

H7 N 7

Eq!Prague/l /5 6

H7 N7

NBury/1 2 3 9/94

antigens can be detected in the early stages of virus replication. Some of the antigens are shared by several groups of isolates and are the basis of division into broad categories. Other antigens are unique to a par­ ticular group of isolates. For instance, influenza type A viruses are distinguished from types B and C by their core nucleoproteins and matrix proteins. Influenza A viruses are divided into subtypes on the basis of their surface haemagglutinin and neuraminidase antigens. Similarly, subtypes are divided further into strains according to more refined differences in the antigenic composition of the haemagglutinins and neuram­ inidases (Table 1 7.6). This refinement in antigenic definition is also termed specificity. This is sometimes more fully termed analytical specificity (Stites et al., to avoid confusion with specificity as a validity parameter of a diagnostic test - more fully termed diagnostic specificity (see below). The epidemiological value of a serological test, for example when tracing the spread or origin of a particu­ lar infection, increases in relation to the test's ability to detect more refined antigenic differences. The new molecular diagnostic techniques are particularly valuable in this respect (see Chapter Serological tests vary in their ability to detect subtle antigenic differences. Table 1 7.7 illustrates varying refinement of serological tests for influenza A viruses. The complement fixation test (CFT), using virus extracted from chorioallantoic membranes as antigen, will detect antibody against virus nucleoprotein, and therefore is specific only to the level of virus type. However, the use of whole virus as antigen results in a CFT that is specific for subtypes because it will detect particular subtypes of haemagglutinins and neuraminidases. Identification of specific strains is possible if carefully selected reference strains are used

1997),

If a population is sampled twice over a period of time, and animals are classified as positive or negative, then a suitable comparison can be made using McNemar's change test (see Chapter If the frequency distribu­ tion of antibodies is to be compared, then a t-test for related samples should be applied - again using log titres to assume Normality (see Chapter The test is described in standard statistical texts. The appropriate non-parametric equivalent is the Wilcoxon signed ranks test (see Chapter Again, confidence intervals can be calculated for the difference between two means or two medians for related samples (see Chapter

14).

14).

14).

14).

I nterpreting serological tests

Refinement Infectious agents have a variety of antigens on their sur­ faces and in their interiors. Additionally, non-structural

2).

lI )

Diagnostic testing

Table 1 7.7

Sum mary of tests for influenza serology. (From Stuart-Harris and Sch i ld, 1 9 76.)

Test antigens

Test

Antibody detected

Recommended useS

Serosurvey

Serodiagnosis ++++

HI

Whole virus

HAl;

++++

NI

Whole v i ru s

NAI;

++++

CF

C A M extract

NP

Whole virus

HA, NA

Whole v i rus*

HA, NA

Disrupted virus*

NP, M P

IDD

Disrupted v i rus*

HA, NA

+

++

NP, M P

+

++

N-IHA

Disrupted vi rus* NA

SRD

HI

=

haemaggluti nation i n h ibition

NI

= neura m i n idase i n h i bition

CF

=

complement fixation

SRD

=

s i ngle rad i a l i m m u nod iffu sion

IDD

++ +++ +++

++++ +++

NA

++++

= i mm u no-double-diffusion

N - I H A = neura m i n idase- i n d i rect haemagglutination HA

=

NA

=

haemaggl u t i n i n neura m i n idase

NP

=

n ucleoprotei n

MP

=

matrix prote i n

CAM

=

chorioallantoic membrane

e

The useful ness of the test for the i nd i cated p u rpose i s expressed on a scale of + (least u sefu l ) to ++++ (most u sefu l ) .

I; Serum contai n i ng h igh anti body titre t o t h e second su rface antigen (HA or NA) may a t l o w d i l utions and u nder certa i n conditions cause i n h i b ition. * Test refinement (specificity) ach ieved by selecting v i ruses or recombinant viruses with the req u i red antigenic composition.

as antigens; the titre of antibodies to haemagglutinins and neuraminidases is highest when the antibodies are directed against the strain-specific antigens. It should be emphasized that one type of test is not always more refined than another (e.g., radial immunodiffusion versus complement fixation) for all antigen/antibody reactions; the refinement also depends on the nature of the antigen that is used in the test.

Table 1 7.8

Reasons for positive and negative results in serological

tests. (From Stites et al., 1 982.) Positive results Actual infection G ro u p c ross-reactions Non-specific i n h i bitors

}

true +ve false +ve

Non-specific aggl uti n i ns Negative results Absence of i n fection

true -ve

Natural or i n duced tolerance

Accu racy In common with other diagnostic tests, 'false positives' and 'false negatives' can occur (see Chapter 9). Table 1 7.8 lists the reasons for positive and negative results in serological tests.

I mproper tim ing I m proper selection of test Non-specific i n h i b itors e.g. anticomplementary serum; tissue culture toxic su bstances

false -ve

Antibiotic i n duced i m m u noglobu l i n suppression I ncomplete or block i n g antibody Insensitive tests

Positive results

A true positive result derives from actual infection. False positive results occur for a variety of reasons. Group cross-reactions can occur between an infec­ tious agent and antibodies to different organisms with similar antigens. For example, infection with Yersinia enterocolitica, 0:9, can produce antibodies that cross­ react with Brucella abortus antigens (Kittelberger et al., 1995). Similarly, cases of paratuberculosis (Johne's

disease) can produce positive reactions to mammalian and avian tuberculin (K6rmendy, 1988). Non-specific inhibitors present in serum may inhibit reactions that normally are associated with the action of intact antigens that are not specifically bound to antibody. These inhibitors therefore mimic the effects of antibody in the latter's absence. An example is non-specific inhibitors in haemagglutination tests

Evaluation and interpretation of diagnostic tests against influenza viruses. Agglutination of antigen by non-specific agglutinins similarly mimics the effect of antibodies that are agglutinins.

Table 1 7.9

Relative analytical sensitivity of assays for antigens and

antibodies. (From Stites et al., 1 997.)

Technique

Negative results

A true negative result indicates absence of infection. Again, false negative results can occur for several reasons. Some animals show natural or induced toler­ ance to antigens and therefore do not produce anti­ bodies when challenged with the agent. Thus, exposure of the bovine fetus to bovine virus diarrhoea in the first half of gestation results in offspring that do not produce detectable antibodies when challenged with the same strain of virus (Coria and McClurkin, 1978). Improper timing may result in a test's failure to detect infection. For instance, sampling of some cows before abortion, using the CFT, may not detect Br. abortus because detectable complement fixing antibodies may not appear until after abortion (e.g., Robertson, 1971 ). Some tests may be unsuitable for detecting infec­ tion. Thus, infection by African swine fever virus cannot be detected using a serum neutralization test because infected pigs do not produce detectable levels of neutralizing antibodies (De Boer, 1 967); an immunofluorescence test will, however, detect antibodies. Some non-specific inhibitors will produce false negative results by their mode of action (d. those above that produce false positive results) . Some sera, notably contaminated and haemolysed specimens, are anticomplementary; thus complement cannot be fixed in the CFT and the test is therefore assumed to be negative although antibodies may be present. This can occur with CFTs for Br. abortus infections (Worthington, 1 982). Similarly, substances that are toxic to tissue culture monolayers may mimic the effects of un-neutralized virus, giving the impression that neutralizing antibodies are absent when they may be present. Some antibodies are incomplete and so cannot take part in antigen/antibody test reactions. A common type of canine autoimmune haemolytic anaemia is characterized by incomplete antibodies on the surface of red blood cells, which can only be detected by an antiglobulin test (Halliwell, 1 978). Occasionally block­ ing antibodies prevent antigen/antibody reactions occurring. This occurs sometimes when conducting CFTs for bovine Br. abortus infection (Plackett and Alton, 1975), as a result of excess IgG1 blocking IgG2 (the latter being responsible for complement fixation) at low concentrations: this is the 'prozone' effect. Finally, a serological test may be too insensitive to detect antibody. Sensitivity in this context again refers to the ability of a test to detect amounts of antibody or

)

Approximate sensitivity (per dl)

Total serum proteins (by b i u ret or refractometry)

1 00 mg

Serum prote i n electrophoresi s (zone electrophoresis) Analytical u ltracentrifugation

1 00 mg 1 00 mg

I mm u noelectrophoresis

5�1 0 mg

I m m u nofixation

5�1 0 mg

S i ngle rad i a l d i ffusion

95% ), values of a proportion. Values of sensitivity and specificity may exceed 95%, and application of this formula can then lead to anomalies (e.g., an upper confidence limit greater than 100%). In such circumstances, Appendix VII may be

.l l {,

Table 1 7. 1 1

Possible results of a d i agnostic test.

True status

Test status

Totals

Diseased

Not diseased

Diseased

a

b

a+b

Not d iseased

c

d

c+d

Totals

a+c

used, if the sample size is small. However, the method of Wilson (1927) is now generally recommended. This involves calculating three values, A, B and C, where, for a 95% interval: A = 2r + 1.962; B = 1.96�1.962 + 4r(1 P) ; C = 2(n + 1.962); where: r = number of individuals with the feature of interest; n = number in the sample; P = observed proportion. The confidence interval is then (A - B)/C, (A + B)/C. For example, if 130 known negative animals are tested, and 128 are test-negative (d in Table 1 7. 1 1 ), the point estimate of specificity = d/b+d = 128/130 = 98.5%, and the 95% confidence interval is derived thus: A = 2 x I28 + 1.962 = 256 + 3.84 = 259.84; B = 1.96 �1.962 + 4 x 128 x (1 - 0.985) 1.96 �3.84 + (512 x 0.015) = 1.96�11.52 = 6.65; C = 2(130 + 1.962) = 267.68. Thus (A - B)/C = (259.84 - 6.65)/267.68 = 0.946, and (A + B)/C = (259.84 + 6.65)/267.68 = 0.996. That is, the 95% confidence interval = 94.6%, 99.6%. (Note that the inappropriate application of the formula for interval estimation of a proportion de­ scribed in Chapter 12 would have generated a lower interval of 96.3%, but an impossible upper interval of 100.6%.) If other confidence intervals are required, then 1.96 is replaced by the appropriate multiplier (Appendix VI). -

Another approach to estimation of the precision of sensitivity and specificity involves modelling the most likely mean, minimum and maximum values from a series of point estimates from several studies. A common method uses the beta-pert distribution2. An example, relating to diagnostic tests for bovine brucel­ losis, is given by Jones et al. (2004b). Alternatively, the two extreme percentiles and the median may be modelled ( Johnson, 1997). Youden's index

Youden's index, I, combines sensitivity and specificity in a single value of test performance: I = sensitivity + specificity - 1; or, using the notation in Table 1 7. 1 1 : a + d 1. 1=a+c b+d It can take values between 1 (when sensitivity and specificity each equal 100%) and - 1 (when sensitivity and specificity each equal 0%: an unlikely situation). An approximate 95% confidence interval is given by: 1 - 1.96

ac + bd , (a + c)3 (b + d)3

ac + bd (a + c)3 (b + d)3 This index assumes that sensitivity and specificity are of equal importance, which, as has already been noted, is not usually the case. Its value in judging the value of a test to a disease control programme is therefore limited. 1 + 1.96

---

=

Pred ictive value

When using either serological or other screening tests to determine the presence of disease in a population, it is important to know the probability that an animal, 'positive' according to the test, is actually positive; alternatively that a test-negative animal is a true nega­ tive. These probabilities are the predictive values of the test. The parameter most often quoted as the predictive value of a test is the predictive value of a positive (as opposed to negative) test result. 2 The beta distribution is a basic distribution of statistics for variables bounded at both sides (Snell, 1 987). 'Pert' (Pleguezuelo et al., 2003) is an acronym for Project Evaluation and Review Techniques (originally developed in the contex t of the Polaris missile system), which are stochas­ tic modelling techniques for estimating probability distributions (see Chapter 19).

......•.. .. ............

The predictive value depends on specificity and sensitivity and prevalence. Sensitivity and specificity are innate characteristics of a test for a given reference population, and (for a defined cut-off point) are relatively stable3, but the prevalence of a disease in a population being tested will affect the proportion of test positive animals, pT, that are actually diseased. There are two components to pT: 1. the true positives; 2. the false positives. The proportion of animals, pT, is then: IF x sensitivity) + {(1 - P) x (1 - specificity)). For example, if P 0.01 (1 %), sensitivity = 0.99 (99%) and specificity = 0.99 (99%), then: pT {0.01 x 0.99) + {(1 - 0.01) x (1 - 0.99)) = 0.02. This represents an overestimation of 100% (the actual prevalence is 0.01 and the estimated prevalence is 0.02). The smaller the prevalence, the larger the proportional overestimation, that is, the lower the predictive value (positive test result). The predictive value (positive test result) is given by: p x sensitivity (P x sensitivity) + {(1 - P) x (1 - specificity)) ' and the predictive value (negative test result) is given by: (1 - P) x specificity {(1 - P) x specificity) + {P x (1 - sensitivity)) (Galen, 1982). (Again, if these parameters are quoted as percentages, 1 is replaced by 100 in the formulae.) Alternatively, the calculation can be expressed more simply in terms of the values in Table 1 7.1 1 : Sensitivity a/(a + c). Specificity d/(b + d). The predictive value (positive test result) =

=

=

=

a/(a + b).

The predictive value (negative test result) d/(c + d).

3 Variations i n sensitivity and specificity, however, can occur. For example, they may be related to differences in severity of lesions, and host characteristics such as body condition (Sergeant et ai., 2003). The underlying continuous traits on which tests are usually based have fre­ quency distributions that vary between populations, and so the distribu­ tion of these traits, relative to the cut-off point, also varies. Since the distribution also determines prevalence, and misclassification of indi­ viduals is more likely when they have values close to the cut-off point, sensitivity and specificity can vary with prevalence (Brenner and Gefeller, 1997). The term 'spectrum bias' has been used to describe the variation in sensitivity and specificity with the distribution of the traits (Ransohoff and Feinstein, 1978).

Evaluation and interpretation of diagnostic tests

117

Table 1 7.1 2 Sensitivity and spec ificity of fou r scree n i ng tests for bovi ne brucel losis.

Sensitivity (%)

Specificity (%)

Tube agglutination test

62.0

99.5

Complement fixation test

97.5

99.0

Brewer card test

95.2

98.5

ELlSA*

96.0

99.0

* Positive threshold 20.220; specificity i n non-vacc i n ated cattle (see Table 1 7. 1 0) .

Predictive values are proportions, and so confidence intervals can be calculated in similar fashion to those for sensitivity and specificity. Five screening tests (or modifications of them) are available for brucellosis testing: the tube agglutination test (TAT), the CFT, the Brewer card test, the ELISA, and the milk ring test. Sufficient data are available to estimate the sensitivity and specificity of the first four (MAF, 1977; Agriculture Canada, 1984). These are summarized in Table 1 7.12. Assume that the TAT will be applied to 100 000 cattle in three different areas in which the prevalence of brucellosis is 3%, 0.1 % and 0.01 % respectively. From these data, and the figures in Table 1 7.12, the sensitiv­ ity, specificity and predictive value (of a positive test result) of the test can be calculated for the populations in each of the three areas. The results are given in Tables 1 7.13a, b and c, respect­ ively. As the prevalence of disease declines, so does the predictive value of the test, which could result in an increasing proportion of healthy animals being destroyed in a test and slaughter programme. This is also demonstrated in Table 1 7.10. At low prevalence levels, even relatively 'good' tests (sensitivity 99%; specificity = 99%) have a low pre­ dictive value (Figure 1 7.2). If a test with a sensitivity of 0.990 (99%) and a specificity of 0.999 (99.9%) were used in a disease eradication campaign, then, if the pre­ valence were 0.1 (10%), a single test conducted on 10 million animals would record 990 000 true positives and 9000 false positives. The test therefore would be acceptable at the beginning of the campaign. However, as the campaign proceeded, the prevalence would fall. When the prevalence was reduced to 0.0001 (0.01 %), the test would record 9900 true positives and 9990 false positives. The number of false positives would be unchanged after the disease was eradicated. Therefore acceptable levels of sensitivity and specificity depend on the stage of a control or eradication campaign. Ideally, towards the end of an eradication campaign, a more sensitive and specific test is required if the campaign depends only upon a single serological test. In practice, other techniques are used, such as serial =

IIH

Diagnostic testing

Table 1 7. 1 3

Predictive value (positive test result) of the tube agglutination test for bovine brucel losis at th ree d ifferent prevalence level s

(sensitivity = 6 2 % ; specificity = 99.5%).

True status

Test status Brucellosis present

Total Brucellosis absent

(a) Prevalence of brucellosis: 3 % Brucellosis present

1 860 (a)

485 (b)

1 1 40 (c)

2345

Brucellosis absent Total

96 5 1 5 (d)

97 655

3000

97 000

1 00 000

Predictive value (positive result) = a/(a + b) = 79.3% (b) Prevalence of brucellosis: 0. 1 % Brucellosis present

62

500

562

Brucellosis absent

38

99 400

99 438

1 00

99 900

1 00 000

Total Predictive va lue (positive result) = 1 1 .0% (c) Prevalence of brucellosis: 0. 0 1 % Brucellosis present

6

500

506

Brucellosis absent

4

99 490

99 494

10

99 990

1 00 000

Total Predictive va lue (positive result) = 1 . 2 %

1 00 80 60 40 20

. \.+\ -+�+" +�\. �." \" ......... +

I I 1 00

Fig. 1 7.2

I 50

I 20

I I 10 5

Prevalence (010)

1-'

2

1

T ,

0.30.1

The relations h i p between prevalence and predictive

val ue of a positive test result.

+:

Sensitivity = 99%; specificity = 99%.

. : Sensitivity = 70%; specificity = 70%.

testing (see below), isolation of infected farms and maintenance of disease-free areas. In some tests there are no false positives, for example, when identifying blood parasites by microscopic examination of blood films. Estimation of true pre­ valence in this circumstance is discussed by Waltner­ Toews et al. 0986c). Further discussion of the predictive value of sero­ logical and other diagnostic tests is provided by Vecchio (966), Galen and Gambino (975) and Rogan and Gladen (978). L i kelihood ratios

The dependence of predictive values on prevalence is a major disadvantage when a summary measure of

a test's performance, when the test is applied in a population, is required. The likelihood ratio provides a suitable summary measure, which is independent of prevalence. It compares the proportion of animals with and without disease, in relation to their test results. The likelihood ratio of a positive test result

(LR+)

is the ratio of the proportion of affected individuals that test positive, and the proportion of healthy indi­ viduals that test positive. Using the notation and data of Table 1 7.13a: LR+ = [a/(a + c)lI[b/(b + d)] = 0860/3000)/(485/97 000) = 0.620 00/0.005 00 = 124. Thus, a positive result is 124 times as likely to come from an animal with brucellosis, as from an animal without the disease. The LR+ is therefore a quantitative indication of the strength of a positive result. The per­ fect diagnostic test would have an LR+ equal to infinity (detecting all true positives, and generating no false positives), and the best test for ruling in a disease is therefore the one with the highest LR+. Note that the above formula comprises a/(a + c), that is, the sensitivity (the true-positive rate); and b/(b + d), that is, 1 - specificity (the false-positive rate). It may therefore be expressed, alternatively, as: LR+ = sensitivity/O - specificity). The likelihood ratio of a negative test result

(LR-)

is the ratio of the proportion of affected individuals

Evaluation and interpretation of diagnostic tests

that test negative, and healthy individuals that test negative; that is: LR- = [ c/(a + c)l! [d/( b + d)] = (1140/3000)/(96 515/97 000) = 0.380 00/0.995 00 = 0.382. Thus, a negative result is approximately only 0.4 times as likely to come from an animal with brucellosis, as from an animal without the disease. The perfect diag­ nostic test would have an LR- equal to zero (producing no false negatives, but detecting all true negatives), and the best test for ruling out a disease is therefore the one with the lowest LR-. Note, again, that the above formula comprises c/(a + c), that is, 1 - sensitivity (the false-negative rate) and d/(b + d), that is, the specificity (the true-negative rate). It may therefore be expressed, alternatively, as: LR- = (1 - sensitivity)/specificity. The above formulae for the LR+ and LR- indicate that these parameters are a function only of sensitivity and specificity. It is for this reason that they are relat­ ively stable. The likelihood ratio is the ratio of two proportions, and approximate confidence intervals can be calcu­ lated via a logarithmic transformation using the for­ mulae for computing approximate confidence intervals for the relative risk, based on cumulative incidence (see Chapter 15). The calculation is not possible with zero values in either cells a or b. Altman et al. (2000) recommend the addition of 0.5 to each of the four cells to facilitate the calculation in this circumstance. Nam (1995) describes a more complex method, which is reputed to perform better than the previous method. Relationship between likelihood ratios and odds

Further characteristics of the likelihood ratio can be explored when the parameter is considered in the context of odds: the ratio of the probability of an event occurring to the probability of it not occurring (intro­ duced in Chapter 15). Four new terms may now be introduced, exemplified using data in Table 1 7.13a. First, the pre-test probability (Bayes' 'prior probab­ ility': see Chapter 3) of disease is the proportion of animals in a population that have a disease before a test is applied; this is simply the prevalence of disease (0.03). Secondly, the post-test probability (Bayes' 'poste­ rior probability') of disease is the proportion of test-positive animals that are diseased. This has been introduced earlier as the predictive value of a positive test result (0.793). Thirdly, the pre-test odds of disease is the ratio of the pre-test probability of disease and the pre-test probability of not being diseased:

)Jq

(3000/100 000)/(97 000/100 000) = 0.0300/0.9700 = 0.030 93. Finally, the post-test odds of disease is the ratio of the post-test probability of disease and the post-test probability of not being diseased: (1860/2345)/(485/2345) = 0.7932/0.2068 = 3.8356. The LR+ is also the ratio of the post-test odds of disease to the pre-test odds of disease; that is, 3.8356/0.030 93 = 124. The pre-test, and post-test, odds of disease are therefore related through the LR+: pre-test odds of disease x LR+ = post-test odds of disease. Probability, however, is a more familiar quantity than odds, and so may be considered a more 'user-friendly' value with which to work. The two quantities are related thus: pre-test probability = pre-test dds, 1 - (pre-test probability) and post-test odds post-test probability. (post-test odds) + 1 For example, using the data in Table 1 7.13a: pre-test probability (i.e., prevalence) = 0.03, LR+ = 124. Therefore, pre-test odds 0.03/(1 - 0.03) 0.030 93, post-test odds = 0.030 93 x 124 = 3.84, and post-test probability = 3.84/(3.84 + 1) 0.793 (i.e., the positive predictive value). These calculations can be obviated by using a nomo­ gram4 (Figure 1 7.3). For example, if the pre-test prob­ ability is 0.30 (30%), and the LR+ is 20, a ruler is placed through the 0.30 point on the left-hand vertical line and through the value 20 on the middle line. A post­ test probability of 0.90 (90%) is then identified on the right-hand line. -'----�-----"'----

=

=

=

likelihood ratios in clinical practice

A major advantage of likelihood ratios over sensitivity and specificity is that they can be computed for dif­ ferent ranges of values of continuous or ordinal test 4 A nomogram is a graphical representation of the relationship between more than two quantities.

0.99

0.001 0.002 0.005

0.95

0.01

1 000

0.90

0.02

200

0.80

50

0.70

500

1 00

0.05

0.60

20 10 5

0.10

0.50

0.40

2

0.20 0.30

0.30

0.20

.5

0.40

.2

0.60

.05 .02

0.50

0. 1 0

.1

0.70

0.05

0.80

.01 .005

0.02

0.90

.001

0.01

.002

0.005

0.95

0.002 0.99

0.001

Pre-test probabil ity

Table 1 7.1 4 et al., 200 1 .)

DLS

Fig. 1 7.3 Nomogram depicting the relationship between pre-test probab i l ity of d isease, l i ke l i hood ratios, and post-test probabi l ity of d i sease. (Modified from Fagan, 1 9 75.)

Likelihood

Post-test

ratio

probability

Likeli hood ratios of a positive test result (LR+) for h i p dysplasia in dogs, u s i ng a dorsolateral subluxation score (DLS). (Data from Lust

Hipdyspfasia present

Hipdyspfasla absent

LR+ for different cut-offs DLS cut-off

LR+

LR+ for different ranges DLS range

LR+

20% as affected: sensitivity = (4 + 5 + 98)/114 = 0.9386, specificity = 070 + 18 + 2)/199 = 0.9548; and so on, for the other cut-off values. Likelihood ratios can now be computed for each cut-off. Thus at the >20% pp point: LR+ = sensitivity/O - specificity) = 0.9386/0 - 0.9548) = 21, and:

6 ROC curves were developed in the 1950s to assess the detection of radar signals, and became established in medicine in the early 1980s (Hanley and McNeill, 1982).

7 In common with other ELISA tests, the test for N. caninum generates an ELISA value by comparison with positive reference serum; this can lead to PP values in excess of 100%.

ROC cu rves

Table 1 7.1 5 Estimates of sensitivity and specificity, and I i kel ihood ratios, for d i fferent bands of percentage positivity values for an ELISA for Neospora caninum i n fection in d a i ry cattle. (Study reported i n Davison et al. ( 1 999); raw data suppl ied by Helen Davison, Veterinary Laboratories Agency, New Haw, U K.)

% positivity

Known positives

0-1 0 >1 0-1 5 > 1 5 -20 >20-25 >25-3 0 >30-1 07 Totals

Known negatives

0 3 4 4 5

1 70

98 1 14

6 1 99

18 2 3 0

Cut-off

Sensitivity

Specificity

LR+

LR-

>1 0 >1 5 >20 >25

1 . 000 0.9737 0.9386 0.9035

0.8543 0.9447 0.9548 0.9648

6.9 18 21 30

0.00 0.03 0.06 0. 1 0

>30

0.8596

0.9648

29.9

0. 1 5

LR+ = l i ke l i hood ratio of a positive test result.

LR- = l i ke l i hood ratio of a negative test result.

Table 1 7.1 6

Cal culation of the area under the ROC c u rve. (Data from Table 1 7. 1 5.)

% positivity >

Number of times

Total scores: number

Number

Total scores:

Total score

known-positive values

known-positive values

ofties

ties (number of

(A + B)

0 3x18 4x2

27 4

known-negative values

>

known negative values (A)

O x 1 70

0-1 0 >1 0-1 5 >1 5-20 >20-25

3 x 1 70 (4 x 1 70) + (4 x 1 8) (4 x 1 70) + (4 x 1 8) + (4 x 2 )

>25-3 0 >30-1 07 Total

(5 x 1 70) + (5 x 1 8) + (5 x 2) + (5 x 3 ) (98 x 1 70) + ( 9 8 x 1 8) + (98 x 2) + ( 9 8 x 3) 2 1 901

LR- ==

(1 - sensitivity)/specificity (1 - 0.9386) /0.9548 == 0.06; and so on, for other cut-off values. The curve is close to the top left-hand corner, sug­ gesting that the test is a good one. Moreover, the PP cut-off point that maximizes sensitivity and speci­ ficity is >15 ({sensitivity + specificity}/2 0.9592 - the largest value obtainable from Table 1 7.15). Altman et al. (2000) describe computation of confid­ ence intervals for the ROC curve. ==

==

Area under the curve

- also termed diag­ is a global assessment of a test's performance. This area equals the probability that a random individual with disease has a higher value of the test variable than a random healthy individual (if the variable is raised in sick individuals). A perfect test thus yields an AUC of 1, whereas an uninformative test gives a value of 0.5. Calculation of the AUC is related to the Mann­ Whitney statistic (see Chapter 14), and is based on every comparison of individuals in the known­ positive and known-negative groups. A score is attached to each comparison pair: the value, one, is The area under the curve (AVC) nostic accuracy -

510 752 760

ties x 0.5): (B)

4x3

6

537 756 766

294 331

965 1 9 208 22 2 3 2

965 1 8 91 4

98 x 6

awarded when the known-positive value is greater than the known negative value; 0.5 is scored when the two values are equal ('ties'); and zero is allotted when the known-positive value is less than the known­ negative value. The scores are then summed, and divided by the number of comparisons. This calculation is exemplified in Table 1 7.16, using the data in Table 1 7.15. Thus, in the >10-15 PP class, three known-positive animals have values greater than 170 known-negative animals (those with PP values 010), and so there are 3 x 170 such comparisons, each with a score of one, resulting in a total score value of 510. Additionally, in this class, there are three known-positive animals and 18 known negatives, con­ stituting 3 x 18 ties, each with a score value of 0.5, that is, a sum of (3 18) 0.5 27. Thus, the total score attributed to this class is 510 + 27 537, and so on for the other classes. (Score values of zero need not be tabulated because they do not contribute to the score total.) The final score total is therefore 22 232, and there are 22 686 comparisons (114 known positive animals multiplied by 199 known negative animals). The AUC is thus 22 332/22 686 0.984. This value is high (the perfect test having a value of one), again providing evidence that the ELISA test is a good one. Confidence intervals can be calculated for the AVC (Altman et al., 2000). x

x

==

==

==

Evaluation and interpretation of diagnostic tests

Greiner et al. (2000) present a fuller discussion of ROC curves. Aggregate-level testing

Tests may also be applied to aggregates o f animals (e.g., pens and herds) with the object of classifying the aggregate, rather than its individual members, as either diseased or healthy. If there is one biological sample (e.g., a bulk milk sample or a pooled faeces sample) from each aggregate, the formulae for sensit­ ivity, specificity and predictive value, described above, may be applied. Assessment of the aggregate's status is also uncomplicated if the true status of test-positive animals can be ascertained quickly using a gold stand­ ard. However, if only a sample of animals is tested in each aggregate, sensitivity and specificity at the aggregate level are affected not only by the sensitivity and specificity at the individual level but also by the sample size. The overall effect is that, for a defined sensitivity and specificity at the individual level, aggregate-level sensitivity increases and aggregate­ level specificity decreases as the sample size increases. Aggregate sensitivity, Sea (the proportion of af­ g fected herds that test positive5, depends on individual­ animal sensitivity, specificity and prevalence, and the number of animals sampled: Seass = 1 - (1 - pT) n where: pT = test prevalence; = number of animals sampled. For example, if the true prevalence, P, is 0.25 in each of several herds, sensitivity = 0.97, specificity = 0.98, and four animals are selected from each herd, then: pT = IP x sensitivityl + 1 (1 - P) x (1 - specificity) l 10.25 x 0.97l + {(1 - 0.25) x (1 - 0.98)} = 0.2575. Thus: Sea '� = 1 - (1 - 0.2575)4 x, = 1 - 0.74254 = 1 - 0.3039 = 0.70. That is, 70% of all affected herds have one or more test­ positive animals in the sample of four animals that are tested in each herd; alternatively, 30% of affected herds will not be detected. Aggregate specificity, SPagg (the proportion of unaf­ fected herds that test negative), depends on individual­ animal specificity and the number of animals sampled: SPagg = (specificity) n n

=

For example, if a test of specificity 0.98 is applied to samples of four animals from several herds, then: SPagg = 0.984 = 0.92. Therefore, 92% of all unaffected herds will have no test-positive animals in the samples of four animals that are tested in each herd; alternatively, 8% of disease-free herds will be scored as affected. Note that the formula for Seagg and SPagg' above, should only be applied when the sampling fraction in each aggregate is less than approximately 5%. Martin (1988) and Jordan and McEwen (1998) discuss this topic in detail. Multi ple testing

Multiple testing involves the use of more than one test, and is commonly encountered in clinical diag­ nosis and herd testing. Two main approaches can be adopted (Fletcher et al., 1982): parallel testing and serial testing; Parallel testing

Parallel testing involves conducting two or more tests on animals at the same time, and animals are considered to be affected if they are positive to any of the tests. For example, during brucellosis eradication in the UK, cows that aborted were tested routinely for brucellosis by means of bacterial culture from a vaginal swab, the Rose Bengal Test on serum and the milk ring test on milk, and animals were defined as affected if they were positive to any test. Parallel testing is often undertaken when animals are admitted to clinics, and an assess­ ment is required quickly. In comparison with each individual test, parallel testing increases sensitivity and therefore the predictive value of a negative test result, but reduces specificity and positive predictive value. A disease is therefore less likely to be missed; however, false positive diagnoses are more likely. Parallel testing effectively asks the animal to 'prove' that it is healthy. The sensitivity of two tests, A and B, applied in parallel, is calculated thus: 1 - [(1 - SeA) x (1 - SeB )] where SeA = sensitivity of test A; and SeB = sensitivity of test B. The parallel specificity is derived thus: SPA x SPB

where SPA = specificity of test A; and SPB = specificity of test B.

Table 1 7.1 7 The effect of para l l e l and serial test i ng on sensitivity, specificity and predictive value for two tests (A and B ) . (Modified from Fletcher et al., 1 988.) Sensitivity (%)

Test

Specificity (%)

Predictive value

Predictive value

(positive resu/tj(%)*

(negative result)(%)*

92 97 99 93

A

80

B

90

60 90

33 69

A and B (para l l e l )

98 72

54 96

35 82

A a n d B (serial) * For 20°!., preva lence.

The derivation of parallel values may be better understood by a numerical example. Consider two tests, A and B (Table 1 7.1 7), applied to a population in which disease prevalence is 0.20 (20%). Test A detects 80%, leaving 20% undetected (i.e., sensitivity = 0.80). Test B detects 90% of the remaining 20% = 18% (i.e., sensitivity = 0.90). Therefore, parallel sensitivity (proportion positive to either test) = 80% + 1 8 % = 98%.

Applying the appropriate formula: parallel sensitivity 1 - [(1 - SeA) x (1 - SeB)] =

1 - [(1 - 0.80) x (1 - 0.90) 1 - (0.20 x 0.10) = 0.98 (98 % ) =

=

Test A categorizes 6 0 % of true negatives as negative (i.e., specificity = 0.60). Test B categorizes only 90% of these as negative (i.e., specificity = 0.90). Therefore, parallel specificity (proportion negative to both tests) = 90% x 60% = 54%.

Applying the appropriate formula: parallel specificity SPA X SPB =

= 0.90 x O.60 = 0.54 (54%).

These parallel values can now be used to complete a contingency table, and compute predictive values (Table 1 7.18).

Positive predictive value

=

Negative predictive value

=

1 9.6/56.4 = 35%. 43.2/43.6 = 99 % .

Serial testing

In serial testing, tests are conducted sequentially (i.e., consecutively), based on the results of a previous test.

Table 1 7. 1 8

Relationships (test status a n d true status) under para l lel

testing, derived from Table 1 7. 1 7.

True + (%) Test + (either) (%) Test - (both) (%) Totals (%)

True - (%)

1 9.6

36.8

0.4

43.2

20

80

Totals (%) 56.4 43.6 1 00

Conventionally, only those animals that are positive to an initial test are tested again; therefore only animals that are positive to all tests are considered to be affected. Thus, Serpulina hyodysenteriae infection (see Chapter 5) is initially diagnosed by a fluorescent antibody test per­ formed on faecal or gut mucosal smears; the status of positive animals is then confirmed by bacterial culture. Serial testing maximizes specificity and the predictive value of a positive test result, but lowers sensitivity and negative predictive value. More credence therefore can be attached to positive test results, but there is an increased risk that disease will be missed. Serial testing effectively asks the animal to 'prove' that it is affected by the condition that is being investigated. The test with the highest specificity should be used first to decrease the number of animals that are tested again. The sensitivity and specificity of two tests, A and B, applied in series, are calculated thus: Sensitivity SeA x SeB Specificity 1 - [(1 - SPA) x (1 - SPB)] using the same notation as above. Employing the values in Table 1 7. 1 7: Test A detects 80%. Test B defines 90% of these as positive. Therefore, serial sensitivity (proportion positive to both tests) 80% x 90% =

= 72%;

that is, SeA x SeB = 0.80 x 0.90 = 0.72 (72%). Test A correctly categorizes 60% of true negatives, leaving 40% . Test B categorizes 90% of these as negative = 90% x 40% = 36%.

Evaluation and interpretation of diagnostic tests

Positive predictive value = 14.4/17.6 = 82%.

For instance, in tuberculosis eradication in the UK, using the comparative intradermal test, reactors are culled, and inconclusive reactors retested after 42-60 days, with usually up to two retests allowed. If visible lesions of tuberculosis are found at post-mortem examination, or laboratory testing of pooled lymph nodes gives a positive result, the whole herd is subjected to two 'short-interval' tests 60 days apart. If post-mortem examination fails to find lesions, and pooled lymph nodes yield negative results, only one 60-day test is required. If the short-interval tests are clear, movement restrictions are lifted, and a further test is carried out in 6 months; if still clear, a further check is conducted in another 12 months' time. If the latter whole-herd test is clear, the herd is returned to a less stringent 4-year testing cycle, or to a routine testing interval for the area9. The important characteristics of multiple test strategies are listed in Table 1 7.20. Multiple testing is discussed in more detail by Smith (2005).

Negative predictive value = 76.8/82.4 = 93%.

Diagnostic tests i n i m port risk assessment

Table 1 7.1 9 Relationships (test status and true status) under serial testi ng, derived from Table 7 7. 7 7. True + (%) Test + (both) ('Yo)

Test - (either) ('Yo) Totals (o,{,)

True- (%)

1 4 .4

3.2

5.6

76.8

30

Totals (%)

80

1 7 .6 8 2 .4 100

Therefore, serial specificity (proportion negative to either test) = 60% + 36% = 96%; that is, 1 - [(1 - SPA) x ( 1 - SPB)] = 1 - [(1 - 0.60) x ((1 0.90)] = 1 - 0.40 x 0.10 = 0.96 (96%). These serial values can again be used to complete a contingency table, and predictive values computed

(Table 1 7.19).

Serial testing is an important part of disease eradica­ tion campaigns in which positive animals are culled from herds (see Chapter 22). Animals defined as dis­ eased by an initial screening testS are subjected to fur­ ther tests to confirm their status, so that false positives are not unnecessarily removed. The formulae for calculating parallel and serial sensitivity and specificity assume that the tests are independent, that is, measure different manifestations of disease (e.g., antibodies or presence of microbes identified microscopically). If tests are not independ­ ent (e.g., two variations of an antibody-detection test), then the parallel and serial sensitivity can only be obtained empirically. Negative-herd retesting

Testing can also be conducted only on animals that are negative to an initial test. This is usually applied at herd level, and involves periodically retesting animals in previously test-negative herds with the same test. Negative-herd retesting is an important component of eradication campaigns. It improves aggregate-level sensitivity; that is, it increases the likelihood of detect­ ing on a premises an infectious agent that eluded detection earlier (e.g., because antibodies had not yet been produced, or the infection was subsequently reintroduced). It therefore asks a herd to 'prove' that it is free from the condition that is being investigated.

8

' }

Ideally, the first test should detect all cases.

Knowledge of a test's sensitivity and specificity enables predictions to be made about the risk of importing infected animals or products with various importation rules. The probability of missing an infected individual using a given diagnostic test is (1 sensitivity); this probability would therefore be 0.05 if a test with a sensitivity of 0.95 (95%) were being applied. Recall, however, that the predictive value of a diagnostic test also depends on disease prevalence. The probability of an animal that is negative to a test being actually infected, Pn' is: P(1 - Se)

P(1 - Se) + (1 - P) x Sp where P is the true prevalence, Se sensitivity, and Sp specificity (Marchevsky et al., 1 989). If animals were being quarantined, exclusion of false positive animals is of little concern, and so specificity can be assumed to be 1 . Table 1 7.21 lists the values of Pn for various values of P when a test with a sensitivity of 0.95 is used. The probability of any test-negative animal being infected increases when the prevalence in the source population increases. Moreover, at a given prevalence, the probability of including even one test-negative infected animal in a group of imported animals, Pc' increases as the number of animals in the group increases ((Marchevsky et ai., 1 989): =

=

9 There are some parishes in England and Wales where disease levels are high enough to warrant a 2-year routine testing interval.

,'i,

Diagnostic testing

Table 1 7.20

Characteri stics of m ultiple test strategies. (Mod ified from S m ith , 1 99 5 .)

Test strategy

Consideration

Effect of strategy

Parallel

Serial

I ncrease sensitivity

I ncrease specificity

Negative-herd retesting I ncrease sensitivity at aggregate level

G reatest predictive value

Negative test resu l t

Negative test result at

Positive test result

aggregate level R u l e out a d isease

Pu rpose Appl ication and sett i ng Comments

R u l e in a d i sease

R u l e out a d i sease Test and removal progra mmes

Rapid assessment of i nd ividual

Diagnosis when t i me is not crucial;

patients; emergencies

test and removal programmes

Useful when there is an i m portant

Useful when there i s an i m portant

Useful when there i s an i m portant

penalty for m i ss i ng a d i sease ( i .e . ,

penalty for fa lse positive results

penalty for m i ss i ng a d i sease ( i .e.,

false negative results)

false negative results)

Table 1 7.21 The proba b i l ity that a test-negative a n i mal i s actu a l l y infected, when sensitivity = 0.95 and specificity = 1 . ( F rom MacD i a rm id, 1 99 1 .) Prevalence

Probability (Pn)

0.01

5 .05 x 1 0-4

0.05

2.63 x 1 0-3

0.10

5 . 5 2 x 1 0-3

0.20

1 .2 3

Table 1 7.23 The proba b i l ity that a test-negative, i nfected animal will be incl uded i n a group destined for i m port (prevalence = 0.0 1 , sensitivity = 0.95 and specificity = 1 ; entire group tested.) (Modified from OlE Scientific and Technical Review, 1 2 (4), December 1 99 3 . ) Croup size

Table 1 7.22

x

Probability

Probability (ifa single

(if reactor animal only excluded) (PeY

group); probability of

reactor disqualifies

no test-positives ({3J

1 0-2

The proba b i l ity that a test-negative, infected a n i mal

w i l l be i ncl uded i n a group destined for i m port when only reactor

1 00

4.92

X

1 0-2

5 . 00 x l 0-2

200

9.61

X

1 0-2

2.50 X 1 0 - 1

300

1 .4 1

X

1 0-1

1 .2 5

X

1 0-4

400

1 .8 3

x

1 0-1

6.25

x

1 0-6

500

2.23

X

1 0-1

3.1 3

X

1 0-7

a n i m a l s are excluded (preva lence = 0.01 , sensitivity = 0.95 and specificity = 1 ) . (From MacD iarmid, 1 99 1 .)

Probability (Pc)

Croup size

5 .04 x 1 0- 1

10 20

1 .00 X 1 0-2

30

1 .50 X 1 0-2

50

2 .49

x

1 0-2

1 00

4.92

X

1 0-2

500

2 .2 3

X

1 0-1

{

(1 - P) X Sp

Pc = 1 (1 - P) x Sp + P(1 - Se)

}n

,

where n is the group size. If a policy dictates that a positive test result only dis­ qualifies the individual animal that reacts positively, then the risks associated with such a policy are Pn (Table 1 7.21 ) and Pc (Table 1 7.22). Alternatively, it may be decided that a positive test result in any one animal will disqualify the entire group (e.g., tests for OlE List A diseases: see Chapter 1 1 ), in which circumstance the probability of disqualifying an infected group increases as the prevalence and/or group size increases. The probability of a test failing to detect at least one test-

positive animal in an infected group, /3, thus identi­ fying the group as infected, can be calculated (MacDiarmid, 1987): /3= { l - (t x Se) / n }l'lI, where t = the number of animals that are tested in the group, n = group size, p = group prevalence. Thus, the difference in risk between these two policies can be compared (Table 1 7.23). The risk of an infected animal being imported is considerably reduced when a single reactor disqualifies the entire group, rather than only the test-positive individual. Jones et al. (2004b) develop this approach for serial testing strategies in the context of the risk of importing brucellosis-infected cattle from Ireland into the UK, where surveillance for infection in the exporting coun­ tries involves an initial screening test using either the serum-agglutination test (Northern Ireland) or the micro-agglutination test (Republic of Ireland), followed by confirmation of test-positives by the complement-fixation test. Import risk assessment is addressed comprehens­ ively by Murray (2002) and OlE (2004).

Evaluation and interpretation of diagnostic tests Table 1 7.24 G u ide l i nes for validation of d iagnostic tests. (Modified from Preventive Veterinary Medicine, 45, Greiner, M. and Gardner, 1 . 0 . Epidemiologic issues i n the validation o f veterinary d i agnostic tests, 3-2 2 . © (2000), with permission from E l sevier.) General The test pu rpose and the analytical u n it are descri bed The test protocol is sufficiently descri bed Reference test (gold standard) The choice of the reference method i s j u stified (a necessary condition i s that it should be more accu rate than the test that i s bei ng evaluated); and the method i s fu l l y described or referenced Selection of reference populations The reference population is sufficiently descri bed (time, location, and a n i ma l characteristics such as breed, age and gender) The reference population should reflect the ta rget population (see Chapter 1 3) and i nclude an appropriate spectrum of d i sease and spectrum of other conditions The sampl ing frame should be an u n b i ased representation of the reference population (see Chapter 1 3 ) Selection criteria must be stated and should reflect the testing situation Sampling of the reference population The sampl i n g procedure is descri bed in deta i l Exclusion o r incl usion criteria ( i f any) are descri bed (see Chapter 1 6) Sample sizes must be stated and shou ld reflect the degree of the req u i red statistical prec ision Random and systematic sampling are the preferred option (see Chapter 1 3 ) Performance of test and reference test The testing protoco ls are sufficiently descri bed ( i nc l u d i n g definition of negative and positive results) Results of test and reference test are evalu ated i ndependently (bli nded) (see Chapter 1 6) Presentation of results Methods of estimating parameters are explai ned by formu l ae; estimates are presented together with sample sizes and confidence intervals (exact confidence i ntervals are preferred to approxi mate); sensitivity and specific ity are always req u i red, add itional parameters may be presented as necessary; the 2

x

2 table used i n generating estimates should be d ispl ayed

ROC analysis shou ld be presented for test outcomes measured on ord i nal or cont i n uous scales The n u mber of i ntermedi ate results and results that cannot be i nterpreted (if any) and reasons for m issing data are given Discussion of results The test-performance parameters should be d i scu ssed i n relation to the study design and the i ntended or cu rrent use of the test; if the gold standard is i m perfect, this should be d i scussed i n relation to the effect on the study results

G u idel i nes for val idati ng d iagnostic tests The components of a comprehensive protocol for valid­ ating a diagnostic test are summarized in Table 1 7.24. Some authorities recommend that at least 300 true positives and 1000 true negatives are used to deter­ mine sensitivity and specificity, respectively ( Jacobson, 2000). Such values will dictate the precision with which the two parameters are estimated. The precision can be varied and predetermined by using the appro­ priate formula for estimation of sample size for a simple proportion (see Chapter 13: 'Estimation of disease prevalence: simple random sampling'). A review of sample size determination for various diagnostic test parameters is presented by Obuchowski (1998).

and specificity) 1 0, in which circumstance agreement between different tests may be assessed, without ll assuming that one test is the best . The logic of using this approach, argued by some authorities, is that agreement between tests is evidence of validity, whereas disagreement suggests that the tests are untrustworthy (although it is possible that tests could agree by being consistently wrong). Table 1 7.25 presents the results of an examination of pigs' heads to identify atrophic rhinitis using two tech­ niques: cross-sectional and longitudinal examination. The observed proportion agreement between the two tests, OF = (a + d)/n, where n = (a + b + c + d). Sub­ stituting the values in Table 1 7.25:

OF = (8 + 223 )/248 =

Agreement between tests The kappa statistic

If a gold standard is not available, it may not be possible to assess easily a test's validity (i.e., sensitivity

0 . 932 .

10 Some complex methods have been developed to assess validity when only an imperfect reference test is available (Hui and Zhou, 1998; Enoe et ai., 2000; Pouillot and Gerbier, 2001; Pouillot et a/., 2002; Frossling et a/., 2003), and are facilitated by appropriate software (AFSSA, 2000). 11 The proportion of all test results on which two or more different tests agree is sometimes termed concordance (Smith, 2005).

Pil

Diagnostic testing

Table 1 7.25

N u mber of pigs' heads showing turbi nate atrophy

by cross-sectional and longitu d i n a l exa m i n ation of 248 heads. (Data derived from Visser et al., 1 988.)

Longitudinal examination

Cross-sectional examination Atrophy present

Atrophy absen t

8 (a) 1 6 (c)

2 2 3 (d)

Atrophy present Atrophy absent

1 (b)

This comparison, however, does not consider the agreement between the two tests that could arise just by chance. A more rigorous comparison can be made by calculating a statistic, kapp a (see Table 14.2), which takes account of chance agreement. First, the expected proportion of agreement by chance, EP, is calculated. This is simply the sum of the expected proportion of agreement for the positive and negative results. Expected proportion agreement by chance (both positive), EP+ = I( a + b)/nl x I( a + c)/nl = { (8 + 1 )/2481 x 1 (8 + 16)/2481 = 0.0363 x 0.0968 = 0.003 5 1 . Expected proportion agreement b y chance (both negative), EP- = { ( c + d)/nl x I ( b + d)/nl = 1 ( 1 6 + 223)/2481 x { ( 1 + 223)/2481 = 0.964 x 0.903 = 0.870 49. Thus:

EP = (EP+) + (EP-) = 0.003 51 + 0.870 49 = 0.874. Observed agreement beyond chance, OA

= OP - EP = 0.932 - 0.874 = 0.058. Maximum possible agreement beyond chance, MA

= l - EP = 1 - 0.874 = 0 . 1 26.

Kappa is the ratio of the observed agreement beyond

chance to the maximum possible agreement beyond chance, that is:

kappa = OA/MA = 0.058/0.126

ates excellent agreement, whereas $;0.40 indicates poor agreement. Everitt (1 989) suggests >0.81 : almost perfect agreement; 0.61-0.80: substantial agreement; 0.41-0.60: moderate agreement; 0.21-0.40: fair agree­ ment; 0-0.20: slight agreement; 0: poor agreement. Altman ( 1 991a) suggests >0.80: very good agreement; 0.61-0.80: good agreement; 0.41-0.60: moderate agree­ ment; 0.21-0.40: fair agreement; and $; 0.2: poor agree­ ment. Thus, the point estimate of kappa, 0.46, suggests moderate agreement between the two methods of examination of pigs' heads. The same approach can be used to assess clinical agreement; kappa values between 0.5 and 0.6 being expected when comparing the results of a diagnosis made on the same animals by different clinicians. Confidence intervals can be calculated for the ob­ served proportion of agreement (Samsa, 1 996) and for kappa (Everitt, 1 989), in which circumstance the lower confidence limit should lie above 0.40 before at least moderate agreement can be inferred (Basu and Basu, 1 995). Sim and Wright (2005) discuss sample size. The kappa statistic can also be generalized to studies involving dichotomous nominal data with several ratings of subjects, to nominal data with several cat­ egories (Fleiss et al., 2003), and to ordinal data (Cicchetti and Allison, 1 971). However, it is not suitable for assessing agreement between tests based on continu­ ous data, where other techniques are more appropriate (Bland and Altman, 1 986; Maclure and Willett, 1987; Bland, 2000). Kappa may also be defined differently in the contexts of agreement and correlation (Bloch and Kraemer, 1 989). Note, too, that the correlation coefficient (see Chapter 14) is not a valid indicator of agreement between two tests or measurement methods (Bland and Altman, 1 986). Perfect correla­ tion will exist between two methods if the points lie along any straight line; whereas perfect agreement is obtainable only if the points lie along the line of equality. Kappa values need to be interpreted with caution. For instance, a low kappa value could indicate that only one test is good, or that both tests are bad, or that both tests are good but negatively correlated (which can occur with some antigen and antibody tests). Moreover, its value depends on the prevalence of the attribute of concern (Sargeant and Martin, 1998). Byrt et al. ( 1 993) and Lantz and Nebenzahl (1996) discuss the bias that can occur in calculating kappa, and methods for correcting it.

= 0.46.

Kappa ranges from 1 (complete agreement beyond chance) to 0 (agreement is equal to that expected by chance), whereas negative values indicate agreement less than is expected by chance. Arbitrary 'bench­ marks' for evaluating observed kappa values have been recommended. Fleiss et al. (2003) suggest �0.75 indic-

Reliability

The value of a diagnostic test is also judged by its reliab­ ility (see Figure 9.6), that is, the extent to which its results are stable. This can be explored by running the test two or more times on the same samples in the same laboratory under the same conditions, and assessing

Practical application of diagnostic tests the repeatability of the results (see Chapter 9). Tests that are used in several laboratories (e.g., those that are recognized as international standards) also require their reproducibility (see Chapter 9) to be determined. The statistical procedures for assessing repeatability and reproducibility are based on agreement between results. Thus, calculation of a kappa is appropriate for nominal and ordinal data. An individual clinician's diagnoses made on the same animals on different occa­ sions, for example, are likely to produce kappa values between 0.6 and 0.8. Again, appropriate methods must be sought for continuous data (Bland, 2000). Serological tests The repeatability of serological tests depends on a variety of factors including the degree of standardization of test reagents and the expertise of the tester; similarly, reproducibility might be affected when the same serum sample is analysed by different laboratory technicians in different labor­ atories. Thus, a twofold difference in antibody titre between samples from the same animal, taken at dif­ ferent times, may reflect either a true change in titre or similar titres associated with low repeatability or reproducibility. Generally, a geometric fourfold change in antibody titre (e.g., from 1/16 to 1/64) is assumed to reflect a real change; a twofold change is not considered to be significant. Table 1 7.26 illustrates the reasoning behind this decision. The table shows typical results when sera from 100 individuals are tested twice. Each of the two readings should be identical for a single serum sample. However, the table shows that this is true only for 62

Table 1 7.26

Typical titres of sera from 1 00 i n d ividuals tested twice.

(From Paul and White, 1 9 73.) First reading

Second reading

(reciprocal titre)

(reciprocal titre)

1;

tion. Since then, many other proposed models have considered how best to control bovine tuberculosis. However, the mode of transmission is still unclear, and so such models cannot be fully exploited. Rabies in foxes

Foxes are hosts of rabies in North America and Europe, and constitute a serious obstacle to control of the disease. The infection became established in foxes in Poland towards the end of the Second World War. The epidemic spread slowly westwards at a rate of about 30 km/year. The standard method of control was slaughter of foxes, but results were disappointing. A mathematical model (Macdonald and Bacon, 1980) suggested that control, other than by slaughter of foxes, would be more successful. The model has two components: 1. prediction of the course of the disease in fox populations; 2. evaluation of different control policies. The model of the disease in fox populations makes plausible assumptions about the host and parasite. Foxes breed once a year in the autumn, and fox mort­ ality is highest in the winter, resulting in an annual fluctuation in fox numbers. The virus has a long incubation period and can therefore survive in hosts of high, changing and low densities (see Figure 6.4); in the last circumstance it can exist for a long time in individuals. If rabies enters a fox population, the future of the host and parasite will be affected by the number of healthy foxes that are infected by rabid foxes; expressed as a ratio, this is the contact rate. If the disease is modelled for various contact rates, there are different predicted outcomes; these are shown in Figure 19.4a. The upper lines of the graphs represent the total fox population, the lower lines the healthy foxes, and the shaded areas the number of rabid foxes. The horizontal lines represent the number of foxes that, theoretically, can be carried by the habitat. A con­ tact rate of 0.5 (one rabid fox infecting half a healthy fox) will, according to Kendall's Threshold Theorem (see Chapter 8), be insufficient to allow the infection to become established; the model supports this. Higher contact rates result in fluctuation in the fox population and in the number of rabid foxes. A contact rate of 1 .4 allows the disease to persist, oscillating annually. A contact rate of 1 .9 produces epidemics every 4 years that are severe enough to reduce the population to a level that will not support infection. The infection again becomes epidemic when the fox population recovers. Field surveys have shown that this periodic­ ity is demonstrated in European foxes. Higher contact rates would lead to extinction of the fox population.

Hil

Modelling '"

VI

x

Rabies begins

.2 0 z VI '" x

.2 0 z '"

VI

x

.2 0 z '" VI

x

.2 0 z (a)

Foxes ext i n ct

2 3 4 5 6

Yea r

Rabies begins

K

Virus extinct

gJ X

_..Lr.......

.2

���� 1 2 �3 �4L-5� �6�7�8�9L-l�

(b)

Year Control strategies:

K

S

V

Fig. 19.4

=

controlled fox kill

=

temporary steril ization of foxes

=

bait vaccination of foxes

(a) Merlewood model of rabies in foxes; (b) Merlewood

model of alternative control strategies for contro l l i ng rabies in foxes. In each graph, the i n itial level of the fox population is the same. (From Macdonald and Bacon, 1 980.)

The second component of the model considers three control techniques (Figure 1 9 .4b): 1 . slaughter; 2. temporary sterilization; 3. bait vaccination of foxes. In case A, a single cull is instituted when rabies is at its earliest detectable level. Although slaughter ini­ tially decreases the prevalence of the disease, the latter soon increases again and then follows a pattern similar to that in the graph in Figure 1 9 .4a depicting a contact rate of 1 .9.

In case B, killing takes place later, probably when rabies in more likely to have been detected. Para­ doxically, although initially there are more cases, the disease and the kill work together because more of the foxes that are not killed are incubating rabies and therefore will die. The virus thus becomes extinct as the fox population is dramatically reduced. Case C represents two killings, separated by 6 months. Again, the virus becomes extinct, but the fox population is reduced below the levels in A and B. Three applications of temporary sterilizing agent are illustrated in case D. The virus again is extinguished, but the fox population is reduced further. Vaccination of foxes using bait vaccine-laden bait, shown in case E, offers the best results: removing the virus from the population and maintaining the num­ ber of healthy foxes (with 60% of foxes assumed to be immunized). This model therefore suggests a more efficient and ecologically acceptable way of controlling fox rabies than slaughter. This type of oral vaccination is being used successfully in Europe (Milller, 1991; Pastoret and Brochier, 1998), where it can be complemented by the control of fox populations (Aubert, 1994). Oral vaccination is also being applied to other sylvatic hosts in North America. A criticism of simple models based on differential calculus is the common assumption that parameters remain constant throughout the period of operation; for example, that the survival rate of infective organisms does not change during a season, whereas, in reality, climatic variation may alter survival rates from day to day. Some models do have time-dependent parameters, but this may lead to a model for which a solution is unobtainable or make the operation of the model clumsy. A major feature of such models is that they enable the long-term behaviour of the parasite popula­ tion to be studied. The population may either become extinct, or increase indefinitely, or reach a steady state. It is often whether or not a steady state exists and the nature of the steady state that is of interest, although for many diseases of production animals the initial progression may be of paramount importance if eco­ nomic losses are to be minimized. Stoch astic differential calculus modelling

The first epidemic models considered that the course of an epidemic must depend on the number of susceptibles and the contact rate between susceptible and infectious indi­ viduals; this is the basic assumption underlying deter­ ministic models. In a deterministic model, the future state of an epidemic process can be predicted precisely if the initial number of susceptible and infectious indi­ viduals is known (e.g., Figures 8.6 and 8.7).

Modelling approaches

-:1

· . . · . ·

I1 " u .� "£;

·

2 :� g

N,mbM 01 �-"""

E 1;) � � '" Cl> 5l � �

�co

�C

Cl> C

C C

"

:;:

,.j,

. . . ..

\ ....

.

.

.. .

.

. . .. .. . .. .

o � z ::2;

o Time

Deterministic and stochastic model cu rves for a s i mple infectious epidemic. (After Bai ley, 1 9 75 .)

Fig.19.5

Fig.19.6

Stochastic exponential decay paradigm

A stochastic analogue of the deterministic model for the changing number of susceptibles in a population, described above, can be formulated. As before, XI denotes the number of susceptibles in the population at time t, and N the number at time O. It is now assumed that XI is a random variable and the prob­ ability of r susceptibles at time t is denoted by Pr(t). A differential calculus approach, similar to that used in the deterministic model, can be applied to obtain an expression for the rate of change of Pr(t). This rate of change, dpr(t)/dt, will be influenced by flows in from the state r + 1 and flows out from the state r. For state r + 1 to have a flow in, there must be two events: first, there must be r + 1 susceptibles at time t; secondly, one of these susceptibles must leave. The probability of these two events is a(r + l)Pr+ l (t). For state r to have a flow out, there must be r susceptibles at time t and one susceptible must leave. The probability of these two events is arpr(t). The instantaneous rate of change of p,(t) is therefore:

2

3

."

.. .. .

4

..

.. .. .. ..

..

..

..

..

.. .

..

� .

...

... ..............

Time t

Mean (-) and 9 5 % probability interval ( - ---) for the

number of susceptibles in the stochastic exponential decay parad igm.

dp r(t)

Later, it was realized that the deterministic approach was not always applicable: variation and choice (of contact between susceptible and infected individuals) should be considered as part of the epidemic process. Stochastic modelling, which includes the probability of infection, therefore evolved. This leads to results that have a probability distribution from which means, variances and probability intervals can be derived. The deterministic and stochastic approaches may produce a different result when modelling a simple epidemic (Figure 1 9.5); the deterministic curve represents the absolute point estimates. The stochastic curve repres­ ents the mean of all the values generated by the various probabilities.

1

..

=

dt

a(r +

1) Pr + l (t) - arpr(t)

where ais a parameter. The solution to such a differential equation may not be easily obtained, but standard methods for solving are available. These methods lead to an expression for p,(t) in terms of t: P r(t)

where

NCr

=

r r NCr0- e-al)N- e-al

is a mathematical shorthand notation for

N! r!(N - r)!

The expression for Pr(t) is known as the time­ dependent binomial probability distribution from which it can be deduced that XI has mean value Ne-al and variance Ne- atO - e- at). Comparing these results with those of the deterministic model, it can be seen that the mean value of XI is identical to the solution obtained before. This is often, but not always (Fig­ ure 19.5), true of deterministic and stochastic models. However, an important distinction between the deter­ ministic and stochastic model is that the latter provides a variance; therefore, the extent to which population susceptible numbers fluctuate at each point in time can be deduced. Figure 19.6 illustrates this point, where the mean of the number of susceptibles at each point is shown along with the 2.5th and 97.5th percentiles (see Chapter 12) of the distribution of the number of susceptibles. This provides a 95% probability interval for the number of susceptibles. The wider the prob­ ability interval, the greater is the range of observed deviations from the mean number of susceptibles. Empirical simulation modelling

The goal of this technique is simulation of the perform­ ance of parasites or diseases in relation to conditions

Model ling "

'

that change either deterministically or stochastically. Although simulation models do not always require a computer for implementation, their power and success have been closely linked to advances in computer tech­ nology. Many simulations undertaken today would have been impossible 50 years ago. Successful simulation models have the potential to accurately forecast disease incidence. These forecasts, like those possible using time series analysis (see Chapter 8), are of value in selecting suitable prophy­ lactic procedures. Empirical models utilize indicators that are obtained

Table 19.1

Assoc iations between I Mtvalues* and losses owing to

fasciol iasis in England and Wales. (Data from O l l erenshaw, 1 966.) Losses

1Mt

North-west England,

Other parts

south-east England

of England

and north Wales

and Wales

45 0

No losses Some losses Heavy losses

* See text for explanation.

by analysing he relationship between morbidity and any . assoczated varzables. Frequently used variables are those

relating to climate. These models are not strictly math­ ematical models because they do not attempt to analyse the d�namics of agents' life-cycles, but simply quantify assocIated phenomena. They are sometimes referred to as 'black-box' models because the relationship between data that are fed into the model and the results that are generated cannot be satisfactorily explained.

This prediction model is deterministic because no element of randomness is included in the formulation. Its simple approach enables its execution without a computer. The model was adapted for use in France (Leimbacher, 1978) and Northern Ireland (Ross, 1978). Process simulation modelling

Fascioliasis

Fascioliasis has been modelled empirically in Britain (Ollerenshaw and Rowlands, 1959; Ollerenshaw, 1966; Gibson, 1978). The life-cycle of Fasciola hepatica is com­ plex, involving stages inside a final and intermediate �ost, and o� herbage. Two important meteorolog­ Ical factors m the development of the parasite are temperatures above lOoC and the presence of free water. In the late 1950s, Ollerenshaw suggested that devel?pment is therefore usually impossible during the wmter (too cold) and that there may be insufficient water during some of the summer months (too dry). This is the basis of the 'Mt' forecasting system for fas­ cioliasis. Mt is a monthly index of wetness given by: (R - p + 5)n,

where, on a monthly basis: R rainfall in inches, p potential transpiration, n number of rain days. Observations suggested that, because parasite development is also temperature-dependent, the rate of development is similar in June, July, August and September, but is halved in May and October, when the Mt index should therefore be halved. A seasonal summation of Mt indices (IMt) can be calculated by adding the Mt values for the 6-month period May to October. This sum simulates the pro­ gression of the disease in relation to changing mete­ orological conditions and so can be used to predict loss.es owing to fascioliasis, so that suitable prophy­ lactlc measures can be undertaken (Table 19.1). =

=

=

Mathematical models that describe the dynamics (i.e., biological processes) of parasite and host populations have been formulated. These more refined techniques �llow the course of a disease to be simulated. They mclude models for forecasting fluke morbidity (Hope­ Cawdery et al., 1978; Williamson and Wilson, 1978), the airborne spread of foot-and-mouth disease (Gloster et al., 1981) and the occurrence of clinical ostertagiasis. Bovine ostertagiasis

The level of pasture contamination by infective �stertagia ostertagi larvae can be predicted by simulat­ mg the course of events experienced by cohorts of par­ asite eggs deposited on pasture (Gettinby et al., 1979). This involves estimating the proportion of eggs that pr?ceed to the first, second and third larval stages usmg development fractions, which quantify the rate of development of the parasite from one stage to the next according to the temperatures that it experiences. In addition, parameters associated with infectivity, fecundity and migratory behaviour of the larvae must be included. Thus, suppose a calf commences grazing on contam­ inated grass on 1 April. The number of infective larvae, L, ingested on 1 April can be estimated from known pasture contamination levels and the daily herbage mtake of the calf. Not all larvae become established. The number of adult worms, A, to be expected in the abomasum of the calf 21 days later on 22 April is modelled using: A (K - Ao)(1 - e-aL) + Ao =

Modelling approaches

20 Calves removed due to clinical ostertagiasis

L---

Cl

� V> o o o

Q) '"

� Q)

> .;::;

10

(J

c

Calves put out to graze

May 5

Fig. 19.7

May 26

......

........... .--........

July 28

--

I September 8

Observed and predicted counts of i nfective Ostertagia ostertagi larvae on pasture in 1975. - Observed pasture count;

- - - - pred icted pasture count; � overwi ntered infective larvae. ( F rom Gettinby et al., 1979.)

where Ao is the number of adults already in the abomasum. The curve of A for different values of L is sigmoidal, reflecting the assumed density-dependent relationship between larval challenge and establish­ ment of adult worms (see also Figure 7.4). The para­ meters K and a control the rate of establishment so that the proportion established is high for low levels of challenge and low for high levels of challenge. The adult worms will produce eggs on 1 April and there­ after. The number of eggs, E, produced on 22 April is estimated from empirical data relating egg output to adult worm burden. These eggs undergo develop­ ment. The time to the appearance of infective larvae is estimated by calculating from daily temperatures the fraction of development to take place each day and summing these fractions until all development has occurred ndays later: 1 1 1 +- + . . . -= 1 D1 D2 Dn where the Ds are the number of days that would be required to complete development under conditions of constant temperature. Adding n to 22 April gives the earliest day on which the infective larvae can appear. Not all developing eggs and larvae survive and so the number of eggs that avoid mortality is the proportion, p", of the egg output on 22 April. The parameter p is an estimate of the daily survival rate. If the values of nand pn are determined for each day during which the calf grazes, then it is possible to estimate the expected

totals of infective larvae on pasture and the number of adult worms infecting the calf. This type of simulation requires iterative calculations, which can only be per­ formed in a reasonable time by using a computer. Figure 19.7 shows the results of such a simulation for calves that grazed on an experimental pasture from May to September 1975. Comparison of predicted and observed larval counts shows a high degree of similarity. A prediction of herbage infective larval burdens using this type of simulation model can facilitate op­ timum use of anthelmintics, and movement of animals to safe pasture before challenge by large numbers of infective larvae, thereby preventing clinical osterta­ giasis. A similar approach has been successfully applied to ovine ostertagia sis (Paton et al., 1984) and tick infes­ tations of sheep (Gardiner and Gettinby, 1983).

-

Monte Carlo simulation modelling

In many cases deterministic and stochastic models can be formulated for which no analytical solution is known. Alternatively, finding the solution may be extremely difficult or tedious. In such circumstances, simulation methods are increasingly being under­ taken. Since simulation studies attempt to mimic the physical process being modelled, they can be very informative and therefore are often preferred. In these methods, random processes are simulated using

Table 19.2

Poss ible nu mber of mated female Ixodes ricinus on one sheep, resu lting from s i m u l ated attachment and sex d istribution of the tick

population. Outcome from one throw of a ten-sided die

1 1 ,2,3,41 1 5,6,71 1 8,91

1 1 01

Simulated sex distribution of engorged ticks from coin tosses

Simulated number

of engorged ticks on a sheep o

M F MM

2

MF FF FM MMM MMF

3

Number of mated females

0 0 0 0 1 0 1 0 1

MFM FMM FFF FMF

MFF FFM

random numbers in order to decide whether or not an event takes place. This is somewhat akin to gambling; hence the term Monte Carlo simulation. Sheep tick paradigm

Suppose a model is to be formulated for the outcome of adult ticks of the species Ixodes ricinus mating on the sheep host. In particular, a measure of the total number of female ticks is required so that future population numbers can be anticipated. Suppose a field study indicates that the total number of engorged ticks found on individual sheep is 0, 1, 2 or 3, and suppose that the respective probabilities are 0.4, 0.3, 0.2 and 0.1. The field study also suggests that male and female ticks are present in equal proportions. Using a fair ten-sided die with faces labelled 1 to 10, and a fair two-sided coin with faces labelled M for male and F for female, it is possible to simulate and obtain the number of mated female ticks on each sheep. The die is thrown and, depending on which of the sets {l,2,3,4}, (5,6,7), {8,9} and {lO} the outcome belongs to, the simulated number of adult engorged ticks on the sheep is taken to be 0, 1, 2 or 3, respectively. The above sets are chosen because the outcomes 0, 1, 2 and 3 will occur with probabilities 0.4, 0.3, 0.2 and 0.1, respectively, which is consistent with the results of the field study. Suppose the out­ come of the throw of the die is a 10, the simulated num­ ber of adult engorged ticks on the sheep is then 3. The coin is now tossed three times and the outcomes used to simulate the sex of the three adult engorged ticks. In the event of all three ticks having the same sex (i.e., outcomes MMM or FFF), there will be no mated females. All other outcomes will lead to at least one male and one female on a sheep and, assuming that

one male mates only with one female, there will be only one mated female. Table 19.2 shows the possible combinations of the outcomes of the throw of the die and the coin tossing. The procedure can be repeated for each sheep to obtain a series of as and Is reflecting the outcomes of the attachment and sex distribution of the tick popula­ tion on the sheep flock. To summarize the results of the simulation: the proportion of the flock with l or a mated female ticks could be reported. When the simu­ lation is carried out, it is found that, on average, only 18 out of every 100 sheep are hosts to one mated female tick. A sensitivity analysis3 could also be undertaken to test the effects of different assumptions or parameter estimates on the outcomes. For instance, if the ratio of male to female ticks was no longer 1:1 but biased towards females, in the ratio 1:2, then the study could be repeated using a biased coin that would give an M outcome with probability 0.33 0/3) and an F outcome with probability 0.67 (2/3) when tossed. The simula­ tion then leads to an average of 15 out of every 100 sheep hosting one mated female tick. Comparison of the results suggests that the analysis is not very sensit­ ive to changes in the sex distribution; consequently further field studies to accurately determine the sex ratio are not warranted. Similarly, if it was thought that male ticks could mate with several females, then the simulation could be repeated. If, for example, 3

The extent to which changes in values of an input parameter affect

output parameters is assessed by sensitivity analysis. If minor changes

in values of an input parameter induce major changes in output parame­ ters, then the model is highly sensitive to that input parameter. Conversely, if major changes in an input parameter induce only minor changes in output parameters, then the model is relatively insensitive to the input parameter.

Model ling approaches

attachment led to the combination of one male and two female ticks on a sheep, then this would produce two, rather than one, mated females. In modern simulation studies the computer takes over the role of the die and the coin. Thus, the results of these 'lotteries' are produced by replacing throws of a la-sided die with an instruction to the computer to produce integer numbers from 1 to 10 in random order such that a large series of generated numbers would produce each of these numbers in equal proportions. Sheep

tick control

Monte Carlo simulation can be used to investigate the behaviour of a stochastic model for the incidence of tick mating which could be of value to control strategies (Plowright and Paloheimo, 1977). Field investigations (Milne, 1950) revealed that tick occurrence was patchy: a pasture may have a heavy burden whereas an adja­ cent field separated from the first only by a fence may have no ticks. This suggested that ticks have problems with effective dispersal. One reason may be that at low densities tick population growth is inhibited by a low rate of mating. The model proposed makes several assumptions: that each adult only mates if it encoun­ ters an individual of the opposite sex on the sheep to which it is attached; that each adult only mates once; that each tick has an equal probability of attaching to a sheep; that all ticks have an equal probability of encountering one another. The last two assumptions are dubious but do not affect the model appreciably. The total number of matings at various sheep densit­ ies, and with varying numbers of ticks on each sheep, can be modelled by applying a Poisson distribution (see Chapter 12). Table 1 9.3 lists the results and demon­ strates the difference between the stochastic and deter­ ministic output. By including a rate of survival in the model, it is possible to predict the growth rate of the tick population for different levels of tick population size and sheep density. When the sheep population is low, the rate of tick population increase is insensitive to changes in the size of the tick population, but highly sensitive to changes in the size of the sheep population. Conversely, when the tick population is low, the rate of tick population increase is relatively insensitive to changes in sheep numbers, but sensitive to changes in tick numbers. This supports the hypothesis that it is difficult for ticks to establish themselves in new pastures. It also suggests that a reduction in host density may not be an effective means of controlling tick infestation because the rate of tick population increase does not always depend on sheep density. The model also predicts that extinction of the tick population takes place over a narrow range of tick population sizes, corroborating field observations of patchy tick distribution.

Table 19.3

HI)

Comparison of the results of determ i n i stic and stochastic

models of i ncidence of mating in Ixodes ricinus for various parameter values. (From Plowright and Paloheimo, 1 9 77.)

p

0. 05

Number of ticks

0. 05

40 40 40 40 40

0. 05

80

0. 05 0. 05

80 80

0. 05 0. 05 0. 05

0. 05

80

0. 05

80 40 40 40 40

0.01 0.01 0.01 0.01

Number of sheep

1 0 20 40 80 1 60 10 20 40 80 1 60 10 20 40 80 1 60

Total number ofmatings Deterministic model

3.3357 4 . 75 3 2 5 . 1 2 71 3 .9683 2 .2 1 43 8.9590 1 3 .2866 1 5 . 3686 1 2 . 6488 7.9 3 2 3

0. 01 0.01 0.01 0.01

40 80 80 80

40

0. 3 02 1 0.5 5 2 8 0.9282 1 . 3 2 79 1 .4345 1 . 0342 1 . 8993 3 .2 2 7 0

0.01 0. 01

80 80

80 1 60

4.71 08 5 .2683

10 20

Stochastic model (mean of 600

replications) 3 .4400 4 . 7833 5.1 533 3 . 8395 2 .2 1 1 7 9 . 0883 1 3 .45 6 7 1 5 .5733 1 2 .845 0 8 . 005 0 0.2933 0.5 5 6 7 0.901 7 1 .2 73 3 1 .4633 1 . 001 7 1 .9483 3 . 05 5 0 4.5867 5.3367

p = proba b i l ity o f a t i c k attach i ng t o a sheep.

Matrix population modelling

The use of matrices to describe population changes became firmly established when Leslie (1945) first pub­ lished his Leslie matrix. Matrices often take the form of a rectangular array containing numbers of hosts or parasites in a defined state or stage of development, known as the state vector, or containing reproduction and survival rates of hosts or parasites in different states or stages known as the transition matrix. In this way, it is possible to obtain the state of the system from one point in time to another. Fascioliasis

The life-cycle of Fasciola hepatica can be used to illus­ trate the formulation of a simple matrix model. The parameters have been estimated from field studies. It is assumed that eggs from the adult fluke develop to miracidia after 4 weeks, that miracidia that penetrate the molluscan host, Limnea truncatula, develop and emerge as metacercariae 8 weeks later, and that the metacercariae can survive up to 3 weeks before desic­ cation. The weekly survival rates of the adult flukes, the developing eggs, the stages in the snail, and the metacercariae are 0.95, 0.3, 0.5 and 0.8, respectively.

\, ( )

Modelling

corresponding elements of the column state vector !.f at time t + 1; that is:

Each adult fluke is assumed to produce 2500 eggs weekly, and each miracidium to penetrate a snail with probability 0.005. The phases of development in the snail are simplified by labelling all of the asexual stages s. It is also assumed that reproduction occurs in the last intra-molluscan stage, and the fecundity is 4.3. A further simplification is that each metacercaria in each week of development has probability 0.02 of becoming an adult worm. Let a be the number of adult flukes and ei, ci and mi be the number of eggs, cercariae and metacercariae, respectively, in the ith week of development. The number of adult flukes from week t to week t + 1 will be those adults in week t that survive plus those meta­ cercariae that are ingested and become established:

a = + 0.95 x a + O x el +0 o o

+ 0.02 x m3·

Other relationships are similarly retrieved. For example, if the number of metacercariae in the first week of development at time t + 1 is required, then the row transition matrix corresponding to this element is turned on its side and corresponding elements in !.f multiplied to give

a(t + 1 ) = 0.95a(t) + 0.02ml (t) + 0.02m2 (t) + 0.02m3 (t).

The number of eggs at time (t + 1) in the first week of development will be those produced by adults in the previous week:

m l (t + 1 ) = 4.3s8(t).

The matrix model proposed for the life-cycle of is similar to that proposed by Leslie (1945) for populations in general. Leslie suggested that mem­ bers of a population can be divided into exclusive age classes of fixed duration, so that every member of a class faces the probability of surviving and the same probability of reproducing. If the vector containing the number in each class during a certain time interval is multiplied by the Leslie matrix describing the popula­ tion dynamics, then the vector containing the number in each class during the following time interval is obtained. For example, if there are k age classes:

e/t + 1) = 2500al(t).

F. hepatica

The number of eggs at time t + 1 in the second week of development will be those surviving from the pre­ vious week: e2 ( t + 1 ) = 0.3el (t).

The change from week to week of all the stages can conveniently be summarized in matrix form (Table 19.4). In shorthand notation, this is written:

nl

where !.f and !.t+1 are the state vectors and correspond to times t and t + I, and E. is the transition matrix. Char­ acters are underlined to denote a matrix. Note that to retrieve the first equation, the first element in the state vector (al+l ) is equated with the sum, after the first row of the transition matrix has been turned on its side and each element of this row multiplied by the Table 19.4

n2

II

fz

A-I

A

P2

n2 n3

Pk-l

nk l nk

0 0

0.02 0

PI

n3

nk l t+l nk

Matrix form u lation of the I ife-cycle of Fa 5ciola hepatica. 0.95 2500

a e1 e2

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0.02 0

0.02 0 0

S1

5

0.5

52

2

0.5

5,

51

0.5

54

54

0.5

So

So

0.5

56

56

0.5

57

57

0.5

58

m,

4.3 t+1

e2

e4

0.002

51

a el

e,

0.3

e4

m2

0 0 0 0.3

e,

m,

0 0 0.3

5a

O.S

m1

O.S

m2 ml

nl

\

Model ling approaches

where ni(t + 1) is the number in the ith class at time t + 1 , and fi and P i are respectively the fecundity and survival rates for age class i. The advantage of the matrix approach is that, once E and the numbers for the state vector at time 0 are known, then the population sizes at any future time can be predicted. For example, the population num­ bers after four units of time could be obtained from the successive calculations: ,II = E ,Io

,I2 E !I ,I3 = E ,I2 =

I

I

Flow of surviving protozoa ready to undergo fission

Flow of newly formed protozoa

2

Fig. 19.8

Network representation in the protozoal paradigm.

,I4 = E ,I3

The matrix equations described above have many interesting properties from which the salient features of the population can be investigated. Details of these are given by Leslie (1945). A more realistic matrix representation of the life­ cycle of F. hepatica was discussed by Gettinby and McClean (1979). This is a state-transition model with five states: mature flukes (in sheep), eggs (on grass), rediae (in snails), metacercariae (on grass), immature flukes (in sheep). A mortality rate is attached to all stages, and fecundity to the adult fluke and redia, which reproduce sexually and asexually respectively. The matrix includes probabilities of transition from one stage to the next, and fecundity, based upon avail­ able field data. The first part of the model describes the natural infection in sheep in Britain and Ireland. The second part investigates and compares various control strategies: the use of flukicides, molluscicides and land drainage. There are three conclusions. Molluscicides are most effective when applied in early spring. Flukicides eradicate the infection when given monthly and control it when given at 2-monthly intervals. If dosing is only annual, then it is best given in August. Good drainage is an effective means of control. Again, the model only indicates possible outcomes, in the absence of accurate field data to support the values of the input parameters in the model. N etwork population modelling

The inability of many other models to cope with chan­ ging inputs during the period of operation of the model can be circumvented using a network representation of a parasite's life-cycle. Network models, although extensively exploited by control engineers, have been largely overlooked in the life sciences, with some exceptions (Pearl, 2000). The same problem often can be formulated using a network and a matrix approach. The network formulation is particularly attractive when time delays are a feature of the life-cycle being modelled, and when the output response of a

biological system is to be measured for a given input. On the other hand, matrix formulations are attractive when the behaviour of several states of a population is of interest at successive points in time. Some element­ ary examples will demonstrate the symbolism used in the network approach. Protozoal paradigm

Consider a population of identical protozoa that reproduce by binary fission. A constant T units of time occurs between successive fissions. The probability that any one protozoon survives this time is P. To con­ struct the network shown in Figure 1 9.8, which repres­ ents the life-cycle, consider the flow of newly formed protozoa in the population. After a time delay, T, only a proportion, P, of these survives. This results in the flow after the time delay being scaled by a factor P. This is immediately succeeded by fission, which results in the flow doubling and so a further scaling by a factor 2 is required. The network convention is to denote time delays by squares and scaling parameters by circles. Since the products of fission are newly formed cells, this flow is connected back into the time delay. This is a very simple network and consists of one loop and no alternative paths. Ostertagiasis

A network can be constructed for the life-cycle of Ostertagia circumcincta, an important parasite respons­ ible for outbreaks of parasitic gastroenteritis in sheep (Paton and Gettinby, 1 983). The network is shown in Figure 1 9.9. The unit of time is 1 week. Ewe and lamb egg inputs, XU) and ZU), voided out to the pasture in week i, undergo a time delay of r1 (gamma) weeks before infective L3 larvae appear. The proportion that survive is a. During the following week, these L3 larvae, plus available over-wintered infective larvae Y(i), either become ingested by the sheep to become adults at rate c, or accumulate on the pasture at rate 1 c. -

I

Model ling

W(i)

Fig. 19.9 Network representation of the I ife­ cycle of Ostertagia circumcincta showing adult parasite output, W, derived from ewe

egg input, X, lamb egg i nput, Z, and over­ wi ntered i nfective larval i n put, Y. The constants a, b, c, d and e are parameters of

L-________� 8

�----��-

Those that accumulate are delayed for 1 week, during which their survival rate is b, before joining the flow of new infective larvae. The L3 larvae that were ingested are delayed for T2 weeks before reaching the adult egg-laying stage. Half of these adults will be females, which reproduce at a rate of e eggs per week. From suc­ cessive egg cohorts, female adults will accumulate from week to week. To facilitate the accumulation, the existing females must enter a feedback loop in which the weekly survival rate is d, and which connects them with the flow of new female adult worms in the sheep. The network therefore consists of a forward loop and two feedback loops. When the model is operated, the effects of various anthelmintic strategies can be investigated by altering components of the network that will be affected by the particular strategy. For example, dosing of lambs will reduce the lamb egg input, and dosing of ewes will decrease the ewe egg input. The simulation suggests that regular dosing of lambs at 4-weekly intervals for the first 6 months of life is very effective. Similarly, dosing lambs three times in July and August is effect­ ive. The single administration of an anthelmintic to ewes at lambing time is the least effective of the anthelmintic strategies. S ystems modelli ng

'Modelling' now has a broad remit, including the con­ ceptual representation of any real event in mathem­ atical terms. Models that assess the cost of disease and its control have also been designed; some of these have been reviewed by Beal and McCallon (1983) and Dykhuizen (1993). Models of livestock feeding have been formulated (Theodorou and France, 2000), and S0fensen and Enevoldsen (1992) review models of herd health and production. Increasingly, models are being linked together to produce large-scale systems models. An example is EpiMAN (see Chapter 1 1 ) . A bibliography of veterinary models, including a discussion of model classification, is given by Hurd and Kaneene (1993).

survival, i nfectivity and fecund ity; r1 and rz are t i me-delays representing parasitic development times on the pasture and i n the lamb, respectively. (Modified from Paton and Gettin by, 1985.)

The rational basis of modelling for active disease control

Many veterinary models have been used to explore the dynamics of disease in order to produce options that might be selected to control disease (e.g., Medley, 2003). However, they may not have faced the critical test of being applied when disease actually occurs. In some cases, they have served as policy guides during actual outbreaks of disease. For example, the 2001 epi­ demic of foot-and-mouth disease in the UK was char­ acterized by a policy to pre-emptively cull cattle on premises contiguous to infected premises, on the basis of model formulations that predicted that this would be an efficacious tactic for control (Ferguson et aI., 2001; MAFF, 2001). A consideration of the conditions under which the validity and appropriateness of a model may be judged is therefore a necessary complement to knowledge of the types of models that have been described. Avai lable knowledge, and th e functions of models

The validity of a model is determined by the level of about a disease's natural history, and the quality and quantity of data relating to the disease (Graat and Frankena, 2001; Taylor, 2003). For example, models of airborne transmission of infec­ tion (see Chapter 6) require information on microbial output from hosts and host susceptibility (epidemio­ logical knowledge), and details of stock distribution (data quality and quantity) in order to predict trans­ mission accurately. Levels of knowledge can be conveniently classified as 'poor' and 'good', so that a general framework for the application of models can be identified (Table 1 9.5). This defines four main applications of models: epidemiological knowledge

1. 2. 3.

development of hypotheses; hypothesis testing; elementary explanation of past events; and

The rational basis of modelling for active disease control

Table 19.5

Uses of models in the context of epidemiological knowledge and data qual ity and quantity. (Modified from Taylor, 2003; based on H o l l i ng, 1 9 78.) Data quality and quantity

Epidemiological knowledge

Good

Poor Poor

Exploration of hypotheses

Hypothesis testing

Good

S i mpl ified

Deta i led representation of past events, and pred iction of futu re events

representation of past events, and guardpd use for prediction of future events

4. detailed representation of past events, and prediction. The applications span not only the model formula­ tions outlined in this chapter but also other numerical analytical procedures such as observational studies (Chapter 15). In reality, levels of knowledge are con­ tinua, and so a considerable degree of judgement may be required in assessing the particular role of a model. Development of hypotheses

Hypotheses can be developed when epidemiological knowledge is poor and good data are not available. For example, case-control studies using retrospective vet­ erinary clinic data that cannot be validated might be used to explore possible intrinsic determinants of dis­ ease, such as breed, age and sex; these studies may then be succeeded by prospective studies with careful control over the quality of the data that are collected. However, this is an uncommon modelling strategy because most modellers usually begin at least with for­ mulations that depend on an underlying hypothesis. For example, the sheep vaccination paradigm is based on the hypothesis that the number of susceptible sheep decays exponentially (Figure 1 9.2). Hypothesis testing

Availability of good data allows hypotheses to be tested by fitting observations to associations or rela­ tionships that are hypothesized to exist. Prospective observational studies frequently follow this approach, carefully validating data as they accrue. Elementary explanation of past events

A sound understanding of the natural history of dis­ ease may be attenuated by lack of high-quality data. For example, the vulpine rabies model described earlier incorporates the major characteristics of the transmis-

sion of the disease. However, accurate data on contact rates are not usually available. Thus, the model may be used to explain previous patterns of disease with assumptions about putative contact rates. However, its use to predict future disease patterns would need to be very guarded because of the lack of information on current parameter levels in the field. Detailed representation of past events, and prediction

The availability of high-quality data, linked to a detailed understanding of the functioning of a system, enables both the accurate representation of past events quantitatively, and sound predictions of future events to be made. A good non-veterinary example is the use of aircraft flight simulators to train pilots. However, this is an example from the physical sciences, which are subject to fewer laws and are usually less complex than biological systems, which display considerable variability. Notwithstanding the weaknesses of induct­ ive reasoning, on which much of science is based (see Chapter 3), in practice the accurate prediction of future complex biological events (including disease occur­ rence) is difficult, although the past may be modelled accurately. The difference between theory, hypothesis and fact - with which models might be labelled - and the strength of evidence and criteria required to shift from theory to fact, should therefore be appreciated. From theory to fact4 Scientific theories

A theory is a supposition that explains something. It cannot be proved in the sense that propositions in logic and mathematics can. However, certain scientific theor­ ies are held with much more confidence than others. The confidence one has in any particular theory, such as the Second Law of Thermodynamics, the atomic theory of matter, or the microbial theory of the cause of infectious disease (see Chapter I ), depends on several factors, including how well tested the theory is, and how often and how seriously this testing has refuted the theory. For example, the theories behind weather forecasting - particularly long-range forecasting - are quite often refuted, thereby reducing the confidence held in future forecasts. The 'testedness' of a theory is difficult to define closely: the concept implies more than just a large 4

This section may be considered as a logical continuation of Chapter

3. Moreover, it is applicable to all areas of epidemiological investigation (e.g., observational studies and clinical trials). It is presented here because of its particular relevance to models that may claim to predict future events, and, in so doing, might be interpreted as factual descrip­ tions of the future.

) ) ·1

Modelling

number of repetitive tests. For example, one might well make 1 0 000 observations of the Sun, and never observe an eclipse. Yet one would not hold with any confidence the theory that 'the path, of the moon never lies between the Earth and the Suns . To be well tested, a theory should have given predictions of what should happen in a variety of different circumstances. If these predictions were extensively tested over a wide range of conditions (either in the field or experimentally), then the theory can be called well tested. Besides 'testedness', a theory can be characterized by other attributes, although there is no general agree­ ment on what these are. In addition to 'testedness', four have been listed (Davies, 1 973): 1 . generality: that is, the unification of existing con­ cepts that is achieved; the greater the unification, the more 'fundamental' the theory is said to be; 2. simplicity: that is, the ability of a theory to be easily tested; 3. precision: that is, its ability to generate precise predictions; 4. 'refutedness': that is, the extent to which it is inconsistent with previous tests, or its inconsis­ tency with established data6. Bertrand Russell viewed 'refutedness' in terms of 'external confirmation': the theory must not contradict empirical facts. However evident this demand may appear in the first place, its application turns out to be quite delicate. For it is often - perhaps even always possible to adhere to a general theoretical foundation by securing the adaptation of the theory to the facts by means of artificial additional assumptions. This point of view is concerned with the confirmation of the theory by the available empirical facts. The confidence that one has in a theory clearly depends on the relative importance attached to these characteristics7. Karl Popper (Chapter 3), for example, , This is reminiscent of Russell's 'inductivist turkey' (see Chapter h

3).

There are other aspects of a theory, which tend to be somewhat

abstract and more suited to pure science. Thus, Albert Einstein was concerned with the 'inner perfection' of a scientific theory: an intellectual elegance, which is aesthetic rather than utilitarian. Similarly, theories underpinned by Euclidian geometry, Newtonian dynamics and the mathematical form of Maxwell's electromagnetism are deemed to be 'beautiful' (Penrose, 2004). 'Testedness' and 'refutedness' are not involved in this idea of 'inner perfection'; however, generality and sim­ plicity are. This is relevant to assessing if one theory is 'better' than

focused on 'testability' in situations of potential refuta­ tion. In epidemiology generally, emphasis has been placed on precision and 'refutedness', whereas some mathematical models might also suggest generality (e.g., the basic reproductive number: Chapter 8). The relative importance of these characteristics may also be determined by the two broad functions of models: strategic or tactical (Holling, 1966). Strategic models explore general issues (e.g., the principles underlying spread of disease within populations), whereas tactical models address specific problems (e.g., the practical control of a specific epidemic). Strategic models sacrifice detail for generality (Levins, 1 966), whereas tactical models may be loaded with so much detail that they become difficult to use and interpret (Thulke et al., 1999). Moreover, the structure of strategic models may not assist the tactical modeller. Thus, the value of a mathematical model, as a theory, should be judged in the context of these five attributes ('testedness', generality, simplicity, precision, 'refuted­ ness') and its function. It is only after such judgement that a model may be deemed to be more than mere hypothesis. Hypotheses and laws

Hypotheses and scientific laws are special cases of theories. A hypothesis is a theory of low generality and low 'testedness'. Many initial formulations of models of specific diseases therefore involve hypotheses. A scientific law is a theory that is reasonably general, simple, and well tested (and its 'inner perfection' therefore is consequently never low). Although some mathematical models may appear to fulfil the first two criteria (e.g., the exponential decay paradigm), they often fail the last criterion. Facts

A fact is held with very high confidence. Theories that are neither very general nor very precise can be held with great confidence if they are well tested but never refuted; they therefore are facts (e.g., the fact that the Earth is round). Theories therefore may become facts if, after much further testing, they were repeatedly confirmed but never refuted. Using these criteria, cur­ rently no mathematical models constitute facts.

another. The better one requires a high degree of confidence, and the 'inner perfection' should be as high as possible (i.e., the generality, sim­ plicity and 'predictiveness' should be as high as possible). Thus, progress in pure science aims at an improvement of 'inner perfection', while also maintaining a reasonably high confidence in the theory. The goal of modern theoretical physics, for example, is to identify a Theory of Everything', which will rationalize the various Laws operating in the Universe in a simple, elegant unity (Laughlin and Pines, 2000). 7 Formulations have been developed to 'measure' these attributes, and therefore the impact of their various combinations on a theory's merit (Davies,

1 973).

Model-building

Model-building requires several steps (Figure 1 9.10), detailed by Dent and Blackie (1 979), Martin et al. (1987) and Taylor (2003). First, the obj ectives of the model must be clearly specified. Thus, a model of the windborne transmission

The rational basis of modelling for active disease control

1 . Defi nition of the system and objectives for modelling

2 . Analysis of data a n d knowledge relevant to the model

3. Model form u lation

t

4. Verificati o n

t

j

5. Sensitivity a n a lysis

I

t

6. Validation

7. Use of model in decision support

Fig. 19.1 0

Stages in model-bu i l d i ng. (Modified from Taylor, 2 003 .)

of Aujeszky's disease may have as its goal prediction of the farms likely to be exposed to infective virus plumes. Secondly, details of the data and knowledge to be included as input parameters to the model are needed. Meteorological variables determining condi­ tions favourable to long-distance transmission of virus, levels of virus excretion from infected pigs, and location of susceptible pigs, for example, would be required in the Aujeszky's disease transmission model. This will then enable the main framework of the model, including the relationships between all of the parameters, to be determined. It is important at this preliminary stage for dialogue to occur between the modellers and those with expert biological knowledge of the candidate disease (e.g., microbiologists, field veterinarians, and epidemiologists)8. Next, the model is formulated; for example, using some of the modelling approaches described earlier in this chapter.

)

)

Fourthly, the model is verified by undertaking checks to confirm that the type of output anticipated by its design is generated. A sensitivity analysis is then undertaken (see earlier). This is particularly important if the model is sensitive to input variables based on data of doubtful quality, because they could lead to erroneous predic­ tions. Additionally, sensitivity analysis is of benefit in determining the stability of the model in relation to the known variability of input parameters (e.g., the ratio of male to female ticks in the sheep tick paradigm, above). The model then needs to be validated9. Initially, affirmative answers to four questions will support a model's validity: 1 . Have all the known determinants that influence occurrence of the disease been included? 2. Can the value of these determinants be estimated with accuracy? 3. Does the model make biological 'common sense'? 4. Does the model behave in a mathematically reasonable way (i.e., is it sensitive to biologically relevant variables)? Validation therefore involves establishing if the model behaves like the actual biological system that it is designed to mirror; for this, two conditions must be met (Spedding, 1 988): 1 . the model is assessed against data not used in its construction; and: 2. the precision of the model is specified in advance, noting that there is likely to be variability in the behaviour of the biological system. The first condition may be difficult to fulfil; notably, when there is a paucity of data (e.g., if rare epidemics are being modelled). This will also limit its 'tested­ ness'. The second condition is eased by stochastic formulations, which provide confidence intervals for outputs as measures of error bounds. The validity of a model may be ultimately assessed in terms of its usefulness (Green and Medley, 2002; Hugh-Jones, quoted by Salman, 2004), the key feature being whether decisions made with the model are more correct than those made without it (Dent and Blackie, 1 979). If the model is deemed to be adequate, it can be used to support decisions, or become part of a larger deci­ sion support system (e.g., the EpiMAN: see Chapter 1 1 ), noting its suitability to particular roles (Table 1 9.5).

H A meeting of various experts, designed to produce a consensus on all available relevant knowledge, is sometimes termed a 'Delphi Con­

9

The importance of validation cannot be emphasized enough, par­

ference' (named after the Classical Greek oracle at Delphi). Modern

ticularly when models' consequences have a profound impact on society,

Delphi conferences usually have well defined rules of engagement for

as was the case with those relating to the 2001 foot-and-mouth disease

the purpose of knowledge elucidation.

epidemic in the UK (Kitching, 2004; Pfeiffer, 2004).

The model-building strategy addresses the main issues in assessment of a theory: generality, simplicity, precision, 'refutedness' and 'testedness'. The extent to which models perform against these criteria deter­ mines the degree to which they may be legitimately and widely applied. Finally, models cannot stand alone in determining efficient control strategies, but should be used in con­ junction with accurate field data and experimentally derived data relating to diseases' natural history. The dangers of applying modelling in isolation from traditional field observation have been noted, both in human epidemiology - in the context of a reappraisal of Snow's classical investigation of cholera (Cameron and Jones, 1983) and in veterinary epidemiology (Hugh-Jones, 1983). Indeed, models should incor­ porate veterinary knowledge and experience, and, as such, should be a 'collective veterinary brain'. Otherwise, they may become exercises in mathem­ atical sophistry. -

De Jong, M.C.M. (1 995) Mathematical modelling in veterin­ ary epidemiology: why model building is important.

Preventive Veterinary Medicine, 25, 183-193 Diekmann, O. and Heesterbeek, J.A.P. (2000) Mathematical

Epidemiology of Infectious Diseases. Model Building, Analysis and Interpretation. John Wiley, Chichester Giordano, F.R, Weir, M.D. and Fox, W.P. (1 997) A First Course in Mathematical Modeling, 2nd edn. Brookes/Cole Publishing Company, Pacific Grove. (A general introduc­ tion to mathematical modelling) Halloran, M.E. (1 998) Concepts of infectious disease epi­ demiology. In: Modern Epidemiology, 2nd edn. Rothman, K.J. and Greenland, S., pp. 529-554. Lippincott-Raven, Philadelphia. (A quantitative introduction to the transmission

of infectious disease) Hurd, H.5. and Kaneene, J.B. (1 993) The application of simu­ lation models and systems analysis in epidemiology: a review. Preventive Veterinary Medicine, 15, 81 -99 Isham, V.

(2005)

Stochastic models for epidemics. In:

Celebrating Statistics. Papers in Honour of Sir David Cox on the Occasion of His 80th Birthday. Eds Davison, A.c., Dodge, Y. and Wermuth, N., pp. 27 -54. Oxford University Press, Oxford Kitching, RP., Thrusfield, M.V. and Taylor, N.M. (2006) Use and abuse of mathematical models: an illustration

Further reading

from the 2001 foot and mouth disease epidemic in the United Kingdom. Review Scientifique et Technique. Office

Ackerman, E., Elveback, L.R and Fox, J.P. (1 984) Simulation

of

Infectious

Disease

Epidemics.

Charles

C.

Thomas,

Springfield Anderson, R.M. and May, RM. (1991) Infectious Diseases of

Humans: Dynamics and Control. Oxford University Press, Oxford (Includes a comprehensive description of the basic

models)

International des Epizooties, 25, 293-3 1 1 Manton, K.G. and Stallard, E . (1988) Chronic Disease Modelling:

Measurement and Evaluation of the Risks of Chronic Disease Processes. Charles Griffin & Company, London/Oxford University Press, New York. (A comprehensive description of models of human chronic diseases and aging) Nunn, M., Garner, G. and White, D. (Eds) (1 993) Animal

Anderson, RM. and Nokes, D.J. (1991) Mathematical models

health. Agricultural Systems and Information Technology,

of transmission and control. In: Oxford Textbook of Public

5 (1) 4- 43. (An overview of epidemiological modelling and

Health, 2nd edn. Vol. 2. Eds Holland, W.W., Detels, R and Knox, G., pp. 225-252. Oxford University Press, Oxford

(An introduction to mathematical modelling of infectious dis­ eases and their control, with emphasis on human infections) Bailey, N.T.J. ( 1 975) The Mathematical Theory of Infectious Diseases and its Applications, 2nd edn. Charles Griffin, London Barnes, B. and Fulford, G.N. (2002) Mathematical Modelling

with Case Studies. Taylor and Francis, London and New York. (An introduction to modelling using differential equations, including some medical and veterinary examples) Becker, N.G. (1 989) Analysis of Tnfectious Disease Data. Chapman and Hall, London. (An introduction to models of

infectious diseases) Black, F.L. and Singer, B. (1 987) Elaboration versus simplific­ ation in refining mathematical models of infectious dis­ ease. Annual Review of Microbiology, 41, 677-701 Caswell, H. (2000) Matrix Population Models: Construction,

Analysis, and Interpretation, 2nd edn. Sinauer Associates, Sunderland

examples of systems models) Proceedings of the Mathematical and Information Models for Veterinary Science Workshop, Wednesday 22 Decem­ ber 1993. Moredun Research Institute, Edinburgh, UK. Moredun Research Institute/University of Strathclyde/ Scottish Agricultural Colleges Veterinary Services Scott, M.E. and Smith, G. (Eds) (1 994) Parasitic and Infectious

Diseases: Epidemiology and Ecology. Academic Press, San Diego. (An introduction to modelling, with case studies of infections in humans, livestock and wild animals) Squire, G.R and Hamer, P.J.c. (Eds) (1 990) United Kingdom Register of Agricultural Models 1990. AFRC Institute of Engineering Research, Wrest Park, Silsoe, Bedford. (A list and summary of agricultural models, including some veterinary ones) Thornley, J. and France, J. (2006) Mathematical Models

in Agriculture: Quantitative Methods for the Plant, Animal and Ecological Sciences, 2nd edn. CAB! Publishing, Wallingford. (Includes discussions of models of animal dis­ eases, animal husbandry and animal products)

The economics of animal disease

The importance of financial evaluations in intensive livestock enterprises has been partly responsible for the increased application of economic techniques to animal disease control at farm, national and inter­ national levels since the late 1960s, when the principles were first broadly outlined (Morris, 1969) and 'veter­ inary economics' ('animal health economics') emerged as a specific area of interest in veterinary medicine1 . There has been a tendency to consider economic evalu­ ations as separate, optional exercises, distinct from epi­ demiological investigations. However, this attitude is erroneous: economic assessments are integral parts of many epidemiological investigations (see Figure 2 .2), providing a complementary perspective to that of biological (Le., technical) studies with which the veter­ inarian is more familiar because of his professional training. This complementarity is explored by Howe (1989, 1992). Other factors have also increased veterinary inter­ est in economics (McInerney, 1988). First, in western countries, government veterinary services are increas­ ingly required to justify budgets, as the role of the public sector diminishes. Secondly, as the relative importance of agricultural output declines in western countries, the economic justification for animal disease control is questioned more closely. Thirdly, diseases of farm livestock are barriers to international trade. This problem has become particularly acute with the harmonization of trade in the European Union (which requires free movement of commodities) and the global attempts to liberalize world trade through the World Trade Organization (WTO). Fourthly, rising incomes 1

There was, therefore, a temptation to conclude that animal disease

economics is a veterinary problem within the veterinarian's sphere of competence, rather than an economic issue to be addressed by

and changing social values focus attention on qualitat­ ive aspects of food production, the welfare of animals, and diseases of companion animals. This necessitates a widening of economic perspectives from the initial, relat­ ively narrow, evaluation of disease in farm livestock. This chapter introduces basic economic concepts and principles, and outlines some economic approaches that are relevant to epidemiological investigations. Detailed analytical methods, which, for empirical economic analysis, frequently include a statistical approach - so-called 'econometrics' (Gujarati, 1999; Dougherty, 2002; Greene, 2003) - are not described because it is assumed that most veterinarians are not practising economists, and therefore do not need to apply the various techniques for which some formal training is recommended. Morris and Dijkhuizen (1997) should be consulted for a discussion of some of these methods. Popular misconceptions

Economics is commonly viewed as being focussed on This notion has been reinforced in veterinary medicine by the publication of 'economic' studies that quote the monetary costs of specific diseases such as rotavirus infection (House, 1978) and dermatophilosis (Edwards, 1985). Sometimes, a considerable degree of precision has been attached to the results of such studies (e.g., that the cost of fowl cholera in turkeys in Georgia is $635 645: Morris and Fletcher, 1988), imbuing the studies with a certainty that may not be justified2 . Such an approach generally focusses on the obvious financial costs; for example, the loss calculated as the money.

economists (McInerney, 1996). A related temptation is to treat it as a distinct discipline - a view considered to be unsound (Howe and Christiansen, 2004).

2

Recall, too (Chapter 1), that ' . . . all numbers pose as true'.

l " il

The economics of animal disease

difference between the monetary value to a farmer of a cow if it had remained healthy and productive, and its salvage value (perhaps zero) given the fact of its death. The 'healthy' valuation reflects the value of a cow's potential for producing milk and calves over its entire expected lifetime. In economic terms, its death actually represents the value of lost output (output foregone). This is different from, say, the additional expenditures made on veterinary services, medicines, and manage­ rial effort (control expenditures) in an attempt to save the cow. Note that the terms 'costs' and 'losses' are often used interchangeably. This can be misleading. In the example, the economic costs are actually the sum total of lost output and additional expenditures. As described, the financial costs accrue only to an individual farmer; that is, they are private costs. But economic analysis in its full sense is concerned with the well-being of either society as a whole, or different groups within society (including farmers) and with questions of who gains, and who loses, as a result of any change in circumstances (e.g., a disease outbreak). Thus, social costs must be taken into account. For instance, disease and mortality in animal populations deprive people of the opportunity to consume, say, milk, meat, eggs, wool, or the companionship of pets. These are all examples of real economic losses; that is, of people being deprived of the economic welfare that flows from using animals for their benefit. Money values are not of interest in themselves. They derive from prices. In a market economy, prices are signals that show how much people value the things they consume, given that choices must be made about the allocation of various scarce resources with compet­ ing uses. Resources used up in production of one thing obviously cannot also be used to produce something else: there is an opportunity cost of a given decision - a benefit foregone as a result of doing one thing rather than another. There are different kinds of costs, and it is strictly meaningless to refer to the cost of disease. Also, when disease strikes in a substantial animal population, as opposed to an individual herd or flock, output losses may be so large that market prices increase as a result. Such changed valuations must be taken into account when computing the economic consequences of major disease outbreaks.

An economist's view of the world is based on a set of concepts and generalized abstractions about the nature of their interrelationship (i.e., a theory). The powerful simplicity of the theory means that it is applicable to a wide range of problems, including animal disease. Economics is a social science that illuminates how people exercise choice in the allocation of scarce resources for production, in the distribution and con­ sumption of products, and in the consequences of those decisions for individual and social benefit (Figure 20. 1 ) . Animal disease therefore has economic, as well as biological, impacts because it affects the well-being of people. As noted above, economic analysis is frequently concerned with identification of the optimum level of output in relation to total resource use, and the

Production

(e . g . motor cars,

grassland, feed,

milk, wheat, wool ,

labour)

pony rides)

t

Cost

Fig. 20.1

Economic concepts and principles

Goods and services

Resources (e . g . mineral deposits,

Sometimes the monetary approach is used to suggest that the larger the financial cost, the more important it is to find a solution. Thus, if mastitis in the UK causes annual output losses of £90 million, and lameness induces losses of £44 million, it might be argued that attention should be directed to mastitis first (Booth, 1989). However, this does not address the technical feasibility, costs or duration of control in each case. The relevant consideration for economic efficiency is by how much output losses are expected to fall for a unit increase in control expenditures. So long as the marginal benefit exceeds the marginal control costs, it pays to keep using more resources. The optimal point is found where the last unit of expenditure just pays for itself in terms of output loss reduction. In the ex­ ample, although the highest absolute value of losses might be associated with mastitis, it could. well be the case that lameness control is the rational choice on the marginal criterion. Marginal analysis is indispensable in economic analysis for defining optimal efficiency, and the marginal criterion appears in different forms according to the specific context. In fact, absolute figures such as those quoted are meaningless for guiding policy decisions.

The basic economic model.

Consumption

People

1

Value

Economic concepts and principles "

most efficient combination of resources within that total. The criteria for efficiency are both economic and technical. Generally, disease in domesticated (and sometimes undomesticated) livestock populations reduces the quantity and/or quality of livestock products available for human consumption (i.e. benefit). Examples of such products range from meat and milk to pony rides and the companionship of pets. To be more precise, disease causes production from a given quantity of resources to be of lower quantity and/or quality than could be obtained in its absence. Disease increases costs in two ways. First, because resources are being used inefficiently, the products actually obtained are for an unnecessarily high resource cost: in the absence of disease, the same (or more) output could be obtained for a smaller (or the same) expenditure of resources. Secondly, there is a cost to people, who are deprived because they have fewer, or lower quality, products to consume; that is, they obtain lower benefits. In summary, dis­ ease increases expenditures (production costs) and decreases output (consumer benefits)3. Production functions

The relationship between the resources that provide the inputs to production and the goods and services that comprise the output is called a production func­ tion (Figure 20.2). The resources may be natural (e.g., land and mineral deposits) or man-made (e.g., build­ ings and machinery). Frequently, these undergo phys­ ical transformation (e.g., iron ore into steel, animal feed into body protein) or else facilitate a physical transformation process (e.g., manpower and man­ agerial expertise). Empirical evidence shows that this

3

In rare cases, disease may increase benefits; for example, if it affects

pests. 4 A variable input is defined as an input whose use varies with the planned level of production.

' 0

) .' J

Disease as an economic process

Livestock production is a specific example of a physical transformation process (Figure 20.3). Disease impairs this process (i.e., reduces output) in a variety of ways (McInerney, 1996): destruction of basic resources (death of breeding and productive animals); reduction of the physical output of a production process or its unit value (e.g., lowered milk yield or quality); lowering of the efficiency of the production pro­ cess and the productivity of resources used (e.g., reduced rates of growth or feed conversion); and has wider effects, including: lowering the suitability of livestock products for processing, or generating additional costs in the distribution chain (e.g., warble-fly larval damage to hides; drug residues); affecting human well-being directly (e.g., zoonotic infections such as salmonellosis and brucellosis); generating more diffuse economic effects that reduce the value of livestock to society (e.g., con­ straints on trade and tourism; concern for poor food quality and animal welfare). Thus, there is a loss of efficiency, which poses both technical and economic problems. Figure 20.4 depicts •

Fig. 20.2 The shape of a general production function, plotting i nputs agai nst output.

'

relationship is typically non-linear because certain inputs are typically fixed, and so beyond a certain point an increase in variable input4 is associated with a less than proportionate increase in output - the 'law of diminishing returns' (Heady and Dillon, 1961; Dillon and Anderson, 1 990). Although the idea initially may seem unusual, tech­ nical and economic efficiency are seldom synonym­ ous. Under normal circumstances of diminishing physical returns, they are the same only if inputs are costless. For example, it is efficient in an economic sense for a dairy farmer to aim for maximum milk yield per cow only when the cow's feed is free. If the farmer has to pay for the feed, which, of course, is invariably the case, then it can be shown that optimum economic efficiency is obtained when the yield per cow is less than the maximum technical potential. Furthermore, the overall economic optimum (max­ imum profits) will change with variations in relative prices of both output and inputs and with methods of production. This observation is important in the con­ text of animal disease, because the incidence of disease that is acceptable from an economic point of view may well change with relative prices and techniques of production.

Inputs

"

) (,(l

The economics of animal disease

Physical transformation process Start

End

Conception

Birth

Growth ------i�� Death

� 'i:� > '

h

:C::

S

PR

ITATES

DISEASE

���� � ��� � �

Tec pr _

l

Efficiency losses

e

n

Biological assessment

em

Production function ('healthy' animals)

()

> :::i

� 2

% �CD

The physical transformation

9=> £,

:;

0 '"

Fig. 20.3

process in relation to l i vestock production.

Economic assessment

Production function ('diseased' animals)

'OJ C)

.EO 01 'CD � CD > :::i

All non-veterinary inputs

Livestock inputs

Fig. 20.4

Fig. 20.5

a n i m als.

The recovery of planned output uti l iz i ng veterinary and non-veterinary i nputs. (Based on Howe, 1 985.)

the technical efficiency loss as the difference between the production functions of 'healthy' and 'diseased' animals. Disease acts as a 'negative input', and the relationship between inputs and output is shifted downwards, reflecting lower output for given inputs in diseased animals compared with disease-free animals. The concept of efficiency loss is therefore a relationship, not a number, and is smaller under low­ input, low-output production systems than under more intensive systems. It follows, therefore, that the potential economic importance of disease varies between farms, regions and countries, and therefore that control measures may be justified in one situation, but not in another. If restoration of technical efficiency is the goal, the corresponding economic objective is to find the least­ cost method to restore health and productivity. The options are presented in Figure 20.5 in which only one output - liveweight gain per day - is considered. For an arbitrary quantity of non-veterinary variable inputs, say Xl ' used with a fixed number of animals, point GI indicates the gain per day when they are 'healthy' animals (curve 1 ); G2 identifies the liveweight

gain if they are 'diseased' animals (curve 2). Thus, GI G2 is the loss in technical efficiency. One option is to control the disease exclusively by veterinary interven­ tion, thus restoring Gz to GI. However, reduction of disease commonly does not depend exclusively on veter­ inary services and medicines. An economist regards these as just particular types of inputs that may have substitutes in the form of greater managerial expertise, use of more land to reduce stocking rate, and so on, all of which may reduce disease. Using Xz - Xl additional non-veterinary inputs also restores G2 to GI. In prac­ tice, the option most commonly adopted corresponds to a movement along some intermediate curve, say curve 3. Production is then lifted from G2 to GI in two parts. The proportion of G I - G2 given by RS is achieved by veterinary expenditures, while the remainder (climbing from 5 to T) is achieved by increasing non-veterinary inputs from Xl to x3 . The main goal of economic evaluation is to identify the path corresponding to RST, which enables GI, rather than G2, to be obtained most cheaply; that is, identi­ fying the combination of veterinary and other inputs that will minimize the costs of recovery.

General production function for 'healthy' and 'diseased'

Assessing the economic costs of disease

Assessing the economic costs of disease

The total economic cost of disease can be measured as the sum of output losses and control expenditures. A reduction in output is a loss because it is a benefit that is either taken away (e.g., when milk containing anti­ biotic residues is compulsorily discarded) or unrealized (e.g., decreased milk yield). Expenditures, in contrast, are increases in input, and are usually associated with disease control. Examples of control expenditures are veterinary intervention and increased use of agricul­ tural labour, both of which may be used either ther­ apeutically or prophylactically. The economic costs are more than just the sum of financial outlays, and it is important not to confuse the two. A full evaluation enters the realm of welfare economics, which is beyond the scope of this introductory chapter. Ebel et al. (1992), Howe (1 992) and Kristjanson et al. (1999), outline basic principles and illustrate their application in animal health economics.

LA ---

g LB

h

----�-­

I I I I I I I I I I I I I I I �I

: bE : I I

EA EB Control expenditures (£)

Fig. 20.6

The general relationship between output losses and control

expenditures. (From Schepers, 1 99 0.)

Optimum control strategies Figures 20.4 and 20.5 have used the basic economic model of a production function to illustrate the implica­ tions of disease and its control for technical and eco­ nomic efficiency. A related approach is to explore the general relationship between control expenditures and output losses as defined by a curve, which again demonstrates the law of diminishing returns (Figure 20.6). The curve is an 'efficiency frontier' if it defines the lowest disease losses that can be attained for any level of control expenditure, or the lowest possible expenditures for restricting losses to a specified level5. Combinations of output losses (L) and control expend­ itures (E) to the 'south west' of the curve are unattain­ able, whereas combinations observed to the 'north east' result from technical deficiencies in livestock management. Two control programmes, A and B, are identified in the figure. A change from programme A to programme B involves an increase in control expend­ itures of DE EB - EAI and a decrease in output losses of DL LA - L B ' It is worth increasing the level of control expenditures by DE because DL is greater than DE ' How­ ever, it becomes increasingly expensive to achieve incremental reductions in output losses. The optimum control strategy is defined by point C in Figure 20.7. At this point, the total costs, Tc (Lc + Ec) are the lowest that can be attained (i.e., the avoid­ able costs £0). To the left of C, £1 of control expend­ itures reduces output losses by more than £1; to the =

=

=

'5 a. '5 o

Lc

Ec Control expenditures (£)

Fig. 20.7

Defi n i ng the econom ica l ly opt i m u m control programme. (From Schepers, 1 99 0.)

right of this point, £1 of control expenditures reduces output losses by less than £ 1 . This is an illustration of marginal analysis and, specifically, the principle that resources should be used up to the point where the expenditure on the last unit of resource is just recouped by the additional returns. An example of identifying an optimum control strategy: bovine subclinical mastitis in the U K (Mci nerney e t a/., 1 992)

=

5

This curve relates to persistent or recurrent conditions, such as

bovine mastitis. If the disease of interest could be eradicated (e.g., swine fever), the frontier would intersect the horizontal (E) axis.

Bovine mastitis is considered to be the most important disease affecting dairy cattle in many developed coun­ tries. In the UK, a national mastitis survey conducted in 1977 provided detailed information on the preval­ ence of subclinical infection and control procedures

Table 20.1

Predicted mastitis i ncidence and economic costs associated with 1 8 d i fferent control strategies employed by d a i ry herds in the National Mastitis Survey, U K, 1 9 77. (Mod ified from Mci nerney et al., 1 992 . ) Control method

Effect on incidence

Teal dip/spray

Dry-period

Testing milk

(period)

therapy (cows)

machine

A l l year

All

Yes No

Some None

Part o f year

All Some None

Not used

All Some None

Yes No Yes No Yes No

Croup

Predicted

Loss/expenditure coordinates

Decrease in

incidence rate

incidence (relative

2

1 8.5 22 . 3

3 4 5

2 3 .4 2 7.2 2 7. 8

24.8 21 .0 1 9 .9

6 7

no.

Yes No Yes No

8 9 10 11 12

Yes No Yes No Yes No

13 14 15 16 17 18

(/100 cows/year)

to no contro/)

Control expenditures

(£/1 00 cows/year) (L)

71 0

2296 2 770

1 6. 1 1 5. 5

6 70 49 0 450 2 70

3 1 .6

1 1 .7

230

33.7 3 7.6

9.6 5.7 4.7 0.9 0.3 -3.5

615 5 75 395 355

1 3.0 9.2 8.2 4.4 3.8

38.6 42.4 43.0 46.8 3 0. 3 34.1 35.1 3 8 .9 39.5 43.3

Output losses

(£/100 cows/year) (E)

2899 3 3 73

Total economic cost (C)

3 006 3440 3389

3446 3923

3 82 3 3 71 6 41 53

1 75 1 35

4 1 48 4657 4786 52 6 0 5333 5 8 07

4799 5232 51 81 561 5 5 5 08 5942

480 440 260 22 0 40 0

3 75 1 422 5 4354 482 7 4 9 00 5 3 74

42 3 1 4665 46 1 4 5 04 7 494 0 5 3 74

Cost-benefit analysis of disease control

practised in over 500 herds (Wilson and Richards 1 980; Wilson et al., 1983). The latter include: teat dipping and spraying; dry-cow therapy; annual testing of milking machines. The losses due to subclinical mastitis include: decreased milk yield; changed milk composition; decreased milk quality (e.g., antibiotic residues); accelerated replacement of dairy cows. Sometimes there are offsetting savings in some input expenditures such as decreased feed intake because of loss of appetite in affected cows. Control expenditures relate to the three control techniques, and sufficient published information was available to attach financial values to these expend­ itures and the losses. The prevalence was expressed as the percentage of quarters that were subclinically infected per day, and annual incidence was estimated assuming that subclinical infection lasts an average of 0.6 years (Dodd and Neave, 1970). Table 20.1 lists the predicted disease incidence and the economic costs associated with the various com­ binations of control strategy. The lowest costs that can be attained are associated with control strategy 1 (teat dipping throughout the year, administering drtcow therapy to all eligible animals, and annual testmg of milking machines), where the total costs £3006 per 100 cows per year. The specific relationship between control expenditures and output losses is displayed in Figure 20.8, and is consistent with the general case (Figure 20.7). The curve identifies the 'best practical' options from a technical point of view, and so the cor­ responding economic optimum must be somewhere along its length. If these results are extrapolated to the national herd, they suggest that if strategy 1 were implemented in all • •

;h ;

dairy herds, the overall cost of mastitis to the �a:ion could be reduced from £172.7 million to £159.6 mllhon, at which level the avoidable costs £0. It is these costs that are relevant to decisions about resource allocation and disease control - not the costs measured from a base of zero, which it may be impossible to reach with current control techniques. The costs cannot be reduced further unless investment is made into research to improve methods of mastitis control. =

=

6

1

18 <J) II) <J) <J)

10

11 16

.Q :;

4

3

12

15 6

9

14 13

8

2 - - - - - - - - - - - -

� --

21 IL__________________L-_ 400 800 200 600 Control expenditures (£)

Fig. 20.8

Output losses and control expenditures of farms in the National Mastitis Survey. ( N u mbers refer to the control strategies l i sted i n Table 20. 1 . ) . (From Mcinerney et al., 1 99 2 . )

Cost-benefit analysis of disease control

The costs and benefits of disease control campaigns can be assessed using several methods including gross margin analysis and partial budgeting (Asby et al., 1975). These are essentially straightforward account­ ing approaches, whereas social cost-benefit a��lysis (Pearce, 1 971; Mishan, 1976; Sugden and WIlhams, 1 978; Campbell and Brown, 2003) is really the applica­ tion of a specific technique that allows for the fact that costs and benefits are commonly distributed over time, and sometimes are more than simple financial values. If it is necessary only to minimize the costs of achieving a given objective, then a cost-effective study is und�r­ taken. The remainder of this chapter introduces partIal budgets and social cost-benefit analysis. Partial farm budgets

Partial farm budgets have been used to assess the suit­ ability of control strategies (notably against en��mic diseases such as mastitis and internal paraSItIsm) on individual farms. A partial budget is a simple description of the financial consequences of parti�u­ lar changes in farm management procedures, of WhICh disease control programmes are a part. 'Partial' indic­ ates that assessment is restricted to the factors that are likely to change as a result of the procedural changes. There are four main components: 1 . additional revenue realized from the change, r1 ; 2. reduced costs stemming from the change, c1; 3. increased costs as a result of the change, r2; 4 . cost of implementing the change, c2 . If (r1 + c1 ) > (r2 + c2), then the proposed change is justified. For example (Erb, 1 984), if a new programme to control subclinical mastitis comprised maintenance of milking machines, routine intramammary dry-cow therapy and teat dipping, then: sales due to increased milk production; r c� savings stemming from fewer cases of clinical mastitis to treat; •

=

=

.I f,,1

The economics of animal disease

r2 =

increased feed costs due to increased milk production; c2 = costs of implementation (disinfectants, drycow intramammary preparations). A one-year partial farm budget for this programme produced values of r1 = £397, c1 = £18, r2 = £77, c2 = £246. Thus: r1 + c1 = £415, •

r2 + c2 = £323.

and so there is a net benefit of £92, indicating that the farm should increase its annual profits by that amount if it invests in the control campaign. Social cost-benefit analysis (CBA)

Social cost-benefit analysis developed as a means of assessing large-scale investment policies. It evolved in the public sector, as an aid to resource allocation in areas where markets do not exist, where there are no clear 'market signals' to guide the size and direction of investments, and where governments are responsible for determining the shape of services (Burchell, 1983). It has been used widely in veterinary medicine to assess national animal disease control campaigns against infectious diseases; for example, swine fever (Ellis et ai., 1977), rinderpest (Felton and Ellis, 1978; Tambi et ai., 1999), rabies (Aubert, 1999), bovine virus diarrhoea (Valle et al., 2000) and foot-and-mouth dis­ ease (Berentsen et ai., 1992a,b; James and Rushton, 2002). Principles of eBA

Social cost-benefit analysis attempts to quantify the social advantages and disadvantages of a policy in terms of a common monetary unit. For example, the building of a road will incur costs to society arising from the resources expended on construction and maintenance, the undesirable side-effects of pollution, increased noise levels and spoiling of the landscape. The benefits include savings in travelling time, reduced congestion and decreased noise levels in a town if the road is a bypass. Some of the costs or benefits (e.g., construction outlays - costs) are expressed easily in pecuniary values. Other costs or benefits (e.g., decreased noise level - a benefit), how­ ever, are much more difficult to translate into monet­ ary terms; these are called intangibles. Only by using the common denominator of money is it possible to aggregate the gains and losses that ultimately interest society as the benefits and costs perceived in reai terms; that is, as adding to or reducing people's sense of well­ being. Consequently, it is important to quantify, in

monetary units, all important factors as comprehens­ ively as possible. Any problem areas should be made explicit, especially where the value of intangibles is assessed subjectively or even not at all. If a disease control programme were initiated, costs would include those of manpower, drugs, vaccines, quarantine buildings, compensation for slaughter, transportation and training programmes. The benefits would include increased productivity, decreased animal and (in the case of zoonotic diseases) human suffering, increased trade and the psychological well­ being accompanying the decreased disease incidence. The prefix 'social' to CBA is often dropped from the name but is important. It emphasizes that CBA is used by an organization to maximize the net benefits to society, rather than maximizing its own purely private benefits (Pearce and Sturmey, 1966). 'Internal' and 'external' costs and benefits

(private costs and benefits) are those that accrue directly to an investment project. Costs and benefits accruing to others are termed externalities. It is the externalities that mainly are not reflected in the price mechanism (which therefore becomes inade­ quate as a guide to correct investment decisions from the point of view of society). For example, a farm mastitis control campaign includes dry-cow antibiotic therapy (a cost) and increased milk yield (a benefit), both of which are part of the farm's budget and there­ fore internal. However, antibiotic residues in milk may have undesirable side-effects on unknowing con­ sumers. If they were aware of the risks, they would be prepared to pay less for the milk (it indeed, they would buy it at all). To protect consumers, and to 'internalize' the external effects, legislation limiting the use of antibiotics and affected milk may be necessary, instead of reliance on a deficient price mechanism. Similarly, in a foot-and-mouth disease campaign in Britain, farmers' loss of slaughtered animals is an inter­ nal cost, whereas the inconvenience of restrictions on movement and access is an external cost. Internalities

Discounting

Control campaigns may operate over several years. The value of a sum of money in hand now is greater than the same sum of money received at a later date. This is because being able to consume now is con­ sidered preferable to having to wait to consume in the future, or because a sum invested now will produce a larger sum in the future as interest accrues. If the interest rate is 5% per annum, then £100 now is worth £105 compound in 1 year's time, £1 10.25 in 2 years, and so on. If costs and benefits, spread over several years, are to be compared, then they must be adjusted to

" , " M' " "" " " "'"""'" "'"'"""

calculate their value now. The process of adjustment, which is the opposite of compounding, is called discounting. The formulae for its calculation are described by Gittinger (1972) and Little and Mirrlees (1974). The calculation uses a rate of discount that is usually defined by governments, for example the World Bank Rate and, in Britain, the Treasury Rate. Cost-benefit analysis is performed in real terms, which means that the rate of interest used in the calculations is adjusted to exclude the effects of price inflation.

Cost-benefit analysis of disease control

Bo - Co B1 - C1

H) ;

B n - Cn

NPV = -- + -- + . . . + --(1 + r)o (1 + r)1 (1 + r)n =

± B t - Ctt

t=O (1 + r)

where: Ct value of costs incurred in time t; Bt = value of benefits gained in time t; r discount rate; n life of project. A project is considered to be viable if the NPV is positive. The benefit:cost ratio (B/C ) is the ratio of the present value of benefits to that of costs. It is given by: =

=

=

Shadow prices

The social value of a benefit may not always be the market price. For example, a litre of milk is valued by the farmer at its market price. However, when govern­ ments use trade barriers to increase product prices for domestic farmers as, for example, happened in the European Union before production quotas were introduced, a milk surplus may develop. Then the real economic value to society of the excess supply must be less than its (supported) market price. A national disease control campaign that resulted in increased milk surpluses under price support therefore would use the value of the excess milk, termed a shadow price, as a better estimate of its true economic value to society. This will be the international market price if supplies are disposed of on the world market. Uncertainty

Any project is accompanied by uncertainty. The results of a control campaign cannot be known with certainty, but it is necessary to have an idea what the outcome might be. There are two approaches to dealing with uncertainty. First, if a model is con­ structed, the 'most probable outcome' can be defined; a sensitivity analysis (see Chapter 19) can then be con­ ducted to determine whether changes in the model's parameters can produce major changes in the out­ come. Alternatively, the likelihood of the various outcomes can be judged using probability theory (Reutlinger, 1970). Criteria for selecting a control campaign

Three important measures of economic efficiency used as criteria for selecting a control campaign are: 1. net present value (NPV); 2. benefit:cost ratio ( B/C); 3. internal rate of return (IRR). The net present value (NPV) is the value of the stream of discounted benefits less costs over n time periods. It is given by:

n B/ C = L { B I (1 + r)i } / { CP + r)i} t=O ±B . t=oCt r

=

t

A project is viable if the ratio is greater than or equal to 1 . The internal rate of return (IRR) is the rate of dis­ count that equates the present value of the costs with the present value of the benefits. It is given by solving for r such that: NPV =

n Bt - Ct I, _ t=O (1 + r)i

_

=

.

If the internal rate of return of an investment project is greater than the actual interest rate, the project is economically worthwhile. An example of CBA: alternative policies for the prevention, control and eradication of infestation with Chrysomyia bezziana in Australia (Cason and Geering, 1 980)

the Old World screw-worm fly (SWF), causes serious economic losses in livestock in Africa, Asia and Papua New Guinea. Damage caused by burrowing larvae can result in a case fatality rate of up to 50% in young animals, and can cause loss of condition, occasional deaths and sterility (if genitalia are struck) in adults. The disease is not present in Australia, but if the fly entered Australia, potential losses have been estimated at around $100 million per annum. The most likely method of entry into Australia would be by movement of infested livestock across the Torres Strait islands from Papua New Guinea, although entry could also occur either by the direct flight of the flies or by transmission of the flies by migratory birds and aircraft. Chrysomyia bezziana,

, b()

The economics of animal disease

Strategies to prevent the introduction and establish­ ment of SWF in Australia include: improved quarantine surveillance, including training of local inhabitants and education programmes; better control of livestock in danger areas, possibly including total destocking of the Torres Strait islands - although this would probably be socially unacceptable to the islanders; the development of a SWF monitoring system, facilitated by a specific chemical bait ('Swormlure'); the construction of a clinic in the Torres Strait islands to neuter dogs and cats (potential hosts of SWF); eradication of SWF from Papua New Guinea. The major strategy to control and eradicate an out­ break of infestation with SWF in Australia is ground control of the fly, consisting of restriction of movement of livestock, dipping and spraying with insecticides, the use of a sterile insect release method, by which ster­ ile male flies compete with fertile male flies for each mating female, and the use of a screw-worm adult sup­ pression system (SWASS), in which poisoned baits are released by aeroplane over infested areas. The quickest response to an outbreak of SWF infestation would be obtained if a sterile SWF facility were built in advance, but not opened until an outbreak occurred. Table 20.2 shows the benefit:cost ratios for the vari­ ous strategies over a 20-year period, assuming that

infestation occurred after 1, 10 or 20 years. In all cases the benefit:cost ratios are greater than 1, indicating that all techniques are economically justifiable. In the example, the benefits do not derive from increased production, but from decreasing the risk of infestation. Although the benefit:cost ratios are high, they have to be weighed against the probability of infestation occurring when a particular policy either is or is not adopted. These and other considerations are discussed by the authors of the study.

Some problems associated with eBA

There are several general problems related to CBA. The technique assumes that the preferences and priorit­ ies of society are known; this may not always be true. The technique also applies current social preferences, rather than future ones. Additionally, as indicated earlier, the costs and benefits of externalities and intangibles may be difficult to assess. There are specific problems relating to disease con­ trol policy formulation (Schepers, 1990). A CBA refers to only one combination of control expenditures and output losses. Thus, point Z in Figure 20.7 represents a benefit:cost ratio greater than 1; that is, the reduction in output losses exceeds the control expenditures. Indeed, the combinations of expenditures and losses furthest to the left of the curve have the greatest benefit:cost ratios, and there may be the temptation to fallaciously conclude that the larger the benefit:cost ratio, the more economically efficient the control technique. However,

Table 20.2 Cost-benefit analysis of strategies for the prevention, control and eradication of infestation with Chrysomyia bezziana in Austra l ia. (The analysis i s i n present values over a 2 0-year period, and assumes that the methods prevent Austra l i a-wide losses commencing i n year 1 , year 1 0, year 2 0; d i scou nted at 9 . 5 %) . (Modified from Cason and Geering, 1 98 0.) Prevention method

Year infestation prevented

Benefjt: $389m C05t ($000)

Benefit:cost ratio

10

20

Benefit: $ 164m

Benefit: $69m

Cost ($000)

Benefit:cost ratio

C05t ($000)

Benefit:cost ratio

Strategic eradication from Papua New G u i nea

2 962

1 31

1 1 734

14

1 6 123

4

Mothba l led factory and maintenance colony Ground contro l *

1 394 2 52 3

2 79 1 54

1 670 1 065

98 1 54

1 8 09 449

38 1 55

Destocki ng of Torres Strait islands I m proving quarantine

657

592

776

212

836

83

1 24

3 1 37

41 7

394

563

123

961

241 91

288 763

1 19 56

583 1 239

'Sworm l u re' trapping and myiasis monitoring Tra i n i ng

30

1 2 966

1 71

26

1 4 96 1

69

Extension Torres Strait c l i n ic

13 7

29 923 55 5 7 1

83 40

* Inc l udes the SWASS tech n i q u e (see text).

2 3 83 1 980 4 110

Cost-benefit analysis of disease control

the economically optimum control programme is indicated by point C; this will be identified by a CBA only if the CBA happens, by chance, to be concerned with evaluating a control policy corresponding to point C. Moreover, CBA is a relatively sophisticated tech­ nique, but may be applied in situations - especially in the developing countries - where accurate basic data are lacking (Grindle, 1980, 1986). For example, there may be inadequate information on livestock numbers, disease morbidity and the actual economic impact of disease. It may also be impossible to predict future market prices (e.g., of beef and milk), which need to be included in analyses. The sophistication of the eco­ nomic techniques therefore needs to be balanced with the quality of the epidemiological data that are avail­ able. However, although CBA and other techniques of project evaluation are, at best, approximate (Gittinger, 1972), they play a useful role in economic evaluation. Despite its limitations, CBA is a rigorous approach to project evaluation, and its application can help towards better informed decisions regarding the efficient use of scarce resources in disease control programmes.

Agriculture, 2nd edn. Pergamon Press, Oxford. (A general introduction to agricultural economics) Howe, KS. (1 992) Epidemiologists' views of economics - an economist's reply. In: Society for Veterinary Epidemio­ logy and Preventive Medicine, Proceedings, Edinburgh, 1-3 April 1992. Ed. Thrusfield, M.V., pp. 157-167 Howe, KS. and Christiansen, K (2004) The state of animal health economics: a review. In: Society for Veterinary Epidemiology and Preventive Medicine, Proceedings, Martigny, 24-26 March 2004. Eds Reid, S.W.J. Menzies, F.D. and Russell, A.M., pp. 153-165 Howe, KS. and McInerney (Eds) (1 987) Agriculture. Disease

in Farm Livestock: Economics and Policy. Proceedings of a symposium in the Community programme for coordina­ tion of agricultural research, 1-3 July 1987, Exeter. Report EUR 11285 EN. Commission of the European Com­ munities, Luxembourg. (A study of economic losses due to

animal disease in the European Union, and methods for the economic assessment of disease control) Kristjanson, P.M., Swallow, B.M., Rowlands, G.J., Kruska, RL. and de Leeuw, P.N. (1999) Measuring the costs of African animal trypanosomosis, the potential benefits of control and returns to research. Agricultural Systems, 59, 79-98 Mather, E.C. and Kaneene, J.B. (Eds) (1 986) Economics of

Animal Diseases. Proceedings of a conference held at Michigan State University, 23 -25 June 1986. Michigan

Further reading

State University, Michigan McInerney, J.P. (1996) Old economics for new problems­

Ansell, D.J. and Done, J.T. (1988) Veterinary Research and

Development: Cost-Benefit Studies on Products for the Control of Animal Diseases. CAS Joint Publication No. 3. Centre for Agricultural Strategy, Reading/British Veterinary Association, London Dykhuizen, A.A. (1993) Modelling animal health economics. In: Society for Veterinary Epidemiology and Preventive Medicine, Proceedings, Exeter, 31 March-2 April 1993. Ed.

McInerney, J.P., Howe, KS. and Schepers, J.A. (1 992) A framework for the economic analysis of disease in farm

livestock. Preventive Veterinary Medicine, 13, 137-154

E.J. (1 982) Cost-Benefit Analysis: An Informal Introduction, 3rd edn. Allen and Unwin, London Morris, RS. and Dijkhuizen, A.A. (Eds) (1997) Animal Health

Mishan,

Economics:

Thrusfield, M.V., pp. ix-xx Ebel, E.D., Hornbaker, RH.

livestock disease: Presidential Address. Journal of Agri­

cultural Economics, 47, 295 -314

and Nelson, C.H.

(1 992)

Welfare effects of the national pseudorabies eradication program. American Journal of Agricultural Economics, 74, 638- 645 Ellis, P.R and James, A.D. (1 979) The economics of animal health-(1) Major disease control programmes. Veterinary

Record, 105, 504-506 Ellis, P.R and James, A.D. (1 979) The economics of animal health - (2) Economics in farm practice. Veterinary Record, 105, 523 -526 Erb, H. (1 984) Economics for veterinary farm practice. In

Practice, 6, 33-37 Hill, B. (1990) Introduction to Economics for Students of

Principles

and

Applications.

Postgraduate

Foundation in Veterinary Science, University of Sydney, Sydney Ngategize, P.K and Kaneene, J.B. (1985) Evaluation of the economic impact of animal diseases on production: a review. Veterinary Bulletin, 55, 153 -162. (A review of some analytical techniques) OlE (1 999) The economics of animal disease control. Revue Scientifique et Technique, Office International des Epizooties, 18, 295-561 Putt, S.N.H., Shaw, A.P.M., Woods, A.J., Tyler, L. and James, A.D. (1987) Veterinary Epidemiology and Economics in Africa. ILCA Manual No. 3, International Livestock Centre for Africa, Addis Ababa

Health schemes

Private health and productivity schemes

The traditional role of the veterinarian has been to attend individual sick animals when requested to do so by the owner: such attention has been called 'fire brigade' treatment. This approach was useful when most diseases, such as the classical epidemic infecti­ ous diseases, had a predominantly single cause and responded to a simple course of treatment. However, an appreciation during the 1960s of the multifactorial nature of many diseases, which coincided with intensification of animal industries in the developed countries, with a relative decrease in the value of individual animals, resulted in a change in attitude towards the management of diseases in livestock units (see Chapter 1). First, it became clear that diseases needed to be controlled by simultaneously manipulat­ ing all determinants: those associated with agent, host and environment. The veterinarian's objective should be to prevent, rather than to treat, disease. Secondly, it became necessary to consider disease in terms of its contribution to reduced performance (and therefore profitability) of a herd 1 . The first change stimulated the development of pre­ ventive medicine programmes in the early 1960s. The second change resulted in the evolution of comprehen­ sive herd health and productivity schemes, encom­ passing preventive medicine and the assessment of productivity (Blood et al., 1978; Cannon et al., 1978; 1

Performance-related diagnosis was introduced in Chapter

1 ; and an

example of multifactorial 'disease', defined in terms of a production

shortfall in a population, was given in Figure 5.2. The concept of a 'sick'

Ekesbo et al., 1994). These programmes and schemes may be run by one or more general practitioners, with data stored by the practitioners (the 'bureaux' approach); alternatively, the data may be managed entirely 'on farm' (Etherington et al., 1995). All are concerned with problems on individual farms; they are therefore private schemes. Structure of private h ealth and productivity schemes Objectives

The goals of a health and productivity scheme were initially summarized by Blood (1976). They should: identify disease and productivity constraints and problems on a farm; rate the problems in order of importance, with reference to technical and economic criteria2; initiate suitable control techniques and measure their success, not only technically but also with regard to the economic efficiency of the utilization of resources at the national and individual farm level, thereby indicating which technique should be increased and which reduced. The scope of service offered by the veterinarian in a comprehensive health and productivity scheme (Grunsell et al., 1969; Ribble, 1989) includes: the diagnosis and prevention of the major epi­ demic diseases; •

population is not confined to veterinary medicine, though. Medical epidemiologists also search for characteristics of 'sick' populations, for example to answer the questions 'Why is hypertension common in London but absent from Kenyans?' and 'Why is coronary heart disease common in Finland but rare in Japan?'

2

The financial impact of production diseases can be measured in

terms of relative health indices such as Healex (Esslemont and Kossaibati,

2002), which compares direct losses due to disease with those in 'top'

herds.

Private health and productivity schemes

• • •

an emergency service for individual animals; the supply of drugs; advice on environmental determinants (nutrition, housing and management); advice on production techniques and general policies of livestock farming.

This scope is broad and indicates that the veterin­ arian requires more than just a knowledge of the diag­ nosis and treatment of clinical disease. In many cases, the veterinarian may need to enlist further expert help from nutritionists, building advisors, and manage­ ment specialists who have some knowledge of farm economics. Components

There are differences between the schemes applied to different species, but the principles are the same. The main components of a scheme are: •

• • • •

the recording of a farm profile comprising details of animal numbers, buildings and feeding sys­ tems, stocking density, nutrition, usual manage­ ment practices, disease status and current levels of production; identification of production shortfalls; monitoring of all aspects of production; identification of the major disease problems; routine prophylaxis against the major disease risks; definition of production targets that are suitable for the system of management operating on the particular livestock units and for the aims of the farmer; advice on management and husbandry, to achieve the predetermined targets; detection of unacceptable shortfalls in production (and therefore in profitability); correction of the shortfalls by eliminating the defects associated with agent, host and environ­ ment, or revising the production targets in the light of experience; identification of farmers' perception of strengths and weaknesses in health, fertility and nutrition.

Regular visits to farms are an important part of health schemes. A health plan is drawn up containing details of procedures (e.g., routine treatments and vac­ cination) to be followed during the year. Health and productivity schemes require accurate records to be kept. Early schemes used longhand records, but most contemporary systems store data on computers where the data can be analysed rapidly. The first computerized systems were run on main­ frames and were organized by central advisory bureaux. There is now a trend towards complete

H/)

decision support systems (see Chapter 1 1 ), mounted on microcomputers, which support farmers in herd management. For example, CHESS (Computerized Herd Evaluation System for Sows) comprises a deci­ sion support system that assesses performance in pig breeding herds, and three expert systems that attempt to identify strengths and weaknesses in the enterprises in an economic context (Huirne and Dijkhuizen, 1994). All of these systems are essentially microscale (see Table 1 1 .2 ) .

Targets

The variables that are used to determine production targets are described below in relation to the different species. Targets usually have been defined as mea­ sures of position (e.g., mean age of dry sows) or as upper or lower limits (e.g., maximum calving interval or minimum first service pregnancy rate in dairy cat­ tle). Measures of location do not indicate the dis­ persion of values in a herd and can be misleading; measures of dispersion, such as the standard deviation (when a variable is Normally distributed) or the semi­ interquartile range are more informative (see Chapter 1 2). Thus, if a farmer bred some cows very soon (less than 35 days) after calving, then the measure of posi­ tion would be reduced, but the measure of dispersion would be increased. This can eliminate the economic benefit that owners think they are achieving because the economic benefit results from most cows calving with intervals close to 365 days (Morris, 1 982); the benefit will not exist with a large dispersion. Some variables that are used as production indices have frequency distributions that are skewed, in which case the mean may be far from the peak of the distribution. For example, the frequency distribution of calving to conception intervals is positively skewed; typically the median may be 1 0 days less than the mean. More appropriate measures of position and dispersion therefore would be the median and semi-interquartile range, respectively. Logarithmic transformation of values (see Chapter 1 2) may be undertaken because this may convert skewed dis­ tributions to Normal ones. Morant (1984) discusses the appropriateness of measures in relation to dairy fertility, giving examples. In practice, mean values usually are used because they are understood by farmers. This approach works, provided they also appreciate the notion of dispersion of values. No single set of standards can be set as production targets because satisfactory performance varies with type of farm and management practices (Kay, 1986). Internal standards can be set, using a farm's historical data (say, over the previous three years). Additionally, external standards, such as the mean performance (with the associated standard deviation) of similar

) 7()

Health schemes

herds, may be specified. In The Netherlands, for example, such standards are published for pig breed­ ing herds (Baltussen et al., 1988) and in the UK for dairy herds (Whitaker et al., 2000, 2004). Measuring shortfalls in production

Shortfalls in production are defined by an action level (also termed an interference level). This is the level at which the recorded production variable ceases to be acceptable in relation to its target level. Action levels are often identified by experience, based on financial criteria; and defined as levels beyond which there is unacceptable financial loss. When the measurement of location of a variable (the mean commonly has been used), recorded over a period of time, is beyond the action level, corrective measures are undertaken. This method does not consider the effects of random vari­ ation. These can be accommodated by defining the action levels as statistical parameters of the target level; the standard error is a suitable parameter for Normally distributed data. Suitable techniques for continuous data are the construction of cusums and Shewhart charts (see Chapter 12). Justification

A herd health and productivity scheme must be eco­ nomically justifiable. The economic justification of these schemes is well documented (e.g., Williamson, 1980, 1987, 1993). Pharo et al. (1984) derived a benefit:cost ratio of approximately 3:1 for a computer­ ized dairy herd health and productivity scheme in Britain over a 5-year period, and a similar value has been estimated for a scheme in the US (Williamson, 1987)3. Similarly, Brand et al. (1996) demonstrated that herd health schemes improved farms' economic results in The Netherlands4. Details of schemes for the various species given below are presented only as introductory examples and therefore are not comprehensive descriptions of the systems. Eddy (1992) gives a concise introduction to these schemes, and Rueg (2001) describes them in detail. 1

Demonstration of benefits requires analysis of appropriate data from

herds, some of which may be large. Chamberlain and Wassell ( 1 995) sug­ gest that, for most variables, adequate precision (see Chapters 9 and 13) to assess poor herd performance is achieved from a sample of animals in a herd (approximately 40 cows from a 200-cow herd, and 20 cows from a 100-cow herd), but that it is not achieved for some variables (e.g., annual culling rate), in which circumstance data from the whole herd should be monitored. 4 Despite the financial advantages and the benefits perceived by vet­ erinarians, uptake by farmers has been slow in some sectors: in the early 1 990s, for example, about one third of dairy practices in the UK had

Dairy h ealth and productivi ty schemes

Dairy health and productivity schemes were devel­ oped in the 1950s and since then have received con­ siderable attention. The main object of a dairy scheme is to improve welfare and productivity by maximizing health, milk yield and milk quality under the particu­ lar system of management on the farm. Optimum milk yield and quality are achieved by: efficient reproduction; decreasing important diseases - especially mastitis and lameness; optimum feeding - both nutritionally and economically. •

Targets

Some suggested targets for efficient reproduction for a dairy enterprise in the UK are listed in Table 21 . 1 . North American targets are given by Fetrow et al. (1997). A target mean calving to conception interval of 85 days is often recommended. This facilitates an annual reproductive cycle (because the cow's gestation period is approximately 280 days, with a calving inter­ val (the interval between calvings for an individual cow) of 365 days, and a calving index (the mean cal­ ving interval for all cows) with a similar value. The index variables used in measuring reproductive performance are complex, and need to be interpreted with care (Eddy, 1992). The calving to conception interval, for example, is related to the calving to first service interval and to the first service to conception Table 21.1

Suggested reprod uctive performance targets for a d a i ry

herd in the U K . (Modified from Eddy, 1 992 . )

Index variable

Target

Interference level

Mean calving to conception i nterva l

85 days

95 days

Mean calving to first service i nterval

65 days

70 days

20 days 60 60

25 days 50 50 >23

Mean first service to conception interval Pregnancy rate to first service (0;;» Pregnancy rate t o a l l services ( %) Overa l l c u l l i ng rate ( % ) Per cent served of cows calved Per cent conceived of cows cal ved Per cent conceived of cows served

1 0% variation

Miscell aneous Pigs reared/sow/year Sow feed (tonnes/year)

7 days 5

9 days

level

(a) The dry sow

Weaning to service interval average Normal repeat service ( %)

Abnormal repeat service ('Yo) Abortions ( %) Sows i nfertile not i n pig ( %)

Low viabil ity Starvation Scour

1 :15

3

5

Morta l ity ( % ) Feed conversion from wea n i n g : Pork ( 6 0 kg) Cutter ( 8 0 kg) Bacon ( 9 0 kg) Heavy ( 1 1 5 kg)

Sow deaths ( % ) Sows cul led due to d i sease ( o,{,)

2

3

"

200

"

170

40

29 50 2

43 46

1 1 11 1 37 40 29 50

25 1 9 2 50

2

15

2 5 2

46

25 2

5 2

Fig. 22.4 The distribution of soi l and grass copper levels (dry mass in parts per m i l l ion, ppm) in an area close to the Kruger National Park, South Africa, 1989. (Redrawn from G u m mow et al., 1991 .)

• •

medical 'detective work' (Chapter 2); exploration of the temporal and spatial distribu­ tion of disease (Chapter 4); reasoning by the method of difference (Chapter 3): the problem was greater during dry years; recording of age-specific values (Chapter 4): the cumulative nature of the poisoning resulted in cases only becoming clinically apparent in older animals.

It also highlights that epidemiological investigations are as concerned with ruling out disease as with ruling it in. The link to low rainfall periods was inconsistent with vector-borne outbreaks and leptospirosis; the age profile of cases was inconsistent with a vector-borne or infectious disease, and the occurrence in Bas indicus a species relatively resistant to tick-borne diseases - also reduced the likelihood of the disease being vector­ borne. -

Veterinary medicine in the 2 1 st century Chapter 1 described how veterinary medicine coped with various challenges during its development. This final chapter ends with some thoughts on the future direction of the veterinary profession, highlighting the contribution that epidemiology will make. The topic is discussed in greater detail by Henderson (1982), Hugh-Jones (1983), Pritchard (1986, 1 989), Michell (1993), IAEA (1998) and Catanzaro and Hall (2002).

L ivestock medicine Multifactorial diseases are the major problems in intensive livestock enterprises. Investigation of their cause does not involve the study of a simple infectious agent, but of several determinants associated with host, agent and environment. The environment is also

,m �)

The control and eradication of disease

recognized as important because of its significance to animal welfare (Ekesbo, 1992). Observational studies (see Chapter 15) provide a critical framework for identi­ fying the many determinants of disease in intensive enterprises. Epidemiological principles and concepts are also applicable to welfare issues (McInerney, 1 991; Willeberg, 199 1 ) . Modelling of livestock units, using variables asso­ ciated with disease and production, will continue to develop, facilitated by microcomputerized decision support systems (see Chapter 1 1 ) . These also facilitate definition of the most suitable technical and economic production variables, and provide methods for assess­ ing individual and herd performance (e.g., Huirne et al., 1991, 1 992; Huirne and Dijkhuizen, 1 994). In developing countries, there is a need for an improvement in the 'quality' of data. For example, the epidemic infectious diseases such as rinderpest still pose problems, and eradication campaigns require application of appropriate sampling techniques in their terminal stages (see Chapter 13). Participatory epidemiology (Chapter 10) is likely to expand to fulfil this goal. Additionally, there is a move towards privat­ ization of veterinary services in these countries, stem­ ming from a decline in the efficiency of public services due to financial constraints (de Hann and Umali, 1 992). This move is likely to expand, although not without some resistance (Turkson and Brownie, 1999). Methods of identifying infectious diseases are becoming more analytically sensitive and refined. Smaller quantities of antigen can be detected, and sub­ tle differences between strains can be identified using ELISA tests, monoclonal antibodies and the newer molecular techniques (see Chapter 2). All of these tech­ niques are now being applied to the diagnosis of bacter­ ial, virus and parasitic diseases of animals (Ambrosio and de Waal, 1 990; Knowles and Gorham, 1 990; OlE, 1993). However, they have some disadvantages, and older techniques therefore still have an important role (Wilson, 1 993). For example, the analytical sensitivity and specificity of DNA probe technology - which involves a whole new level of complexity - is similar to conventional microscopy in diagnosing human malaria. Similarly, the polymerase chain reaction can produce false positive results due to contamination (Pang et al., 1992) and is relatively slow. New techniques are producing vaccines that are safer than formerly. For example, sub-unit vaccines comprise only virus capsid antigens and lack nucleic acid, and therefore cannot be pathogenic. Vaccines against helminths (e.g., Dictyocaulus viviparus) are few but they have a considerable advantage over the cur­ rent anthelmintics, with the latter's associated risk of resistance and short period of action. The breeding of resistant stock may be a more useful technique because techniques such as embryo cloning, superoVUlation

and nuclear transplantation can accelerate this other­ wise slow process.

Companion-animal medicine In developed countries, the number of pet-owning households is increasing (e.g., Singleton, 1993), and there is a concomitant increase in the proportion of veterinarians engaged in companion-animal practice (e.g., Figure 1 .4). The public'S expectation of veterinary services will continue to rise and this will be reflected in improvements in the quality of patient care, invol­ ving better surgical techniques and medical therapy, and newer diagnostic methods (Leutenegger et al., 2003). All of these are now subject to more critical evalu­ ation than previously in properly designed clinical trials (see Chapter 1 6) and diagnostic-test validation (see Chapter 1 7) . Advances in gene-targetted cancer therapy, recently evidenced in human medicine (Kaelin, 1999), may also be directed to companion­ animal tumours. However, the impact of advances in biotechnology, in general, may be slower than initially anticipated (Nightingale and Martin, 2004). The aim of medical epidemiologists is to ensure that each person enjoys a long life with morbidity confined to a short period before death12. This goal can be shared by veterinarians, and its achievement requires research on improved preventive techniques, such as vaccination, and on the determinants associated with chronic and refractory diseases, such as canine heart disease and dermatoses. Observational studies (see Chapter 15) again provide a critical framework for such research. This research is still hampered by a lack of basic demographic and morbidity data from a wide cross-section of the companion-animal population, although more data are becoming available (Table 4.2). However, the increasing availability of inexpensive microcomputers to veterinary practitioners, and the expansion of computer networks, notably the Internet, should facilitate the gathering and sharing of these data. Epidemiology plays a central role in the continu­ ing development and improvement of livestock and companion-animal veterinary medicine. Its contem­ porary objectives have many similarities with those of ancient Greek medicine, described by Hippocrates, in the 'Second Constitution' of Book 1 of his Epidemics, as to: 'Declare the past, diagnose the present, foretell the future' ( Jones, 1923) 12 In some western countries, increased life expectancy is an added goal (USDHHC, 2000).

Veterinary medicine in the 21 st century

F u rther reading Artois, M., Delahay, R, Guberti, V. and Cheeseman, C. (2001) Control of infectious diseases of wildlife in Europe. The Veterinary Journal, 162, 141-152 Babiuk, L.A (2002) Vaccination: a management tool in veter­ inary medicine. The Veterinary Journal, 164, 188-201 Biggs, P.M. (1985) Infectious disease and its control. Philosophical Transactions of the Royal Society of London, Series B, 310, 259-274 Blancou, J. (2003) History of the Surveillance and Control of Transmissible Animal Diseases. Office International des Epizooties, Paris Bourne, F.J. (1993) Biotechnology and farm animal medicine. In: The Advancement of Veterinary Science. The Bicentenary Symposium Series. Volume 1: Veterinary Medicine beyond 2000. Ed. Michell, AR, pp. 41-57. CAB International, Wallingford. (A discussion of the application of modern biotechnology to animal disease control) Brander, G.c. and Ellis, P.R (1976) The Control of Disease. Bailliere Tindall, London. (A general discussion of the pre­ vention of infectious diseases in animals, including zoonoses) Correa Melo, E. and Gerster, F. (Coordinators) (2003) Veterinary Services: organisation, quality assurance, evalu­ ation. Revue Scientifique et Technique, Office International

des Epizooties, 22, 355 -768. (A global review of veterinary services) England, J.J. (Ed.) (2002) Animal health emergency diseases. Veterinary Clinics of North America, Food Animal Practice, 18 (3), 1-583. (A general description of some exotic diseases, including their control) Geering, W.A, Roeder, P.L. and Obi, T.u. (1999) Manual on the Preparation of National Animal Disease Emergency Preparedness Plans. FAO Animal Health Manuual No. 6. Food and Agriculture Organization of the United Nations, Rome. (A comprehensive discussion of the procedures and structures necessary for controlling outbreaks of infectious dis­ eases; also containing a list of training aids, including books, interactive software, and videos) Geering, W.A, Penrith, M.-L. and Nyakahuma (2001) Manual on Procedures for Disease Eradication and Stamping Out. FAO Animal Health Manual No. 12. Food and Agriculture Organization of the United Nations, Rome. (A detailed consideration of the practical aspects of destruction and disposal ofanimals, and decontamination procedures) Gregg, M.B. (Ed.) (2002) Field Epidemiology, 2nd edn. Oxford University Press, Oxford. (A medical text, which contains the basic principles of outbreak investigation) Hanson, RP. and Hanson, M.G. (1983) Animal Disease Control. Iowa State University Press, Ames. (A description of principles and techniques relating to regional control pro­ grammes in developed and developing countries) House, J.A., Kocan, K.M. and Gibbs, E.P.J. (Eds) (2000) Tropical Veterinary Diseases: Control and Prevention in the Context of the New World Order. Annals of the New York Academy of Sciences, Vol. 916. The New York Academy of Sciences, New York New Technologies in the Fight against Transboundary Animal Diseases. FAO Animal Production and Health Paper No. 144 (1999) Food and Agriculture Organization of the United Nations, Rome. (Includes descriptions of advances in

Ii I ;

epidemiological and diagnostic techniques, and vaccines, relev­ ant to the control of infectious diseases) Nielsen, T.G., Christensen, B. and Dantzer, V. (Eds) (1996) Decision of vaccination strategy in relation to increased trade of animals and animal products. Acta Veterinaria Scandinavica, Suppl. 90, 1-1 18 Pastoret, P.-P., Blancou, J., Vannier, P. and Verschueren, C. (Eds) (1997) Veterinary Vaccinology. Elsevier, Amsterdam Patterson, D.F. (1993) Understanding and controlling inherited diseases in dogs and cats. Tijdschrift voor Diegeneeskunde, 118, Suppl. 1, 23S-27S Perry, B., McDermott, J. and Randolph, T. (2001) Can epidemiology and economics make a meaningful con­ tribution to national animal-disease control? Preventive Veterinary Medicine, 48, 231-260 Peters, AR (Ed.) (1994) Vaccines for Veterinary Applications. Butterworth Heinemann, Oxford Rees, W.G.H. and Davies, G. (1992) Legislation for health. In: Livestock Health and Welfare. Ed. Moss, R, pp. 1 18-159. Longman Scientific and Technical, Harlow. (A description of national and international control and eradication schemes) Report of a British Veterinary Association Trust Project on the Future of Animal Health Control (1982) The Control of Infectious Diseases in Farm Animals. British Veterinary Association, London Royal Society (2002) Infectious Diseases in Livestock: Scientific questions relating to the transmission, prevention and control of epidemic outbreaks of infectious diseases of livestock in Great Britain. Policy document 15/02, The Royal Society, London. (A broad discussion of the issues relating to epidemic control, focussing on the UK, but addressing general principles of wider relevance) Schnurrenberger, P.R, Sharman, R.S. and Wise, G.H. (1987) Attacking Animal Diseases: Concepts and Strategies for Control and Eradication. Iowa State University Press, Ames. (A general discussion of disease control, mainly with American examples) Schudel, A and Lombard, M. (Eds) (2004) Control of Infectious Animal Diseases by Vaccination. Developments in Biologicals, Vol. 1 19. Karger, Basel Schultz, RD. (Ed.) (1999) Veterinary Vaccines and Diagnostics. Advances in Veterinary Medicine, 41, 1-815 . Academic Press, San Diego US Department of Health and Human Resources (1998) Preventing Emerging Infectious Diseases. A Strategy for the 21st Century. US Department of Health and Human Resources, Centres for Disease Control and Prevention, Atlanta. (A comprehensive discussion of the control of emerg­ ing human infections in the US, but also including some general principles and details of zoonotic and foodborne infections) Winkler, J.K. (1982) Farm Animal Health and Disease Con­ trol, 2nd edn. Lea and Febiger, Philadelphia Wobeser, G.A (1994) Investigation and Management of Disease in Wild Animals. Plenum Press, New York Woods, G.T. (Ed.) (1986) Practices in Veterinary Public Health and Preventive Medicine in the United States. Iowa State University Press, Ames. (A general discussion of veterinary public health, including environmental health, and animal dis­ ease control in the United States) Yekutiel, P. (1980) Eradication of Infectious Disease - A Critical Study. Contributions to Epidemiology and Biostatistics, Vol. 2. Karger, Basel

G eneral Read i n g

Books Blaha, T. (Ed.) (1989) Applied Veterinary Epidemiology. Elsevier, Amsterdam Campbell, RS.F. (Ed.) (1983) A Course Manual in Veterinary

Epidemiology. Australian Universities' International Devel­ opment Program, Canberra Dohoo, I., Martin, M. and Stryhn, H. (2003) Veterinary Epidemiologic Research. A VC Inc, Charlottetown Elliot, RE.W. and Tattersfield, J.G. (1979) Investigating Animal Disease Status. Ministry of Agriculture and Fisheries, Wellington, New Zealand Halpin, B. (1975) Patterns of Animal Disease. Bailliere Tindall, London Houe, H., Ersbol, AK and Toft, N. (Eds) (2004) Introduction to Veterinary Epidemiology. Biofolia, Frederiksberg Hugh-Jones, M.E., Hubbert, W. and Hagstad, H.V. (1995) Zoonoses: Recognition, Control, and Prevention. Iowa State University Press, Ames. (Includes some general epidemiolog­ ical principles and methods) Leech, F.B. and Sellers, KC (1979) Statistical Epidemiology in Veterinary Science. Charles Griffin and Company Ltd, London and High Wycombe Lessard, P.R and Perry, B.D. (Eds) (1988) Investigation of disease outbreaks and impaired productivity. The Veter­ inary Clinics ofNorth America: Food Animal Practice, 4 ( 1 ) Martin, S.W., Meek, A . H . and Willeberg, P. (1987) Veterinary Epidemiology: Principles and Methods. Iowa State University Press, Ames Meek, AH. and Martin, S.W. (1991) Epidemiology of infec­ tious disease. In: Microbiology of Animals and Animal Products. World Animal Science, A6. Ed. Woolcock, J.B., pp.141-180. Elsevier, Amsterdam. (Abridged adaptation of Martin et al., 1987) Noordhuizen, J.P.T.M., Frankena, K, Thrusfield, M.V. and Graat, E.A.M. (2001) Application of Quantitative Methods in Veterinary Epidemiology, revised reprint. Wageningen Pers, Wageningen Putt, S.N.H., Shaw, AP.M., Woods, AJ., Tyler, L. and James, A.D. (1987) Veterinary Epidemiology and Economics in Africa,

ILCA Manual No. 3, International Livestock Centre for Africa, Addis Ababa Schwabe, CW. (1984) Veterinary Medicine and Human Health, 3rd edn. Williams and Wilkins, Baltimore and London Schwabe, CW., Riemann, H.P. and Franti, CE. (1977) Epidemiology in Veterinary Practice. Lea and Febiger, Philadelphia Sergeant, E.s.G., Cameron, A and Baldock, F.C (2004) Epidemiological Problem Solving. AusVet Animal Health Services, Brisbane Slater, M.R (2003) Veterinary Epidemiology. Butterworth Heinemann, St Louis Smith, RD. (2005) Veterinary Clinical Epidemiology. 3rd edn. CRC Press, Boca Raton Toma, B., Dufour, B., Sanaa, Nm., Benet, J.J., Moutou, F., Louza, A and Ellis, P. (1999) Applied Veterinary Epidemiology and the Control of Disease in Populations. AEEMA, Paris Waltner-Toews, D. (Ed.) (1991) Veterinary Epidemiology in the Real World: a Canadian Potpourri. Canadian Association of Veterinary Epidemiology and Preventive Medicine, Ontario Veterinary College, Guelph

Proceedings Epidemiology at Work (1990) Refresher Course for Veterinar­ ians. Proceedings 144. North Head, 5-7 October 1990. Post Graduate Committee in Veterinary Science, University of Sydney Epidemiology in Animal Health (1 983) Proceedings of a symposium held at the British Veterinary Association's Centenary Congress, Reading, 22-25 September 1982. Society for Veterinary Epidemiology and Preventive Medicine Epidemiological Skills in Animal Health (1990) Refresher Course for Veterinarians. Proceedings 143. Sydney, 15 October 1990. Post Graduate Committee in Veterinary Science, University of Sydney

General Reading

Proceedings of the Dutch Society for Veterinary Epidemiology and Economics. 1989- (1989-1990 in Dutch) (continuing) (annual) Proceedings of the International Society for Veterinary Epidemiology and Economics. 1976- (continuing) (triennial) 1 Proceedings of the Society for Veterinary Epidemiology and Preventive Medicine. 1984- (continuing) (annual)

40 )

American Animal Hospitals Association, also publish epidemiological papers. Epidemiology and Infection (formerly the Journal ofHygiene, Cambridge) focusses on infectious diseases. The Bulletin of the Pan American Health Organization, Bulletin of the World Health Organization, Revue Scientifique et Technique - Office International des Epizooties, Tropical Animal Health and Production and the World Animal Review (now defunct) contain material relevant to developing countries.

Journals Papers on veterinary epidemiology are published in a wide range of journals. Preventive Veterinary Medicine is the main journal devoted to the subject.2 National veterinary journals such as Acta Veterinaria Scandinavica, the American Journal of Veterinary Research, the Australian Veterinary Journal, the Canadian Veterinary Journal, the

Journal of the American Veterinary Medical Association, the New Zealand Veterinary Journal, Veterinary Journal (formerly the British Veterinary Journal) and the Veterinary Record; disciplinary journals such as Cancer Research, the International Journal of Parasitology, the Journal of National Cancer Institute and the Journal of Pathology; and journals specializing in particular species, such as the Equine Veterinary Journal, the Journal of Small Animal Practice and the Journal of the

1

Available at:

http: //www.sciquest.org.nz/default.asp ?pageid=68&pub=10 2

An overview of the contents of this journal, from 1982 to 1 997, is

given in volume 30 (1997), pages 181-333; and, from 1 997 to 2001, in volume 50 (2001), pages 187-218.

Emerging Infectious Diseases publishes reports of new infections and infections that are increasing in import­ ance. Animal Health Research Reviews provides broad descriptions of many diseases. The American Journal of Epidemiology (formerly the American Journal of Hygiene) is primarily medical, but occasionally publishes veterinary material. It, Epi­ demiology, and the International Journal of Epidemiology, also contain papers on quantitative methods. These methods are also published in statistical journals such as Applied Statistics, Biometrics, the Journal of the Royal

Statistical Society (Series A and B), Mathematical Biosciences and Statistics in Medicine. Evidence-Based Medicine reports clinical trials (including meta­ analyses) and assessments of procedures; although primarily medical, the veterinary reader will find some of the methods that are reported in this journal to be of value.

Appendices

Appendices V , IX, XXI and XXIII are taken from Tables III, IV, VII and V, respectively, in Statistical Tables for Biological, Agricultural and Medical Research, 6th edition (1974), edited by Fisher, R. and Yates, F. and published

by Longman Group Limited (previously published by Oliver and Boyd Limited, Edinburgh), and are reproduced with the permission of the authors and publishers.

Append ix

I

G lossary of terms

This glossary provides brief definitions of some com­ mon epidemiological terms that are used in this book. More comprehensive guides are Dictionary of Veterinary Epidemiology (edited by B. Toma, J.-P. Vaillancourt, B. Dufour, M. Eloit, F. Moutou, W. Marsh, J.-J. Benet, M. Sanaa and P. Michel, Iowa State University Press, Ames, 1999) 1 , A Dictionary of Epidemiology, 4th edition (edited by J.M. Last, Oxford University Press, New York, 2001)2, and The Cambridge Dictionary of Statistics in the Medical Sciences (B.S. Everitt, Cambridge Univer­ sity Press, Cambridge, 1995), from which some of the definitions below are derived. Accuracy: the degree to which an individual measure­

ment represents the true value of the attribute that is being measured: the greater the accuracy, the greater the degree. Adjustment: a summarizing procedure for a para­ meter (see Appendix 11), for example, incidence or mortality, in which the effects of differences in the composition of populations compared (e.g., differ­ ent age distributions) are minimized. Two common techniques are direct and indirect standardization. Antibody: a protein produced by an animal's im­ munological system in response to exposure to a foreign substance (an antigen; q.v.). Sometimes anti­ bodies are produced against the individual's own proteins, causing autoimmune disease. Antibodies display specificity (q.v.) to particular antigens. Antigen: a substance (usually a protein) that induces a specific immune response (e.g., circulating anti­ body production). 1

An earlier, shorter French glossary of veterinary epidemiology,

with English/German/Spanish/Italian/Portuguese-French indices, is available (Toma et al., 1991). 2

An English-French and French-English dictionary, based on the

1st edition (1983), is also published (Fabia et aI., 1988).

Association: a general term to describe the relation­

ship between two variables (see Appendix 11). The association is 'positive' when the variables occur together more frequently than is expected by chance; the association is 'negative' when they occur less frequently than is expected by chance. Asymptotic method: any statistical method based on an approximation to a Normal distribution (q.v.) or other probability distribution that becomes more accurate as sample size increases. Bias: systematic (as opposed to random) departure from true values. Binomial distribution: a probability distribution relating to two mutually exclusive and exhaustive outcomes (e.g., the birth of either male or female animals), where successive outcomes (e.g., births) are independent and occur with constant probability. Biosecurity: management-practice activities that reduce the opportunities for infectious agents to gain access to, or spread within, a food animal production unit. Carrier:

1.

an animal that is infected with a n infectious agent without displaying clinical signs, and that can be a source of infection to other animals; 2. (of foot-and-mouth disease virus) an animal in which virus persists in the pharyngeal region for more than 4 weeks after infection; 3. (genetic) an animal that is heterozygous for a normal and an abnormal gene, the latter of which is not expressed but may be detected by tests. Case: an animal in a population or study group identified as having a particular disease or other health-related event that is being investigated. Case-control study: an observational study (q.v.) in which a group of diseased animals (cases) is compared with a group of non-diseased animals

1011

Appendices

(controls) with respect to exposure to a hypothe­ sized cause. Causality: the relating of causes to the effects that they produce. Clinical trial: a systematic study in the species for which a prophylactic or therapeutic procedure is intended in order to establish the procedure's pro­ phylactic or therapeutic effects. A 'field trial' is a clinical trial undertaken in the field, that is, under husbandry and management practices typical of those under which the procedure is intended to be used. Cohort study: an observational study (q.v.) in which a group of animals exposed to a hypothesized cause is compared with a group not so exposed, with respect to development of a disease. Commensals: microbes found on the skin or within the body that do not usually cause disease (d. pathogens) . Confidence interval: a range o f values within which the value of a parameter (see Appendix II) lies with a specified level of confidence. Confounding: the inseparability from a given data set of the effects of two possible causes of an observed result, because both occur together. Continuous variable: a variable (see Appendix II) that may take any value in an interval; the interval may be finite or infinite. Correlation: see Association. Cost-benefit analysis: see Social cost-benefit analysis. Cross-product ratio: see Odds ratio. Cross-sectional study: an observational study (q.v.) in which animals are classified according to presence or absence of disease, and presence or absence of exposure to a hypothesized causal factor, at a par­ ticular point in time. Cross-sectional survey: a survey (q.v.) undertaken at a particular point in time. Database: a structured collection of data, organized so that it can be accessed easily by a range of com­ puter software. Determinant: a factor that affects the health of a population. Discrete variable: a variable (see Appendix II) for which there is a definite distance from one value of the variable to the next possible value (e.g., numbers of cases of disease: 1 , 2, 3 . . . where the distance is 1 ) . Endemic:

1. 2.

the predictable level of occurrence of disease, infection, antibody, etc.; the usual presence of disease, infection, antibody, etc.

Endogenous:

normally from within an animal; (characteristic) an innate characteristic of an animal (e.g., breed) . Epidemic: a n occurrence o f disease i n excess o f its anticipated frequency (also used adjectivally).

Epidemic curve: a graph plotting the number of

new cases against time of onset of disease; thus, an epidemic curve plots incidence. Epidemiology (veterinary): the investigation of dis­ ease, other health-related events, and production in animal populations and the making of inferences from the investigation in an attempt to improve the health and productivity of the popUlations. Evidence-based medicine: the process of finding relevant information in the veterinary literature to address a specific clinical problem; the application of simple rules of science and common sense to determine the validity of information; the applica­ tion of the information to a clinical question; that is, patient care based on the best available studies. Exogenous:

1. 2.

normally from outside an animal; (characteristic) a characteristic that is not innate, to which an animal is exposed (e.g., climate, toxic substances and microbes). Experimental study: a study (q.v.) in which the invest­ igator can allocate animals to different categories; thus, the conditions of the study are controlled by the investigator. Extrinsic factor: see Exogenous (2). Extrinsic incubation period: the time between the entry of an infectious agent into an arthropod vec­ tor and the time at which the arthropod becomes infectious. Field trial: see Clinical trial. Fomites (singular: fomes): inanimate communicators of infection (d. vector). Health and productivity schemes: systems for record­ ing disease and productivity in groups of animals (usually herds and flocks), their aim being to improve health and productivity of the groups. Horizontal (lateral) transmission: transmission of an infection from an individual to any other individual in a population, but excluding vertical transmission (q.v.) . Hypothesis: a proposition that can be tested form­ ally; after which the hypothesis may be either 'supported' or 'rejected' . Inapparent infection: an infection that does not pro­ duce clinical signs. Incidence: the number of new cases that occur over a specified period of time. It is usually expressed in relation to the population at risk and the time during which the population is observed. Informatics: the supply of information through the medium of the computer.

1.

Interaction:

2.

1.

(biological) the interdependent operation of two

2.

or more causes to produce an effect; (statistical) in an epidemiological context, a quant­ itative interdependence between two or more

Appendix I

factors, such that the frequency of disease when two or more factors are present is either in excess of that expected from the combined effects of each factor (positive interaction) or less than the com­ bined effect (negative interaction). Intrinsic factor: see Endogenous (2). Likelihood: the probability of a set of observations, given the value of a parameter (see Appendix II) or set of parameters. Longitudinal study:

a cohort study (q.v.); a general description of both cohort and case­ control studies (q.v.), so called because these studies investigate exposure to a hypothesized cause and development of disease (the effect) when cause and effect are separated temporally. Longitudinal survey: a survey (q.v.) that records events over a period of time. Misclassification: the incorrect allocation of individu­ als or features to categories to which they do not belong (e.g., the classification of a diseased animal as non-diseased) . 1. 2.

Model:

1.

(biological) a system that uses animals to study diseases, pathological conditions and impaired function; the model may be induced experiment­ ally or may be constructed using naturally occur­ ring conditions; 2. (mathematical) a representation of a system, pro­ cess or relationship in mathematical form in which equations are used to simulate the behaviour of the system or process under study. Monitoring: the routine collection of information on disease, productivity and other characteristics pos­ sibly related to them in a population. Morbidity: the amount of disease in a population (commonly defined in terms of incidence or pre­ valence; q.v.). Mortality: a measure of the number of deaths in a population. Multifactorial disease: a disease that depends on the presence of several factors for its induction. Most diseases are multifactorial, although some may have one major component cause (e.g., foot­ and-mouth disease virus is the cause of foot-and­ mouth disease), in which case they are commonly termed 'unifactorial'. Multivariate analysis: a set of statistical techniques used to study the variation in several variables simultaneously. Necessary cause: a cause that must always be present for a disease to occur (e.g., Mycobacterium tuberculosis is the necessary cause of tuberculosis). Nidality: the characteristic of an infectious agent to occur in distinct nidi (q.v.) associated with particular geographic, climatic and ecological conditions.

! ( )=

greater than (e.g., 6 > 5) than (e.g., 5 < 6) ?: = greater than or equal to :s; = less than or equal to < = less

A line through any of these symbols means 'not', for example, :1> means 'not greater than'.

Approximation notation The symbol "'", read as 'approximately equal to', is used to indicate approximation. For example, the base of natural logarithms e = 2. 71 8 281 . . . and may be written as e "'" 2.72.

Estimation notation Order of cal culation Multiplication and division are conducted before addition and subtraction. Thus: 6 x 3 + 1 = 18 + 1 = 19. Brackets are used to indicate the order of calculation, taking precedence over multiplication and division when calculations would otherwise be ambiguous. Three types of brackets are commonly used: paren­ theses ( ), braces { }, and square brackets [ ], usually, but not always, in that order. Thus: 3 [3 + {6(4 + 2) } ] is calculated as 4 + 2 = 6 then 6 x 6 = 36 then 3 + 36 = 39 then 3 x 39 = 1 1 7. Similarly: 1 + 6 x 3 = 19, but (1 + 6) x 3 = 21 . Pocket calculators compute values following the order of calculation described above. Therefore, in circumstances in which brackets are required to avoid ambiguity, calculations must be undertaken in unam­ biguous stages. This is circumvented on some calcula­ tors by the presence of appropriate bracket keys on the keypad.

Parameters are frequently estimated from a sample drawn from a population. The sample produces an estimate of the population parameter. An estimate is indicated either by /\ (a 'hat') or by a single asterisk, * . Thus, a sample estimate o f disease prevalence is pre­ sented as either P (P 'hat') or P*. The 'hat' notation is used in this book.

Factorial notation : xl X! is used to denote the successive multiplication of all positive integers (whole numbers) between X and 1 . For example: 6! = 6 x 5 x 4 x 3 x 2 x l = 720 2! = 2 x 1 = 2 I! = 1. (Note that O! conventionally equals 1 .)

Mod u l u s notation : Ixl Vertical lines o n each side o f a numerical quantity, x, mean that the positive sign of the value of X should be used. The value thus obtained is known as the absolute value of x. For example, 1 -2 1 is read as +2. Similarly, 1 - 6 + 1 1 will simplify to I -5 1, which is read as +5. Also, -6 + 1 = -5, but 1 - 6 1 + 1 = 7.

Appendix

III

Some computer software

This directory lists some computer software packages that are of value to veterinary epidemiology. The list is not exhaustive; emphasis is placed on the simpler ana­ lytical packages, rather than on software suitable for multivariate analyses. The descriptions of the various packages also differ in the degree of detail and, for some packages, the list is hardly more than enumer­ ative, but should be sufficient to allow potential users to identify appropriate software1 . Relevant references are in square brackets, follow­ ing the names of the packages. (Package manuals are not included.)2

1

The packages subsume most of the individual applications listed, in

Appendix III of the second edition of this book, as being available from the Epidemiology Monitor. 2 A useful review of software for power analysis is presented by Thomas and Krebs (1997).

Most of the packages run in the MS Windows envir­ onment. The main addresses of suppliers are listed. Some suppliers also have local offices in various countries. Note that the Internet URLs of suppliers may change. If this occurs, most Internet 'Search Engines' (e.g., GOOGLETM; http: //google.com), specifying either the package name or its supplier, should locate the new URLs.

AnnPlnt1,,1{

Package/reference

Functions

Further informafion/Supplier/URL

AGG

Aggregate-level sensitivity and specificity

A. Donald 1 0 1 -5805 Balsam Street Vancouver BC Canada V6M 2 B9

Confidence i nterva l estimation means and thei r d i fferences med ians and the i r d i fferences proportions and their d i fferences regression and correlation relative risks and odds ratios standard ized rates and ratios su rvival analyses sensitivity and specificity

Suppl ied with Statistics with Confidence (Altman et al., 2000) BMJ Bookshop, BMA House London WC1 H 9JR, UK http ://www.bmjbookshop.com

[Donald et a/., 1 994]

CIA [Altman et a/., 20001

III

,1 J i

kappa l i ke l i hood ratios ROC curves cli nica l trials and meta-analyses

Biostatistical software

Statistical d istributions C l i nical trials Qual ity control Environmental and ecological statistics Agreement Regression Time series ROC cu rves Capture-release-recapture Correlation and contingency tables

Paul Johnson PO Box 4 1 46 Davis CA 9561 7-41 46, USA http ://www.biostatsoftware.com

EGRET

Descriptive statistics Contingency tables (relative risks and odds ratios), logistic and other types of regression, survival analysis

Cytel Software Corporation 675 Massachusetts Avenue Cambridge MA 021 39, USA http ://www.cytel .com

Epi Info

Questionnaire design Descriptive statistics and graphics Su rveys: simple random, stratified and cluster sam p l i ng Contingency tables (relative risks and odds ratios) Logistic regression Sample size determ i nation: surveys case-control, cohort and cross-sectional studies Survival analysis Mapping

Centers for Disease Control and Prevention Division of Public Health S u rvei l l a nce and Informatics, Epidem iology Program Office 4770 Buford H ighway, Northeast (Mail Stop K-74) Atlanta Georgia 30341 -3 7 1 7, USA http ://www.cdc.gov/epii nfo

Freecalc [Cameron and Baldock, 1 998a,b]

Su rvey sam ple size, accommodating sensitivity and specificity Survey analysis, accommodating sensitivity and specificity

AusVet Animal Health Services 1 9 B rereton Street, PO Box 3 1 80 South Brisbane, Q L D 4 1 0 1 , Austra l i a Austra l i a/AusVet A n i m a l Health Services PO Box 2 3 2 1 Orange, NSW 2800 Austral i a Austral i a/AusVet A n i mal Health Services 1 40 Falls Road Wentworth Falls NSW 2 782 Austral i a http ://www.ausvel.com.au/content.php?page=res_software

GENSTA T

Comprehensive statistical analyses

NAG Ltd Wilki nson House, Jordan H i l l Road Oxford OX2 8 D R, UK http ://www,nag.co.uk/stats/G DG E_soft.asp

(Some parts req u i re SAS software)

[McConway et al., 1 999]

41h

Package/reference

Functions

Further Information/Supplier/URL

GUM

Logistic regression

NAG Ltd W i l k i nson House, Jordan H i l l Road Oxford OX2 8 D R, U K http ://www. nag.co.uk/stats/G DG Csoft.asp

Minitab

Comprehensive statistical analyses

M i n itab Inc. Qual ity Plaza, 1 829 Pine H a l l Road State College PA 1 6801 -3008, USA http://www. m i n itab.com

Mode! Assist

Tra i n i ng software for risk analysis

Risk Media Ltd Le Bou rg 24400 Les Leches France http ://www.risk-mode l l i n g.com

Ness

Comprehensive statistical analyses

NCSS 329 North 1 000 East Kaysv i l le Utah 84037, USA http ://www.ncss.com

nQuery Advisor

Sample size and power means, proportions, non parametric methods, agreement, superiority/equ ivalence/non­ inferiority trials, regression, survival

Statistical Solutions Stoneh i l l Corporate Center Su ite 1 04, 999 B roadway Saugus MA 01 906, USA http://www.statsol usa.com

PASS

Sample size and power correlation, d i agnostic tests, superiority/equ i valence/non-i nferiority trials, i nc idence rates, means, proportions, regression, survival

NCSS 329 North 1 000 East Kaysv i l l e Utah 84037, USA http://www.ncss.com

PEP!

Contingency tables (relative risk, odds ratio) Power and sample size calcu l ations D iagnostic tests (sensitivity, specificity, ROC cu rves, optimum cut-off poi nts) Random sampl i ng Agreement Survival analysis Life tables

Sagebrush Press, 225 1 0th Avenue Sa It Lake City UT 841 03, USA, and 1 2 H i l lbury Road, London SW1 7 8JT, U K http ://www.sagebrushpress.com/pepibook.html

Power and Precision

Power analyses and confidence i nterval estimation

Lawrence Erlbaum Associates I nc. 1 0 Industrial Avenue Mahwah NJ 07430-2262, USA http ://www.erl baum.com/software.htm

Powersim Studio

General simulation mode l l i ng

Powersim PO Box 3961 Dreggen N-5835 Bergen, Norway, and Fays Busi ness Centre Bedford Road G u i ldford G U 1 4SJ, U K http ://www.powersi m .com

@RISK

Quantitative risk analysis

Pa l i sade Eu rope The Blue House, U n i t 1 , 30 Calvin Street London E1 6NW, U K http ://www. palisade.com

(Req u i res @RISK)

Appendix I I I

417

Package/reference

Functions

Further informatlon/Supplier/URL

Risk Matrix

Construction of risk matrices

The MITRE Corporation 202 B u rl i ngton Road Bedford MA 01 730-1 420, USA http ://www. m itre.org/work/sepo/tool kits/risk/ ToolsTechniques/RiskMatrix.html

SCALC [Tryfos, 1 9961

Sampl ing simple random, stratified, cl uster

Suppl ied with Sampling Methods for Applied Research (Tryfos, 1 996)

SPSS

Comprehensive statistical analyses

SPSS lnc 2 3 3-2 3 5 Wacker Drive, 1 1 th F l oor Chicago IL 60606, USA http://www.spss.com

Stata

Comprehensive statistical analyses, notably i ncluding su rveys

StataCorp LP 4905 Lakeway Drive Col lege Station Texas 77845 , USA http ://www.stata.com

StatXact

Exact p-values for contingency tables and non-parametric tests

Cytel Software Corporation 675 Massachusetts Avenue Cambridge MA 0 2 1 39, USA http ://www.cytel .com

Survey Toolbox

Random sam p l i ng Random geographical coordi nate samp l i ng Two-stage preva lence survey design and analysis Survival analysis sample size Captu re-release- recapture methods

AusVet Animal Health Services 1 9 B rereton Street, PO Box 3 1 80 South Brisbane, Q L D 41 01 , and Austral ia/AusVet Animal Health Services PO Box 2 3 2 1 Orange, N S W 2800 Australia, and Austra l i a/AusVet Animal Health Services 1 40 Falls Road Wentworth Falls NSW 2 782 Austra l i a http ://www.ausvet.com.au!content. php?page=res_software

Winepiscope

Diagnostic test parameters point and i nterval estimates of sensitivity, specificity, predictive value, Kappa, area under the ROC cu rve Sample size determ ination detection of d i sease, proportion and their d i fferences, d i fferences between means Observational studies si mple, stratified and matched case-control studies, si mple and stratified cohort studies (cu m u l ative i ncidence and incidence rate data) Reed-Frost model (determ i n istic)

Veterinary Faculty of the University of Zaragoza (Spai n ) http ://i nfecepi . u n izar.es/pages/rat io/soft_u k. htm Wageningen Agricultural Un iversity (The Netherlands) http ://www.zod .wau . n l/qve/home. htm I Royal ( Dick) School of Veterinary Studies, Un i versity of Edinburgh (UK) http ://www.cl ive.ed .ac. u k/winepiscope

[Thrusfield et al., 200 1 1

Appendix

IV

Veteri nary epidemiology on the I nternet

This Appendix lists the 'addresses' ( 'uniform resource locators': URLs) of some veterinary and related Internet sites of relevance to veterinary epidemiology. Site URLs may change, in which case users may be

redirected to alternative locations. If this does not occur, an Internet search on the title, using an appropriate search engine (e.g., GOOGLETM: http: // google.com) should locate any new URL.

Title (subject)

URL

AGRICOLA

http ://agricol a. na I .usda.gov/

(General agricultural bibl iographic database)

AHEAD ILIAD

http ://www.fas.org/ahead.index.html

(Infectious a n i mal and zoonotic d i sease su rvei l l ance [ProM ED-AHEAD])

American College of Veterinary Public Health

http ://www.acvpm.org/cgi-bi n/start/i ndex.htm

Animal Health in Australia

http ://www.aahc.com.au/sitemap.htm

Association for Veterinary Epidemiology and Preventive Medicine

http ://www.cvm.uiuc .edu/atvphpm/

CABI

http ://www.cabi-publ ishing.org/AnimaIScience.asp/

(Animal-science bibl iographic database)

Canadian Cooperative Wildlife Health Centre

httpj/wildl ifel .usask.ca/ccwhc2003/

Centers for Epidemiology and Animal Health

httpj/www.aphis. usda.gov/vs/ceah/

Cochrane Collaboration

http ://www. cochrane.org/index l . htm

(Reviews of c l i n ical trials and other i n terventions) Epidem iology and rel ated 'Su percou rses'

http ://www.pighealth.com/Scou rse/ma in/index.htm http ://www.pitt.edu/-super l /i ndex.htm

Epidemiology Monitor

http ://www.epimonitor. net

(Developments and resources for epidemiology)

EpiVetNet

http ://www.vetsc hools.co.uk/EpiVetNet/

(Repository of i nformation rel ated to veteri nary epidem iology, and electronic mai l i ng l ist EpiVet-L)

European College of Veterinary Public Health

http ://www.vu-wien.ac .at/ausland/ECVPH.htm

EXCITE (Excellence in Curriculum Integration through Teaching Epidemiology)

http ://www .cdc.gov/exc ite/

FOCUS

http ://www.sph.u nc.edu/nccphp/focus/i ndex.htm

( F ield epidemi ology)

Appendix IV

Title (subject)

,1 1 ()

URL

Food and Agriculture Organization of the United Nations (FAO)

http ://www.fao.org/

International Veterinary Information Service

http ://www. ivis.org

Journals in Epidemiology

http://www.epidemiol ogy.esmartweb.com/Journals.htm

National Animal Health Monitoring System (NAHMS)

http ://www.aphis. usda.gov/vs/ceah/cahm/index.htm

National Centre for Animal Health Surveillance

http ://www .aph is. usda.gov/vs/ceah/ncahs/nsu

(Includes l i n k to NAHMS)

Net-Epi

http ://www.netepi.org/

( Network-enabled Epidemiology) ( F ree tools for epidemiology and public health)

Office International des Epizooties (OlE)

http ://www.oie.int

Pan American Health Organization

http ://www.paho.org/

Participatory Epidemiology

http ://www.partici patoryepidemiology.i nfo/

ProMED

http ://www.fas.org/promed/

(Monitoring of emerging disease)

PubMed

http ://www.ncb i . n l m . n i h .gov/pubmed/

(Med ical bibl iographic database)

Regional International Organization for Animal and Plant Health (OIRSNCentral America) [In Spanish]

http://nsl .oi rsa.org.sv/

Society for Veterinary Epidemiology and Preventive Medicine

http ://www.svepm.org.uk

SNOMED

http://www.snomed.org http ://www.snomed.vetmed.vt.edu

Statistics Calculators

http ://calcu l ators .stat.ucla.edu

Veterinary Medical Database

http ://www.vmdb.org.

Web-agri

http ://www.web-agri.com/recherche .asp

(Agricultural Search Engi ne)

World Health Organization (WHO)

http ://www .who.i nt/en/

WWWeb Epidemiology & Evidence-based Medicine Sources for Veterinarians (Epidemiology, evidence-based med icine and

http://www.vetmed .wsu.edu/courses­ j mgay/Epi l i n ks.htm

biostatistics academ ic resources)

Append ix V Student's I-d istribution

Probability Degrees of freedom

.9

.

8

.7

.6

.5

.4

.3

.2

.1

.05

.02

.01

.001

3 .078 1 . 886 1 . 638 1 .5 3 3 1 .476

6.3 1 4 2 .920 2.353 2.1 32 2.01 5

1 2 .706 4.303 3 . 1 82 2 . 776 2.571

3 1 .82 1 6.965 4.541 3 . 747 3.365

63.657 9.925 5 . 841 4.604 4.032

636.61 9 3 1 .598 1 2 .924 8.6 1 0 6.869

1 2 3 4 5

. 1 58 . 1 42 . 1 37 . 1 34 . 1 32

.325 .289 .277 .271 .267

.510 .445 .424 .41 4 .408

.727 .61 7 . 5 84 .569 .559

1 .000 .81 6 .765 .741 .727

1 . 3 76 1 .061 .978 .941 .920

1 . 963 1 . 386 1 .250 1 . 1 90 1 . 1 56

6 7 8 9 10

.131 . 1 30 . 1 30 . 1 29 . 1 29

.265 .263 .262 .261 .260

.404 .402 .399 .398 .397

.553 .549 .546 .543 .542

.71 8 .71 1 .706 . 70 3 .700

.906 .896 .889 .883 .879

1 . 1 34 1 .1 1 9 1 . 1 08 1 . 1 00 1 .093

1 .440 1 .41 5 1 . 397 1 .3 8 3 1 .3 7 2

1 .943

2 .447

3 . 1 43

1 . 895 1 .860 1 .8 3 3 1 .8 1 2

2 .365 2 .306 2 . 262 2.228

2.998 2 .896 2 .82 1 2 . 764

3. 707 3 .499 3.355 3 .250 3 . 1 69

5 .959 5 .408 5 .041 4.781 4.587

11 12 13 14 15

. 1 29 . 1 28 . 1 28 . 1 28 . 1 28

.260 .259 .259 .258 .258

.396 .395 .394 393 .393

.540 .539 .538 .537 .536

.697 .695 .694 .692 .691

.876 .873 .870 .868 .866

1 .088 1 .083 1 .079 1 .076 1 .074

1 . 363 1 . 356 1 .350 1 . 345 1 . 341

1 . 796 1 . 782 1 . 771 1 . 761 1 . 753

2 .201 2 . 1 79 2 . 1 60 2 . 1 45 2.1 31

2.7 1 8 2 .681 2 .650 2 . 624 2 .602

3 . 1 06 3 .055 3 .0 1 2 2 .977 2 .947

4.437 4.3 1 8 4.221 4. 1 40 4.073

16 17 18 19

. 1 28 . 1 28 .127 . 1 27

.258 .257 .257 .257

. 3 92 .392 .392 .391

.535 .534 .534 .533

.690 .689 .688 .688

.865 .863

1 .071 1 .069 1 .067 1 .066

1 .3 3 7 1 .3 3 3 1 .330 1 .3 2 8

1 . 746 1 . 740 1 . 734 1 . 729

2 . 1 20 2.1 1 0 2.1 01 2 .093

2.583 2 . 567 2.552 2 .5 3 9

2 .921 2 .898 2 . 878 2 .861

4.01 5 3 .965 3 .922 3 .883

20 21 22 23 24 25

. 1 27 .127 .1 27 . 1 27 .127 .1 27

.257 .257 .256 .256 .256 .256

.391 .391 . 3 90 .390 .390 . 3 90

.533 .532 .532 .532 .531 .531

.687 .686 .686 .685 .685 .684

.860 .859

1 .064 1 .063 1 .061 1 .060 1 .059 1 .058

1 .325 1 .323 1 .321 1 .3 1 9 1 .3 1 8 1 .3 1 6

1 . 725 1 .721 1 .71 7 1 .71 4 1 .71 1 1 . 708

2 .086 2 .080 2 .074 2 .069 2 .064 2 . 060

2.528 2.5 1 8 2 .508 2 .500 2. 492 2 .485

2 .845 2.831 2.81 9 2.807 2 . 797 2 . 787

3 .850 3.81 9 3 . 792 3 . 767 3 . 745 3 . 725

26 27 28 29 30

. 1 27 .1 27 .127 .127 .127

.256 .256 .256 .256 .256

.390 .389 .389 . 3 89 . 3 89

.531 .531 .530 .530 .530

.684 .684 .683 .683 .683

.856 .855 .855 .854 .854

1 .058 1 .057 1 .056 1 .055 1 .055

1 .3 1 5 1 .3 1 4 1 .3 1 3 1 .3 1 1 1 .3 1 0

1 . 706 1 . 703 1 . 701 1 .699 1 .697

2 .056 2.052 2 .048 2 .045 2 .042

2 .479 2 .473 2 .467 2.462 2 .457

2 . 779 2.771 2 . 763 2 . 756 2.750

3 . 707 3 .690 3 .674 3 .659 3 . 646

40 60 1 20

. 1 26 . 1 26 . 1 26 . 1 26

.255 .254 .254 .253

.388 .387 . 3 86 .385

.529 .527 .526 .524

.681 .679 .677 �74

.851 .848 .845 .842

1 .050 1 .046 1 .041 1 .036

1 . 303 1 .296 1 .289 1 .282

1 . 684 1 .6 7 1 1 .658

2.021 2 .000 1 .980 1 .960

2 .423 2 . 390 2.358 2 .3 2 6

2 . 704 2 . 660 2.61 7 2 .576

3.551 3 .460 3 . 3 73 3 .291

.862 .861

.858 .858 .857 .856

1 .645

The table gives the percentage poi nts most frequently req u i red for sign ificance tests and confidence l i m its based on Student's t-d istribution. Thus the probabil ity of observing a va l u e of t, with 1 0 degrees of freedom, greater in absolute value than 3 . 1 69 (i.e. < -3 . 1 69 or > +3 . 1 69) is exactly 0.01 or 1 per cent.

Appendix VI

" m"",m",,,,,m',,m',,m, """",,,,,,,""'"

Multipl iers used in the construction of confidence i ntervals based on the Normal d istri bution , for selected levels of confidence

These multipl iers are based o n two-ta i led probabi l ities for critical sign ificance levels, extracted from Appendix xv. Confidence interval Multipl ier

80% 1 .282

90% 1 . 645

95% 1 .960

99% 2 . 5 76

99.9% 3.291

Append ix V I I

WOOOOOOOOOOOOOOOOOOOooooOOoooooo

Val ues of exact 9 5 % ( F rom Beyer, 1 968)

confidence l im its for proportions

These tables give exact confidence limits for a propor­ tion, based on the binomial distribution. The first (x) column indicates the numerator in the proportion; the first (n x) row indicates the sample size; n, minus the numerator, x. For example, if 14 animals were -

2 0

2 3 4 �

5

.�

6

2

7

c:

0 Q Q Q)

'�

.9

� Q)

=

-

=

=

=

Denominator minus numerator (n - x) 4 5

6

7

8

9

975

842

708

602

522

459

41 0

369

336

000

000

000

000

000

000

000

000

000 445

987

906

806

716

641

579

527

483

01 3

008

006

005

004

004

003

003

003

992

932

853

777

710

651

600

556

518

094

068

053

043

037

032

028

025

023

994

947

882

816

755

701

652

610

572

1 94

1 47

118

099

085

075

067

060

055

995

95 7

901

843

788

738

692

651

614

284

223

1 84

1 57

1 37

1 22

1 09

099

091

996

968

915

863

813

766

723

684

649

359

290

245

212

1 87

1 67

1 51

1 39

1 28

996

968

925

878

833

789

749

71 1

677

421

349

299

262

234

21 1

1 92

1 77

1 63

997

972

933

891

849

808

770

734

701

473

400

348

308

277

251

230

21 3

1 98

8

997

975

940

901

861

823

787

753

722

51 7

444

390

349

316

289

266

247

230

9

997

977

945

909

872

837

802

770

740

555

482

428

386

351

323

299

2 78

260

10

998

979

950

916

882

848

81 6

785

756

587

516

462

41 9

384

354

329

308

289

11

998

981

953

922

890

858

827

797

769

615

546

492

449

41 3

383

357

335

315

998

982

957

927

897

867

837

809

782

640

572

519

476

440

410

384

361

340

998

983

960

932

903

874

846

819

793

661

595

544

501

465

435

408

384

364

14

998

984

962

936

909

881

854

828

803

681

61 7

566

524

488

457

430

407

385

15

998

985

964

939

91 3

887

861

836

812

698

636

586

544

509

478

451

427

406

E

:oJ

2'.

3

sampled, of which 6 were diseased, then x 6, n = 14, and n x 8. Thus, the point estimate of prevalence is 6/14 0.428 (42.8%) and, from the table, the interval estimate 0.177, 0.71 1 (1 7.7%, 7 1 . 1 %).

12 13

Appendix V I I

2

16

Denominator m in us numerator (n - x) 345

6

7

8

9

999

986

966

943

918

893

868

844

820

71 3

653

604

563

529

498

471

447

425

999

987

968

946

922

898

874

851

828

727

669

621

581

547

516

488

465

443

999

988

970

948

925

902

879

85 7

835

740

683

637

597

564

533

506

482

460

999

988

971

950

929

906

884

862

841

751

696

651

612

579

549

522

498

476

999

989

972

953

932

910

889

868

847

762

708

664

626

593

564

537

51 3

492

999

990

975

956

937

91 7

897

877

858

781

730

688

651

61 9

590

565

541

519

999

991

976

960

942

923

904

885

867

797

749

708

673

642

61 4

589

566

545

26

999

991

978

962

945

928

910

893

875

81 0

765

726

693

663

636

61 1

588

567

28

999

992

980

965

949

932

916

899

882

822

779

743

71 0

681

655

631

609

588

999

992

981

967

952

936

920

904

889

833

792

757

725

697

672

649

627

607

35

999

993

983

971

958

944

930

91 6

902

855

81 8

786

758

732

708

686

666

647

40

999

994

985

975

963

951

938

925

91 2

871

838

809

783

759

737

71 7

698

679

45

999

995

987

977

967

956

944

933

921

885

855

828

804

782

761

742

724

707

50

1 000

995

988

979

970

960

949

939

928

896

868

843

82 1

800

781

763

746

730

60

1 000

996

990

983

975

966

95 7

948

939

912

888

867

848

830

81 3

797

782

767

80

1 000

997

992

987

981

974

967

960

953

933

915

898

882

868

855

842

820

81 6

1 00

1 000

998

994

989

984

979

973

967

962

946

931

91 7

904

892

881

870

859

849

200

1 000

999

997

995

992

989

986

983

980

973

965

957

951

944

938

932

926

920

500

1 000

1 000

999

998

997

996

995

993

992

989

986

983

980

977

974

972

969

967

1 000

1 000

1 000

1 000

1 000

1 000

1 000

1 000

1 000

1 000

1 000

1 000

1 000

1 000

1 000

1 000

1 000

1 000

10

11

12

16

17

18

17 18 19 20 22 24

30

Denominator minus numerator (n - x)

o

2 3 4 5 6

13

14

15

308

285

265

247

232

218

206

1 95

1 85

000

000

000

000

000

000

000

000

000

41 3

385

360

339

31 9

302

287

273

260

002

002

002

002

002

002

001

001

001

484

454

428

405

383

364

347

331

317

021

01 9

01 8

01 7

01 6

01 5

01 4

01 3

01 2 363

538

508

481

456

434

414

396

379

050

047

043

040

038

036

034

032

030

581

551

524

499

476

456

437

41 9

403

084

078

073

068

064

061

057

054

052

616

587

560

535

512

491

471

453

436

118

110

1 03

097

09 1

087

082

078

075

646

61 7

590

565

543

522

502

484

467

1 52

1 42

1 33

1 26

119

113

1 07

1 02

098

424

Appendices

7 8 9 10

t:Jenorninaror minus numerator (n - Xl 13 14 15

11

12

671

643

616

592

570

1 84

1 73

1 63

1 54

1 46

692

665

639

616

593

16

11

18

549

529

512

494

1 39

1 32

1 26

121

573

553

535

518

215

203

1 91

1 81

1 72

1 64

1 56

1 49

1 43

71 1

685

660

636

61 5

594

575

557

540

244

231

218

207

1 97

1 88

1 80

1 72

1 65

728

702

678

655

634

614

595

577

560

2 72

257

244

232

221

21 1

202

1 94

1 86

11

743

718

694

672

651

631

612

594

578

298

282

268

256

244

234

224

21 5

207

12

756

732

709

687

666

647

628

61 1

594

322

306

291

2 78

266

255

245

235

227

13

768

744

722

701

680

661

643

626

609

345

328

313

299

287

275

264

255

245

14

779

756

734

71 3

694

675

657

640

624

366

349

334

320

306

295

283

273

264

789

766

745

725

705

687

669

653

637

15

386

369

353

339

325

313

302

291

281

16

798

776

755

736

71 7

698

681

665

649

405

388

372

357

343

331

319

308

298

17

806

785

765

745

727

709

692

676

660

423

406

389

3 74

360

347

335

324

314

814

793

773

755

736

719

702

686

671

440

422

406

391

376

363

351

340

329

821

801

782

763

745

728

71 2

696

681

456

439

422

406

392

3 79

366

355

344

827

808

789

771

753

737

720

705

690

472

454

437

421

407

393

381

369

358

839

820

803

785

768

752

737

722

707

500

481

465

449

434

421

408

396

385

849

831

81 4

798

782

766

751

737

723

525

507

490

475

460

446

433

42 1

41 0

858

841

825

809

794

779

764

750

736

548

530

51 3

497

483

469

456

444

432

866

850

834

819

804

790

776

762

749

569

551

535

519

504

491

478

465

453

873

858

843

828

814

800

786

773

760

588

571

5 54

539

524

510

498

485

473

888

874

860

847

834

821

809

797

785

628

612

596

581

567

5 54

541

529

51 7

900

887

875

862

850

838

827

815

804

662

646

631

616

602

590

578

566

555

45

909

898

886

875

864

853

842

831

821

690

675

661

647

633

621

609

598

587

50

91 7

906

896

885

875

865

854

844

835

714

700

686

673

660

648

636

625

614

60

929

920

91 1

902

893

884

874

866

857

752

740

727

71 5

703

692

681

670

660

80

945

938

931

923

91 6

909

901

894

887

18 19 20 22 24 26 28 30 35 40

804

793

783

773

763

753

744

734

726

1 00

955

949

943

937

93 1

925

919

913

907

838

829

820

81 1

802

794

786

778

770

200

977

974

970

967

964

961

95 7

954

950

914

909

903

898

893

888

883

878

873

991

989

988

986

985

984

982

981

979

500

964

962

960

957

955

953

950

948

946

1 000

1 000

1 000

1 000

1 000

1 000

1 000

1 000

1 000

1 000

1 000

1 000

1 000

1 000

1 000

1 000

1 000

1 000

An,npntiliy V I I

19 o

2 3

20

Denomina tor minus numerator (n - x) 22 24 26

28

30

35

;

40

1 76

1 68

1 54

1 42

132

1 23

116

1 00

088

000

000

000

000

000

000

000

000

000

249

238

219

203

1 90

1 78

1 67

1 45

1 29

001

001

001

001

001

001

001

001

00 1

304

292

270

251

235

221

208

1 82

1 62

01 2

01 1

010

009

009

008

008

007

006

349

336

312

292

274

257

243

214

1 91

029

028

025

024

022

020

01 9

01 7

01 5

388

374

349

327

307

290

275

242

21 7

050

047

044

040

038

035

033

029

025

421

407

381

358

337

31 9

303

268

241

071

068

063

058

055

05 1

048

042

037

6

45 1

436

410

386

364

345

328

292

263

094

090

083

077

072

068

064

056

049

7

478

463

435

41 1

389

369

351

314

283

116

111

1 03

096

090

084

080

070

062

502

487

459

434

412

391

373

334

302

1 38

1 32

1 23

115

1 07

1 01

096

084

075

524

508

481

455

433

412

393

353

321

1 59

1 53

1 42

1 33

1 25

118

111

098

088

544

528

500

475

452

431

412

372

338

1 79

1 73

1 61

1 51

1 42

1 34

1 27

112

1 00

11

561

546

519

493

470

449

429

388

354

1 99

1 92

1 80

1 60

1 59

1 50

1 42

1 26

113

12

578

563

535

510

487

465

446

404

369

218

21 1

1 97

1 86

1 75

1 66

1 57

1 40

1 25

13

594

579

551

525

503

481

461

419

384

237

229

215

202

1 91

1 81

1 72

1 53

1 38

14

608

593

566

540

517

496

476

433

398

255

247

232

21 8

206

1 96

1 86

1 66

1 50

15

621

607

579

554

531

509

490

446

41 0

2 72

263

248

234

221

210

200

1 79

1 62

16

634

619

592

567

544

522

502

459

422

288

280

263

249

236

224

214

1 91

1 73

17

645

631

604

579

556

535

515

471

434

304

295

2 78

263

250

238

227

203

1 85

4 5

8 9 10

)

>

421>

"

"

19

20

DenomlnatormlrJl:l$ fll:lm�ratQr (rJ":" x) U· M a

656

642

61 5

590

568

547

527

483

319

310

293

277

264

251

240

21 5

1 96

19

666

652

626

601

578

557

538

494

456

334

324

307

291

277

264

252

227

207

20

676

662

636

612

589

568

548

504

467

348

338

320

304

289

276

264

238

21 7

22

693

680

654

631

614

588

568

524

487

3 74

364

346

329

314

300

287

260

237

709

696

671

648

626

605

586

543

505

399

388

369

352

337

322

309

281

257

723

71 1

686

663

642

622

603

559

522

422

41 1

386

3 74

358

343

330

300

276

736

724

700

678

657

637

61 8

575

538

443

432

41 2

395

3 78

363

349

31 9

294

748

736

71 3

691

670

651

632

590

552

462

452

432

41 4

397

382

368

337

311

35

773

762

740

719

700

681

663

622

586

506

496

476

457

441

425

410

378

351

40

793

783

763

743

724

706

689

649

61 4

544

533

513

495

478

462

448

414

386

45

81 1

801

781

763

745

728

71 1

673

639

5 76

566

548

528

51 1

495

480

447

41 9

50

825

816

797

780

763

746

73 1

694

660

604

594

575

557

540

525

510

476

447

848

840

823

807

792

777

763

728

697

650

64 1

622

605

589

5 74

559

526

497

880

874

860

846

833

820

808

778

750

71 7

708

692

676

662

647

634

603

575

901

895

883

872

860

847

838

812

787

762

755

740

726

71 3

700

687

658

632

947

943

937

930

923

91 7

910

894

878

868

863

854

845

836

828

81 9

799

780

978

976

973

970

967

964

961

954

947

18

24 26 28 30

60 80 1 00 200 500

30

35

40 445

944

941

937

933

928

924

920

91 0

901

1 000

1 000

1 000

1 000

1 000

1 000

1 000

1 000

1 000

1 000

1 000

1 000

1 000

1 000

1 000

1 000

1 000

1 000

VII

2 3 4

,

I

l- I

"0

.�

1 � C.

I

6000 4000 2000

C

t-

800 0> N

I� 18

;:

.;;;

I�

0 ..J

1000

-

.. ·e I:::

30

�"-

40

60 40

20

,

"

50

Percentage

10 60

70

80

90

Appendix XI

20%

Sample size required to attain desired confidence interval around expected percentage of

6000

4000

·�I

Q. E III

�:J

r:r CI> a:

ICI> I g'"

18

�I .31 I

It

1000 800 lI 600 I lI 400 99%1 I 1 200

\

I \

\

\\

,

'/95% II i�

\'

\\

95%\ \

\1\

20 / o

100 80 - 60 40 20

, \

/}

-if 10 Y 10

199%

,I

I

40

- 1000 - 800 - 600 400 200

�� j:>

l-

100 80 60 -

2000

-&-:2 I'C

5t �J

CI>

�I ;g l

2000

·in

I 1· I:::

.§ t:1

CI> N

- 6000 4000

I 1

l-

\

,

\ \\

,, �' , 50 60 70

'\

20

30

40

,

Percentage

80

90

10 Fig. 3

4 ) /'

Sample size required to attain desired confidence interval around expected percentage of 30% 6000

I

l-

I

'E :.:/ t I c:

4000 I-.

Q)I

;g

2000

1000 800 Q) N ' ;;; Q)

a. E �

600

g I �I

� C' Q) a:

-

...J, I

-

I

l-

80 60

l-

f I /

l-

1% I::>

\99%

It \\ � �

-

95

/j

10

600

200

\

100

\

80

\\

\\ \

30

800

-

-

\

40

-

\\

50

Percentage

60 40

\

\

20

1000

400

\

1

I

o

-

./

I-

10

-

I

/f

40

20

2000

I �

99%1

Fig. 4

,:Q

�g I U

I

200

6000 4000

It ,g

I

400

100

E

�,

'0

t ,

-

-

I ...

,

20 "

,

\.'

60

'"

70

10 80

90

Appendix XI Sample size required to attain desired confidence interval around expected percentage of 40% 6000

2000 800 CP N ;;; CP

'

Q. E m

11

,!:

� C' CP a:

600

311

.3, I

60

I

" //

fff-

40

/

fI

20

/

10

o

I

V\

99% 100 80

\\ 95% \

\

V

20

\

40

50

Percentage

60

-

\

40 -

,

�\

\

30

600

200

11'

/j

800

-

V \\ 95•

1000

400

1

/j

10

-

\

IJ

200

-

\

99%/

-

,

,

400

80

,�

��

�T

f-

2000

I�

cl 8 , �

6000 4000

�� fl,;g , g

CP

l-

100

II.::: E I:.: I� 1 �

_, 'E 1 ::1

-

I

I

4000

1000

I

I

60

\.

20

\.

70

,

,

80

10

90 Fig. 5

! ;'1

440

50%

Sample size required to attain desired confidence interval around expected percentage of 6000

-

...

4000

-

800 II> N 'in II>

a. E :J!

600

-

� 0Il> a:

i200

I

80 60

" I J I I

..... -

40

f-

I

/

I /

10 o

I

/)

20

Fig. 6

�L : I

,� :t:3-

, �

10

j

1

\

\

40

-

99% \ \

100 80

\\

\

-

\

'\

60

70

60 40

\1\\

Percentage

800

600

200

1\ \

1000

400

'.

5

4000

-

\'

//95% V

30

-

V 95%\

V

20

-

,

\

6000

2000

, g ,�

II 99%

40(1

100

fl-;g

I

"0

.�

�, ]1

:�

, -; u

-'I

i-

...

]/ g , u /

i-

-

I

� I

2000

1000

I

I I

20

\

80

\.

10

90

Appendix XII The probability of detecting a small number of cases in a population (Modified f rom Can non and Roe, 1982)

Example A 40% sample from a herd of 20 animals would have a 97.6% chance of including at least one positive if six were present in the herd.

These tables give the probability of detecting at least one case for different sampling fractions and numbers of cases in the population.

20% Sampling Number ofpositives in the population Population size

Number 2

sampled

3

4

5

6

7

8 0.978

10

2

0.200

0.378

0.533

0.667

0.778

0.867

0.933

20

4

0.200

0.368

0.509

0.624

0.7 1 8

0 . 793

0.852

0 . 898

30

6

0.200

0.366

0.501

0.61 2

0.702

0.773

0.830

0. 874

40

8

0.200

0.364

0.498

0.607

0.694

0.764

0.8 1 9

0.863

50

10

0.200

0.363

0.498

0.603

0.689

0.758

0.81 3

0.857

60

12

0.200

0.363

0.495

0.601

0.686

0.755

0 . 809

0.853

70

14

0.200

0.362

0.494

0.599

0.684

0.752

0 . 807

0.850

80

16

0.200

0.362

0.493

0.598

0.683

0.7 5 1

0.804

0.847

90

18

0.200

0.362

0.492

0.597

0.682

0.749

0.803

0.846

1 00

20

0.200

0.362

0.492

0.597

0.681

0.748

0.802

0.844

0.200

0.360

0.486

0.590

0.672

0.738

0.790

0.832

8

30% Sampling Number ofpositives in the population Population size

Number sampled

2

3

4

5

6

7

10

3

0.300

0.533

0 . 708

0.833

0.91 7

0.967

0.992

1 .000

20

6

0.300

0.521

0.681

0.793

0.871

0.923

0.956

0.976

30

9

0.300

0. 5 1 7

0.672

0.782

0.857

0.909

0.943

0.965

40

12

0.300

0.5 1 5

0 . 668

0.776

0.851

0.902

0.936

0.960 0.956

50

15

0.300

0.5 1 4

0.666

0.773

0.847

0.898

0.933

60

18

0.300

0.5 1 4

0.665

0.770

0.844

0.895

0.930

0.954

70

21

0. 300

0.5 1 3

0.663

0.769

0.842

0.893

0.928

0.952

80

24

0.300

0.5 1 3

0.663

0.768

0.841

0.892

0.927

0.95 1

90

27

0.300

0.5 1 2

0 . 662

0.767

0 . 840

0.891

0.926

0.950

1 00

30

0.300

0. 5 1 2

0.661

0.766

0.839

0.890

0.925

0.949

0.300

0.5 1 0

0.657

0.760

0.832

0.882

0.9 1 8

0.942

442

40% Sampling Number ofpositives in the population

Population size

Number sampled

2

3

4

5

6

7

8

10

4

00400

0.667

0.833

0.929

0.976

0.995

1 .000

1 .000

20

8

00400

0.653

0.807

0.898

0.949

0.976

0.990

0.996

30

12

00400

0.648

0.799

0.888

0.940

0.969

0.984

0.993

40

16

00400

0.646

0. 795

0.884

0.935

0.965

0.981

0.990

50

20

00400

0.645

0. 793

0.881

0.933

0.963

0.980

0.989

60

24

00400

0.644

0.791

0.879

0.93 1

0.961

0.978

0.988

70

28

00400

0.643

0. 790

0.878

0.930

0.960

0.977

0.987

80

32

00400

0 . 643

0. 789

0.877

0.929

0.959

0.977

O.91:l7

90

36

00400

0 . 643

0. 789

0.876

0.928

0.959

0.976

0.987

1 00

40

00400

0 . 642

0. 788

0.876

0.927

0.958

0.976

0.986

00400

0.640

0. 784

0.870

0.922

0.953

0.972

0.983

7

8

50% Sampling

Number of positives in the population Populato i n

Number sampled.

size '2

3

4

5

6

10

5

0.500

0 . 7 78

0.91 7

0.976

0.996

1 .000

1 .000

1 .000

20

10

0.500

0. 763

0.895

0.957

0.984

0.995

0.998

0.994

30

15

0.500

0.759

0.888

0.950

0.979

0.992

0.997

0.999

40

20

0.500

0.756

0 . 885

0.947

0.976

0.990

0.996

0.998

50

25

0.500

0. 755

0.883

0.945

0.975

0.989

0.995

0.998

60

30

0.500

0.754

0.881

0.944

0.974

0.988

0.995

0.998

70

35

0.500

0.754

0. 880

0.943

0.973

0.988

0.994

0.998

80

40

0. 500

0.753

0.880

0.942

0.973

0.987

0.994

0.997

90

45

0.500

0.753

0.879

0.942

0.972

0.987

0.994

0.997

100

50

0. 500

0.753

0.879

0.941

0.972

0.987

0.994

0.997

0.500

0.750

0.875

0.9 3 7

0.969

0.984

0.992

0.996

6

7

8

60% Sampling Number ofpositive s in the population

Population size

Number sampled

2

3

4

5

10

6

0.600

0.867

0.967

0.994

1 .000

1 .000

1 .000

1 .000

20

12

0.600

0.853

0.951

0.986

0.994

0.997

1 .000

1 .000

30

18

0.600

0.848

0.946

0.982

0.994

0.997

1 .000

1 .000

40

24

0.600

0.846

0.943

0.980

0.993

0.997

0.999

1 .000

50

30

0.600

0.845

0.942

0.979

0.993

0.997

0.999

1 .000

60

36

0.600

0.844

0.941

0.978

0.992

0.997

0.999

1 .000

70

42

0.600

0.843

0.940

0.978

0.992

0.997

0.999

1 .000

80

48

0.600

0.843

0.940

0.977

0.992

0.997

0.999

1 .000

90

54

0.600

0.843

0.939

0.977

0.991

0.997

0.999

1 .000

1 00

60

0.600

0.842

0.939

0.977

0.991

0.997

0.999

1 .000

0 . 600

0 . 840

0.936

0.974

0.990

0.996

0.998

1 .000

Appendix XIII "�. . �-��

.�." ... ".��". "."�

-.. -. """-.

The probability of failure to detect cases in a population ( F rom Can no n and Roe, 1982)

The table gives the probability o f failure t o detect dis­ eased animals from an 'infinite' population with the specified proportion of positives in the population.

Tests of a series of random samples of 25 animals from a large population in which 1 0% of animals are positive would fail to detect any positives in 7.2% of such sample groups.

Example

Number of animals in sample tested

Prevalence 5

10

25

50

75

100

200

1%

0.951

0.904

0.778

0.605

0.471

0.366

0 . 1 34

2%

0.904

0.81 7

0.603

0.364

0.220

0. 1 3 3

0.0 1 8

0.000

3%

0.859

0.737

0.467

0. 2 1 8

0 . 1 02

0.048

0.002

4%

0.8 1 5

0.665

0.360

0. 1 30

0.047

0.01 7

0.000

5%

0. 774

0.599

0.277

0.077

0.021

0 .006

0.000

6%

0.734

0.539

0.21 3

0.045

0.01 0

0.002

0.000

7%

0.696

0.484

0 . 1 63

0.027

0.004

0.001

0.000

8%

0.659

0.434

0 . 1 24

0.01 5

0.002

0.000 0.000

9%

0.624

0.389

0.095

0.009

0.001

1 0%

0.590

0.349

0.072

0.005

0.000

1 2%

0.528

0 . 2 79

0.041

0.002

0.000

1 4%

0.470

0.221

0.023

0.001

0.000

1 6%

0.41 8

0 . 1 75

0.01 3

0.000 0.000

1 8%

0.371

0. 1 3 7

0.007

20%

0.328

0 . 1 07

0.004

0.000

24%

0.254

0.064

0.001

0.000

28%

0 . 1 93

0.037

0.000

32%

0 . 1 45

0.021

0.000

36%

0 . 1 07

0.01 2

0.000

40%

0.078

0.006

0.000

50%

0.031

0.001

0.000

60%

0.0 1 0

0.000

500

1000

0.081

0.007

0.000

0.006

0.000

250

Appendix

XIV

Sample sizes required for detecting disease with probability, Pl' and threshold number of positives (in brackets) (probability of incorrectly concluding that a healthy population is diseased [in square brackets])

These tables give the number of animals that need to be sampled, and the upper limit of the number of test­ positive animals that can be identified in the sample, while still concluding, with probability PI' that disease is absent. Example (consult the first table)

A diagnostic test has a sensitivity of 99% and specificity of 99% . If 1 73 animals are sampled from a population of 500 in which, if disease is present, the minimum prevalence is 5%,

up to four test-positive animals can be identified in the sample, while still concluding, with probability, PI' 0.99, that disease is absent. The probability of observ­ ing more than four test-positive animals in a disease­ free population is no greater than 0.05. Thus, if more than four test-positive animals are identified in the sample, the probability of incorrectly concluding that a healthy population is diseased is no greater than 0.05 (i.e., it can be concluded that the population is diseased, with at least 95% 'confidence').

·H

XIV

P1 =0.99; sensitivity = 99%; specificity = 99% Prevalence

Population

size

*

?

1%

5%

10%

20"/"

50% [1.0)

fO.05]

[0.01]

(LO]

[0.05]

[0.01]

11.0]

10.05]

[0.01]

[1.0]

[0.05]

[O.OlJ

9 (1 )

1 5 (0)

20 ( 1 )

24 (2)

23 (0)

28 (1 )

*

27 (0)

*

*

*

*

*

1 0 (1 )

1 0 (1 )

1 7 (0)

24 ( 1 )

29 (2)

29 (0)

44 (2)

7 (0)

1 0 (1 )

1 0 (1 )

1 9 (0)

26 (1 )

33 (2)

34 (0)

*

*

1 50

7 (0)

1 0 (1 )

1 0 (1 )

1 9 (0)

27 ( 1 )

35 (2)

36 (0)

200

1 0 (1 )

1 0 (1 )

35 (2)

3 7 (0)

66 (2)

78 (3)

*

1 0 (1 )

1 0 (1 )

1 9 (0) 20 (0)

28 (1 )

300

7 (0) 7 (0)

*

29 ( 1 )

36 (2)

38 (0)

69 (2)

500

7 (0)

1 1 (1 )

1 1 (1 )

20 (0)

29 (1 )

37 (2)

39 (0)

*

*

1 000

7 (0)

1 1 (1 )

1 1 (1 )

20 (0)

29 (1 )

37 (2)

40 (0)

*

5000

7 (0)

1 1 (1 )

1 1 (1 )

20 (0)

30 (1 )

38 (2)

4 1 (0)

2754 (40)

1 0 000

7 (0)

1 1 (1 )

1 1 (1 )

20 (0)

30 (1 )

38 (2)

4 1 (0)

=

=

[1.0]

[0.05]

[0.01]

30

6 (0)

9 (1 )

50

7 (0)

1 00

*

*

*

*

*

*

*

*

*

44 (2)

44 (0)

5 8 (2)

67 (3)

55 (0)

63 (2)

74 (3)

59 (0)

1 1 3 (3)

1 26 (4)

1 2 3 (0)

1 60 (5)

1 5 7 (0)

82 (3)

65 (0) 68 (0)

1 29 (3) 1 6 1 (4)

1 79 (5)

1 82 (0)

71 (2)

98 (4)

71 (0)

1 73 (4)

2 1 5 (6)

202 (0)

73 (2)

1 0 1 (4)

74 (0)

1 83 (4)

229 (6)

2 1 7 (0)

*

75 (2)

1 03 (4)

76 (0)

1 9 1 (4)

264 (7)

228 (0)

2078 (28)

75 (2)

1 04 (4)

76 (0)

1 93 (4)

267 (7)

230 (0)

2406 (32)

*

96 (3)

99 (0)

in the population . Req u i red accuracy can not be achieved, even by sam p l i n g all animals Unable to compute (population size too l a rge).

P1 =0.99; sensitivity = 95%; specificity =99% Prevalence

Population

size

(0.05]

[1.0J

[0.05]

[0.Q1]

[1.0]

[0.05]

10.01]

[l.0J

30

7 (0)

1 0 (1 )

1 0 (1 )

1 6 (0)

21 (1 )

25 (2)

24 (0)

30 ( 1 )

50

7 (0)

1 0 (1 )

1 0 (1 )

1 8 (0)

1 00

7 (0)

1 1 (1 )

1 1 (1 )

1 50

7 (0)

1 1 (1 )

200

7 (0)

300

1%

5%

10%

20%

50%

[1.01

[0.05]

[0.01]

[1.0]

[O.05J

[0.Q11

*

28 (0)

*

*

*

*

*

46 (2)

46 (0)

*

*

*

*

*

*

*

*

[0.01]

*

*

*

*

*

*

*

*

30 (2)

30 (0)

1 9 (0)

25 (1 ) 28 (1 )

46 (2)

35 (2)

35 (0)

60 (2)

70 (3)

58 (0)

1 00 (3)

*

1 1 (1 )

20 (0)

29 (1 )

36 (2)

3 8 (0)

66 (2)

7 7 (3)

6 1 (0)

1 1 8 (3)

1 43 (5)

1 2 8 (0)

1 1 (1 )

1 1 (1 )

20 (0)

29 (1 )

37 (2)

39 (0)

69 (2)

8 1 (3)

67 (0)

1 34 (3)

1 67 (5)

1 63 (0)

7 (0)

1 1 (1 )

1 1 (1 )

2 1 (0)

30 ( 1 )

38 (2)

40 (0)

72 (2)

98 (4)

71 (0)

1 6 7 (4)

204 (6)

1 88 (0)

500

7 (0)

1 1 (1 )

1 1 (1 )

21 (0)

30 (1 )

39 (2)

4 1 (0)

74 (2)

1 02 (4)

74 (0)

1 80 (4)

2 2 3 (6)

208 (0)

1 000

8 (0)

1 1 (1 )

1 1 (1 )

21 (0)

3 1 (1 )

39 (2)

42 (0)

76 (2)

1 05 (4)

76 (0)

1 90 (4)

260 (7)

2 2 2 (0)

*

*

5000

8 (0)

1 1 (1 )

1 1 (1 )

2 1 (0)

3 1 (1 )

39 (2)

42 (0)

78 (2)

1 07 (4)

78 (0)

1 98 (4)

2 7 3 (7)

232 (0)

2242 (30)

2929 (42)

1 0 000

8 (0)

1 1 (1 )

1 1 (1 )

2 1 (0)

31 ( 1 )

40 (2)

42 (0)

78 (2)

1 08 (4)

79 (0)

226 (5)

2 76 (7)

235 (0)

2579 (34)

P1 =0.99; sensitivity =95%; specificity =95% Prevalence

Population

size

1%

5%

10%

20%

50% [1.0]

[0.05]

(0.01]

[1.01

[0 ..05]

[0.01]

f1.0}

[0.05}

[O.Ol}

[1.0]

[0.051

[0.Q1]

[1.0]

[O.OS}

[0.01]

30

6 (0)

1 2 (2)

1 4 (3)

1 4 (0)

*

*

22 (0)

*

*

26 (0)

*

*

*

*

*

50

7 (0)

1 3 (2)

1 5 (3)

1 6 (0)

37 (4)

45 (6)

25 (0)

48 (3)

1 00

7 (0)

1 3 (2)

1 6 (3)

1 7 (0)

47 (5)

57 (7)

28 (0)

94 (8)

*

*

*

69 (0)

*

*

1 50

7 (0)

1 3 (2)

1 6 (3)

1 7 (0)

49 (5)

60 (7)

29 (0)

1 1 8 (1 0)

1 45 (1 4)

42 (0)

200

7 (0)

1 3 (2)

1 6 (3)

1 7 (0)

50 (5)

66 (8)

30 (0)

1 24 (1 0)

1 6 1 (1 5)

44 (0)

*

*

300

7 (0)

1 4 (2)

1 6 (3)

1 8 (0)

51 (5)

68 (8)

30 (0)

1 3 7 (1 1 )

1 78 (1 6)

45 (0)

*

500

7 (0)

1 4 (2)

1 6 (3)

1 8 (0)

69 (8)

30 (0)

1 5 1 (1 2 )

1 93 ( 1 7)

400 (27)

*

*

*

1 000

7 (0)

1 4 (2)

1 7 (3)

1 8 (0)

52 (5) 53 (5)

46 (0)

70 (8)

3 1 (0)

1 54 ( 1 2 )

1 07 ( 1 8)

46 (0)

465 (3 1 )

604 (43)

76 (0)

5000

7 (0)

1 4 (2)

1 7 (3)

1 8 (0)

53 (5)

3 1 (0)

1 66 ( 1 3)

220 ( 1 9)

504 (33)

687 (48)

76 (0)

*

*

1 0 000

7 (0)

1 4 (2)

1 7 (3)

1 8 (0)

53 (5)

7 1 (8) 7 1 (8)

46 (0)

3 1 (0)

1 67 ( 1 3)

2 2 1 ( 1 9)

4 7 (0)

705 (49)

76 (0)

*

39 (0) 41 (0)

*

*

*

520 (34)

*

*

*

*

*

68 (0) 73 (0) 74 (0) 75 (0)

*

*

*

*

*

*

*

*

*

*

44()

Appendices

" " , , ",o" o" «""",""�"o'w�",,o,"""",_@,o, ',"0 ,0' o,,�, o

Pl =0. 95; sensitivity =99%; specificity =99%

Prevalence

Population size

1%

5%

10%

20%

50%

[O.Q1]

[1.0]

[0.(5)

[0.0 1 ]

*

*

*

*

*

*

*

*

[1.0)

[0.05]

[0.01]

11.0]

[0.(5)

[0.01]

[1.0]

[0.05]

[0.01)

[1.01

30

5 (0)

5 (0)

7 (1 )

1 1 (0)

1 7 (1 )

2 1 (2)

1 8 (0)

2 6 (1 )

30 (2)

2 3 (0)

50

5 (0)

5 (0)

7 (1 )

1 2 (0)

1 9 (1 )

24 (2)

21 (0)

32 ( 1 )

40 (2)

37 (0)

1 00

5 (0)

5 (0)

8 (1 )

1 3 (0)

20 ( 1 )

26 (2)

24 (0)

48 (2)

57 (3)

4 1 (0)

77 (2)

99 (4)

1 50

5 (0)

5 (0)

8 (1 )

1 3 (0)

20 ( 1 )

27 (2)

2 5 (0)

50 (2)

61 (3)

41 (0)

82 (2)

1 1 3 (4)

97 (0)

200

5 (0)

5 (0)

8 (1 )

1 3 (0)

21 (1 )

28 (2)

52 (2)

63 (3)

45 (0)

1 09 (3)

1 20 (0)

300

5 (0) 5 (0)

8 (1 )

1 3 (0)

21 (1 )

2il (2)

46 (0)

1 1 6 (3)

1 54 (5)

1 30 (0)

8 (1 )

1 3 (0)

21 (1 )

28 (2)

2 6 (0)

53 (2) 55 (2)

66 (3)

500

5 (0) 5 (0)

2 6 (0) 26 (0)

1 2 7 (4)

6 7 (3)

48 (0)

1 2 1 (3)

1 63 (5)

1 3 9 (0)

1 000

5 (0)

5 (0)

8 (1 )

1 3 (0)

21 ( 1 )

29 (2)

2 6 (0)

56 (2)

69 (3)

49 (0)

1 25 (3)

1 69 (5)

1 3 (0)

22 ( 1 )

29 (2)

27 (0)

56 (2)

70 (3)

50 (0)

1 2 9 (3 )

1 3 (0)

27 (0)

5 7 (2)

70 (3)

50 (0)

1 29 (3)

1 7 5 (5) 1 76 (5)

5000

5 (0)

5 (0)

8 (1 )

1 0 000

5 (0)

5 (0)

8 (1 )

29 (2)

22 (1 )

[O.05! 30 ( 1 ) 49 (1 )

*

*

*

*

*

*

1 45 (0)

*

*

1 49 (0)

1 487 (2 1 )

2 1 04 (32)

1 50 (0)

1 641 (23)

2338 (35)

*

*

89 (0)

*

*

Pl =0.95; sensitivity =95%; specificity =99%

Prevalence

Population size

1%

5%

10%

20%

50% IT .OJ

[0.05]

[0 . 01]

11.0]

[0.05)

[0.01}

[1.01

[0.05]

[0.011

[1.0]

[0.05]

[0.01]

[1.00]

[0.05J

[0.01]

5 (0)

5 (0)

8 (1 )

1 2 (0)

1 8 (1 )

22 (2)

1 9 (0)

27 (1 )

*

24 (0)

*

*

*

*

*

30 50

5 (0)

5 (0)

8 (1 )

1 2 (0)

1 9 (1 )

25 (2)

22 (0)

3 3 (1 )

41 (2)

39 (0)

1 00

5 (0)

8 (1 )

1 3 (0)

2 1 (1 )

2 5 (0)

50 (2)

60 (3)

42 (0)

*

*

*

1 00 (0)

*

80 (2)

1 50

5 (0)

8 (1 )

1 4 (0)

2 1 (1 )

28 (2) 28 (2)

2 6 (0)

53 (2)

64 (3)

43 (0)

1 02 (3)

1 1 8 (4)

200

5 (0)

5 (0)

8 (1 )

1 4 (0)

22 (1 )

29 (2)

2 6 (0)

54 (2)

66 (3)

47 (0)

1 1 3 (3)

1 48 (5)

1 2 3 (0)

300

5 (0)

5 (0)

8 (1 )

1 4 (0)

22 ( 1 )

29 (2)

2 7 (0)

5 6 (2)

68 (3)

48 (0)

1 20 (3)

1 60 (5)

1 34 (0)

500

5 (0)

5 (0)

8 (1 )

1 4 (0)

22 (1 )

30 (2)

27 (0)

5 7 (2)

70 (3 )

49 (0)

1 26 (3)

1 69 (5)

1 42 (0)

1 000

5 (0)

5 (0)

8 (1)

1 4 (0)

22 (1 )

30 (2)

2 7 (0)

58 (2)

71 (3)

50 (0)

1 30 (3)

1 75 (5)

1 48 (0)

5000

5 (0)

5 (0)

8 (1 )

1 4 (0)

22 ( 1 )

30 (2)

2 8 (0)

59 (2)

72 (3)

5 1 (0)

1 3 3 (3)

204 (6)

5 (0)

8 (1 )

1 4 (0)

23 (1 )

30 (2)

2 8 (0)

59 (2)

73 (3)

52 (0)

1 34 (3)

205 (6)

5 (0)

*

*

*

*

*

*

*

93 (0)

5 (0) 5 (0)

1 0 000

*

*

*

*

*

*

*

1 52 (0)

1 636 (23)

2263 (34)

1 5 3 (0)

1 735 (24)

2503 (37)

Pl =0.95; sensitivity =95%; specificity =95%

Population

Prevalence

size

50%

1%

5%

10%

20%

[0 ,01 ]

[1.0]

[0.05]

[0.01]

*

*

*

*

*

47 (0)

*

*

[1.0!

[0.05]

[0.01]

[1.0]

[0.05]

[0.01)

[ 1.0]

[0 . 0 5 ]

[0.01]

[1.0]

[0.05]

30

5 (0)

7 (1 )

1 2 (3)

1 0 (0)

25 (3)

*

1 6 (0)

*

*

20 (0)

*

50

5 (0)

1 0 (2)

1 3 (3)

1 1 (0)

28 (3)

36 (5)

1 8 (0)

49 (5)

1 00

5 (0)

1 0 (2 )

1 3 (3)

1 1 (0)

35 (4)

45 (6)

1 9 (0)

79 (7)

*

1 50

5 (0)

1 0 (2)

1 3 (3)

1 2 (0)

36 (4)

46 (6)

20 (0)

91 (8)

1 2 1 (1 2)

200

5 (0)

1 1 (2)

1 3 (3)

1 2 (0)

36 (4)

47 (6)

20 (0)

94 (8)

1 3 2 (1 3)

29 (0)

*

300

5 (0)

1 1 (2)

1 3 (3)

1 2 (0)

3 7 (4)

48 (6)

20 (0)

1 04 (9)

1 3 6 (1 3)

30 (0)

268 ( 1 9)

*

48 (6)

20 (0)

1 06 (9)

1 48 (14)

30 (0)

300 (2 1 )

423 (32)

49 (0)

54

20

1 08 (9)

150 (1 4)

30 (0)

3 3 1 (23)

459 (34)

50 (0)

30 (0)

349 (24)

492 (36)

50 (0)

30 (0)

3 5 1 (24)

507 (37

50 (0)

*

5 (0) 5 (0)

11 (2) 11 (2)

13 (3) 13 (3)

12 (0) 37 (4) 12 (0) 37 (4)

5000

5 (0)

1 1 (2)

1 3 (3)

1 2 (0)

38 (4)

54 (7)

20 (0)

1 09 (9)

1 52 ( 1 4)

1 0 000

5 (0)

1 1 (2)

1 3 (3)

1 2 (0)

38 (4)

54 (7)

20 (0)

1 09 (9)

1 6 1 ( 1 5)

500 1000

(7)

(0)

29 (0) 28 (0) 28 (0)

*

*

*

*

*

*

*

46 (0) 49 (0) 49 (0)

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

Appendix XIV P1 =0.90; sensitivity = 99%; specificity =99% Prevalence

Population size

30

1%

5%

10%

20%

50%

[0.05J

[O.OlJ

[1.0J

[0.05]

[0.01]

*

*

*

*

*

*

[1.0]

[0.051

[0.011

[1.0]

[0.05J

[O.OlJ

[1.0]

6 (1 )

9 (0)

1 5 (1 )

1 5 (1 )

1 5 (0)

24 (1 )

29 (2)

2 0 (0)

29 (1 )

1 6 (1 )

21 (2)

1 7 (0)

2 8 (1 )

3 7 (2)

32 (0)

47 (1 )

47 (1 ) 96 (4)

79 (0)

[1.0J

[0. 05J

[O.OlJ

4 (0)

4 (0)

*

*

*

50

4 (0)

4 (0)

6 (1 )

1 0 (0)

1 00

4 (0)

4 (0)

7 (1 )

1 0 (0)

1 7 (1 )

23 (2)

1 9 (0)

31 (1 )

42 (2)

3 3 (0)

70 (2)

24 (2)

1 9 (0)

3 2 (1 )

42 (2)

3 3 (0)

73 (2)

1 05 (4)

80 (0)

*

*

56 (3) 58 (3)

3 5 (0)

1 1 6 (4)

36 (0)

79 (2) 82 (2)

1 22 (4)

98 (0) 1 04 (0)

*

*

1 06 (3)

1 2 7 (4)

1 09 (0)

1 50

4 (0)

4 (0)

7 (1 )

1 0 (0)

1 7 (1 )

200 300

4 (0)

4 (0)

7 (1 )

1 7 (1 )

4 (0)

4 (0)

7 (1 )

1 0 (0) 1 0 (0)

500

4 (0)

4 (0)

7 (1 )

1 0 (0)

1 8 (1 )

24 (2)

20 (0)

34 (1 )

59 (3)

3 7 (0)

1 000

4 (0)

4 (0)

7 (1 )

1 0 (0)

1 8 (1 )

24 (2)

20 (0)

35 (1 )

60 (3)

38 (0)

1 09 (3)

1 5 1 (5)

1 1 2 (0)

9 8 1 (1 5)

5000

4 (0)

4 (0)

7 (1 )

1 0 (0)

1 8 (1 )

25 (2 )

2 1 (0)

35 (1 )

60 (3)

38 (0)

1 1 1 (3)

1 1 5 (0)

1 2 2 6 (1 8)

1 781 (28)

1 0 000

4 (0)

4 (0)

7 (1 )

1 0 (0)

1 8 (1 )

25 (2)

21 (0)

3 5 (1 )

60 (3)

38 (0)

1 1 2 (3)

1 55 (5) 1 5 6 (5)

1 1 6 (0)

1 305 (1 9)

1 8 75 (29)

24 (2) 24 (2)

1 8 (1 )

20 (0) 20 (0)

3 3 (1 ) 34 (1 )

*

*

*

*

*

P1 =0.90; sensitivity =95 %; specificity =99% Prevalence

Population size

[1.0]

[0.05]

{O.OT]

30

4 (0)

4 (0)

7 (1 )

50

4 (0)

4 (0)

7 (1 )

1%

5%

10%

20%

50%

[0.05]

[0.01]

[1.0]

[0.05]

10.01]

*

*

*

*

*

*

[0.05J

(O.Ol]

[1.0]

[0.051

[0.Q1]

[l.OJ

9 (0)

1 5 (1 )

1 5 (1 )

1 6 (0)

25 (1 )

*

2 1 (0)

1 0 (0)

1 7 (1 )

22 (2)

1 8 (0)

29 (1 )

38 (2)

3 3 (0)

49 ( 1 )

49 (1 )

20 (0)

3 3 (1 )

44 (2)

34 (0)

73 (2)

1 00 (4)

82 (0) 83 (0)

{1.0]

30 (1 )

*

1 00

4 (0)

4 (0)

7 (1 )

1 0 (0)

1 8 (1 )

24 (2)

1 50

4 (0)

4 (0)

7 (1 )

1 1 (0)

1 8 (1 )

25 (2)

20 (0)

34 (1 )

57 (3)

37 (0)

75 (2)

1 09 (4)

21 (0)

34 (1 )

58 (3)

38 (0)

82 (2)

1 20 (4)

1 0 1 (0) 1 07 (0)

*

*

*

*

*

*

*

*

200

4 (0)

4 (0)

7 (1 )

1 1 (0)

1 8 (1 )

25 (2)

300

4 (0)

4 (0)

7 (1 )

1 1 (0)

1 8 (1 )

25 (2)

21 (0)

35 (1 )

60 (3)

39 (0)

1 06 (3)

1 2 6 (4)

25 (2)

21 (0)

49 (2)

6 1 (3)

39 (0)

1 1 0 (3)

1 5 2 (5)

1 1 1 (0) 1 1 5 (0)

*

*

*

*

500

4 (0)

4 (0)

7 (1 )

1 1 (0)

1 8 (1 )

1 000

4 (0)

4 (0)

7 (1 )

1 1 (0)

1 9 (1 )

25 (2)

21 (0)

49 (2)

62 (3)

39 (0)

1 1 3 (3)

1 5 6 (5)

21 (0)

50 (2)

63 (3)

40 (0)

1 1 5 (3)

1 60 (5)

1 1 7 (0)

1 3 1 0 (1 9)

1 875 (29)

21 (0)

50 (2)

63 (3)

40 (0)

1 1 6 (3)

1 6 1 (5)

1 1 8 (0)

1 3 9 1 (20)

2029 (3 1 )

5000

4 (0)

4 (0)

7 (1 )

1 1 (0)

1 9 (1 )

26 (2)

1 0 000

4 (0)

4 (0)

7 (1 )

1 1 (0)

1 9 (1 )

26 (2)

P1 =0.90; sensitivity =95 % ; specificity =95% Prevalence

Population size

30

[1.0]

[0.05]

[0.01]

[1.0]

[0.05]

[0.Q1]

4 (0)

6 (1 )

9 (2)

8 (0)

23 (3)

30 (5) 34 (5)

[0.05]

[0.01]

1 3 (0)

*

*

1 4 (0)

46 (4)

[1.0]

1%

5%

10%

20%

50%

*

50

4 (0)

6 (1 )

9 (2)

9 (0)

25 (3)

1 00

4 (0)

7 (1 )

9 (2)

9 (0)

26 (3)

36 (5)

15 (0)

66 (6)

*

2 7 (3)

3 7 (5)

1 5 (0)

77 (7)

1 07 ( 1 1 )

£1.0]

[0.05]

{O.Ol]

1 7 (0)

*

*

23 (0) 22 (0) 2 2 (0)

*

*

*

*

*

*

[1.0]

[0.05]

[0.Q1]

*

*

*

*

*

*

*

45 (0) 37 (0) 36 (0)

9 (2)

9 (0)

4 (0)

7 (1 ) 7 (1)

9 (2)

9 (0)

27 (3)

3 7 (5)

1 5 (0)

78 (7)

1 09 ( 1 1 )

2 3 (0)

*

4 (0)

7 (1 )

9 (2)

9 (0)

27 (3)

43 (6)

1 6 (0)

79 (7)

1 20 (1 2 )

23 (0)

233 (1 7)

500

4 (0)

7 (1 )

9 (2)

9 (0)

2 7 (3)

43 (6)

1 6 (0)

8 1 (7)

1 22 (1 2 )

2 3 (0)

249 (1 8)

3 6 1 (28)

3 8 (0)

1 6 (0)

81 (7)

1 2 3 (1 2)

2 3 (0)

265 ( 1 9)

380 (29)

38 (0)

1 50

4 (0)

200 300

*

*

38 (0) 38 (0)

1 000

4 (0)

7 (1 )

9 (2)

9 (0)

2 7 (3)

44 (6)

5000

4 (0)

7 (1 )

9 (2)

9 (0)

28 (3)

44 (6)

1 6 (0)

91 (8)

1 24 ( 1 2)

24 (0)

2 8 1 (20)

4 1 0 (3 1 )

3 8 (0)

1 0 000

4 (0)

44 (6)

1 6 (0)

91 (8)

1 3 3 ( 1 3)

24 (0)

282 (20)

4 1 1 (3 1 )

38 (0)

7 (1 )

9 (2)

9 (0)

28 (3)

*

*

*

*

*

*

*

*

*

*

*

*

*

*

Appendix

XV

Probabilities associated with the upper tail of the Normal distribution (Derived f rom Beyer, 19 8 1)

The body of the table gives the one-tailed probability,

The table can also be used to calculate multipliers for confidence intervals based on the Normal distribution. For example, the multiplier for a 95% confidence inter­ val is derived from a two-tailed significance level of 0.05, corresponding to a one-tailed level of 0.0250, for which z:=: 1 .96: the value of the multiplier.

P, under the null hypothesis, of a random value of the standardized Normal deviate, z[(x ,u)/a], being greater than the value in the margin. For example, the one-tailed probability of Z � 0.22 or :s; -0.22 is 0.4129. The probability is doubled for a two-tailed test. -

z

.

00

.

01

.02

.03

.

04

.05

06

.07

.08

.09

.

.0 .1 .2 .3 .4

.5000 .4602 .4207 .382 1 .3446

.4960 .4562 .41 68 . 3 783 .3409

.4920 .4522 .41 29 . 3 745 .3372

.4880 .4483 .4090 . 3 707 .3336

.4840 .4443 .4052 .3669 . 3 300

.4801 .4404 .40 1 3 .3632 .3264

.4761 .4364 .3 974 . 3 594 .3228

.472 1 .4325 .3936 .3557 .3 1 92

.468 1 4286 .3897 .3520 . 3 1 56

.4641 .4247 .3859 .3483 .31 2 1

.5 .6 .7 .8 .9

.3085 . 2 743 .2420 .21 1 9 . 1 84 1

.3050 .2 709 . 2 3 89 .2090 .1814

.301 5 .2676 .2358 .2061 . 1 788

.2981 .2643 .2327 .2033 . 1 762

.2956 .2 6 1 1 .2296 .2005 . 1 736

.29 1 2 .2578 .2266 . 1 977 . 1 71 1

.2877 .2546 .2236 . 1 949 . 1 685

.2843 .2 5 1 4 .2206 . 1 922 . 1 660

. 28 1 0 .2483 . 2 1 77 . 1 894 . 1 635

.2 776 .2451 .2 1 48 . 1 867 .161 1

1 .0 1 .1 1 .2 1 .3 1 .4

. 1 587 . 1 357 .1 1 51 .0968 .0808

. 1 562 . 1 335 .1 1 31 .09 5 1 .0793

. 1 539 .1314 .1 1 12 .0934 .0778

.1515 . 1 292 . 1 093 .09 1 8 .0764

. 1 492 .1 271 . 1 075 .0901 .0749

. 1 469 . 1 25 1 . 1 056 .0885 .0735

. 1 446 . 1 230 . 1 038 .0869 .072 1

. 1 42 3 .1210 . 1 020 .0853 .0708

. 1 40 1 . 1 1 90 . 1 003 .0838 .0694

. 1 3 79 . 1 1 70 .0985 .0823 .0681

1 .5 1 .6 1 .7 1 .8 1 .9

.0668 .0548 .0446 .0359 .0287

.0655 .05 3 7 .0436 .03 5 1 .0281

.0643 .05 2 6 .0427 .0344 .0274

.0630 .05 1 6 .04 1 8 .0336 .0268

.06 1 8 .0505 .0409 .0329 .0262

.0606 .0495 .0401 .0322 .02 5 6

.0594 .0485 .0392 .03 1 4 .0250

.0582 .0475 .0384 .0307 .0244

.0571 .0465 .0375 .0301 .02 39

.0559 .0455 .0367 .0294 .0233

2.0 2.1 2.2 2.3 2 .4

.02 2 8 . 0 1 79 . 0 1 39 .01 07 .0082

.0222 .01 74 .01 36 .01 04 .0080

.02 1 7 .01 70 .01 32 .01 02 .0078

.02 1 2 . 0 1 66 .01 2 9 .0099 .0075

.0207 . 0 1 62 .01 2 5 .0096 .0073

.0202 .0 1 58 .0 1 22 .0094 .00 7 1

.01 97 .01 54 .01 1 9 .009 1 .0069

.01 92 .0 1 50 .01 1 6 .0089 .0068

.0 1 88 .01 46 .01 1 3 .0087 .0066

.01 83 .01 43 .01 1 0 .0084 .0064

2.5 2.6 2.7 2.8 2.9

.0062 .0047 .0035 .0026 .00 1 9

.0060 .0045 .0034 .0025 .00 1 8

.0059 .0044 .0033 .0024 .00 1 8

.0057 .0043 .0032 .0023 .00 1 7

.0055 .0041 .003 1 .0023 .00 1 6

.0054 .0040 .0030 .0022 .00 1 6

.0052 .0039 .0029 .002 1 .00 1 5

.0051 .0038 .0028 .002 1 .00 1 5

.0049 .0037 .0027 .0020 .00 1 4

.0048 .0036 .0026 .00 1 9 .00 1 4

3.0 3.1 3 .2 3.3 3 .4

.00 1 3 .00 1 0 .0007 .0005 .0003

.00 1 3 .0009

.00 1 3 .0009

.00 1 2 .0009

.00 1 2 .0008

.001 1 .0008

.00 1 1 .0008

.00 1 1 .0008

.00 1 0 .0007

.00 1 0 .0007

3.5 3.6 3.7 3.8 3.9

.00023 .000 1 6 .000 1 1 .00007 .00005

4 .0

.00003

Appendix XVI Lower- and upper-tail probabilities for Wx, the Wilcoxon-Mann-Whitney rank-sum statistic ( F rom Siegel and Castellan, 1 988)

null hypothesis; Wx is the rank sum for the smaller group.

The body of the table gives the one-tailed probability,

P, of obtaining a value of Wx:::; Cu and Ws � Cu under the

m=3 CL

n=3

Cu

n=4

Cu

n=5

Cu

n= 6

Cu

n",7

Cu

n =:: a Cu

n=9 Cu

n"'10 Cu

.0061 30 .01 2 1 2 9

.0045 33

.0035 36

.0027 39

.0022 42

.0091 3 2

.0070 3 5

.0055 38

.0044 4 1

n= 11 Cu

n= 12 Cu

6

.0500 1 5

.0286 1 8

.01 79 2 1

.01 1 9 24

.0083 2 7

7

. 1 000 1 4

.0571

.03 5 7 20

.02 38 23

.0 1 67 2 6

8

.2000 1 3

. 1 1 43 1 6

.07 1 4 1 9

.0476 2 2

.0333 25

.0242 2 8

. 0 1 82 3 1

.0 1 40 34

.01 1 0 37

.0088 40

9

.3500 1 2

.2000 1 5

. 1 250 1 8

.0833 2 1

.0583 24

.0424 27

. 03 1 8 30

.0245 33

. 0 1 92 36

.01 54 39

10

.5000 1 1

. 3 1 43 1 4

. 1 964 1 7

. 1 3 1 0 20

.09 1 7 23

.0667 2 6

.0500 29

.0385 32

.0302 35

.0242 38

11

.6500 1 0

.4286 1 3

.2857 1 6

. 1 905 1 9

. 1 333 22

.0970 2 5

.0727 28

.0559 3 1

.0440 34

.0352 3 7 .0505 36

17

12

.8000

9

. 57 1 4 1 2

.3929 1 5

.2738 1 8

.191 7 2 1

. 1 394 24

. 1 045 2 7

.0804 30

.0632 3 3

13

.9000

8

.6857 1 1

.5000 1 4

.3571

17

.2583 2 0

. 1 879 2 3

. 1 409 2 6

. 1 084 29

.0852 32

.0681

35

14

.9500

7

.8000 1 0

.6071

13

.4524 1 6

.3333 1 9

.2485 2 2

. 1 864 25

. 1 434 28

. 1 1 26 3 1

.0901

34

15

1 .0000

6

.8857

9

. 7 1 43 1 2

.5476 1 5

.41 6 7 1 8

.3 1 5 2 2 1

.2409 24

. 1 853 2 7

. 1 456 30

. 1 1 65 3 3 . 1 473 32

16

.9429

8

.8036 1 1

.6429 1 4

.5000 1 7

.3879 20

.3000 23

.2343 2 6

. 1 841

17

. 97 1 4

7

.8750 1 0

.7262 1 3

.5833 1 6

.4606 1 9

.3636 22

.2867 25

.2280 2 8

. 1 824 3 1

18

1 .0000

6

.9286

9

.8095 1 2

.6667 1 5

.5394 1 8

.43 1 8 2 1

.3462 24

.2775 27

.2242 30

29

29

19

.9643

8

.8690 1 1

.741 7 1 4

.61 2 1 1 7

. 5000 20

.4056 23

.3297 2 6

.2681

20

.9821

7

.91 67 1 0

.8083 1 3

.6848 1 6

. 5 682 1 9

.4685 22

.3846 25

.3 1 65 2 8

21

1 .0000

6

.3670 2 7

.9524

9

.8667 1 2

. 75 1 5 1 5

.6364 1 8

.53 1 5 2 1

.4423 24

22

.9762

8

.9083 1 1

.81 2 1 1 4

.7000 1 7

.5944 20

.5000 23

.41 98 26

23

.9881

7

.94 1 7 1 0

.8606 1 3

.7591 1 6

.6538 1 9

.5577 22

.4725 25

24

1 .0000

6

.9667

.9030 1 2

. 8 1 36 1 5

. 7 1 33 1 8

.6 1 54 2 1

. 5 2 75 24

9

,IS(J

Appendices

m=4 n=8

Cu

n=9

Cu

n::l0 cU

n=11

Cu

n=12

Cu

10

.01 43

26

.0079

30

.0048

34

.0030 3 8

.0020 42

.00 1 4 46

.00 1 0

50

.0007

54

.0005

58

11

.0286

25

.0 1 59

29

.0095

33

.006 1

37

.0040 4 1

.0028 45

.0020

49

.001 5

53

.00 1 1

57

12

.05 7 1

24

.03 1 7

28

.01 90

32

.01 2 1

36

.0081

40

.0056 44

.0040

48

.0029

52

.0022

56

13

.1 000 23

.0556 2 7

.03 3 3

31

.02 1 2

35

.01 4 1

39

.0098

43

.0070

47

.0051

51

.0038

55

14

.1 7 1 4 2 2

.0952

26

.05 7 1

30

.0364 34

.0242

38

.01 68 42

.0 1 20

46

.0088

50

.0066

54

15

.2429

21

. 1 429

25

.0857

29

.0545 3 3

.0364 3 7

.0252

41

.01 80

45

.01 32

49

.0099

53

16

.3429

20

.2063

24

. 1 286

28

.08 1 8

32

.0545

.0378

40

.0270

44

.01 98

48

.0 1 48

52

17

.4429

19

.2778

23

. 1 762

27

. 1 1 52

31

.0768 35

.05 3 1

39

.0380

43

.0278

47

.0209

51

18 19

.5571

18

.2381

26

34

.0741

38

.0529

42

.0388

46

17

. 3 048

25

. 1 576 30 .2061 2 9

. 1 07 1

.6571

. 3 6 5 1 22 .4524 2 1

.1 4 1 4

33

.0993

37

.0709

41

.0520

45

.0291 .0390

50 49

20

.7571

16

.5476 2 0

.381 0

24

.2636 28

. 1 838

32

. 1 301

36

.0939

40

.0689

44

.05 1 6

48

21

.8286

15

.6349

19

.45 7 1

23

.3242 2 7

.2303

31

.1 650 35

.1 1 99

39

.0886

43

.0665

47

22

.9000

14

. 7222

18

.5429

22

.3939

.2848

30

.2070 34

.1 5 1 8

38

. 1 1 28

42

.0852

46

26

36

23

.9429

13

.7937

17

. 6 1 90 2 1

.463 6 2 5

. 34 1 4

29

.25 1 7

33

.1 868

37

. 1 399

41

. 1 060

45

24

.97 1 4

12

.8571

16

. 6 9 5 2 20

.5364 24

.4040

28

.302 1

32

.2268

36

.1714

40

.1 308

44

25

.9857

11

.9048

15

.76 1 9

19

.6061

23

.4667 2 7

.3552

31

.2697

35

.2059

39

. 1 582

43

26

1 .0000

10

.9444

14

.82 38

18

.6758

22

.5333

26

.41 2 6

30

. 3 1 77

34

.2447

38

. 1 896

42

27

.9683

13

.871 4

17

.7364 2 1

.5960 2 5

.4699

29

.3666

33

.2857

37

.22 3 1

41

28

.9841

12

. 9 1 43

16

.7939

. 6 5 8 6 24

.5301

28

.41 96

32

.3 304

36

.2 604

40 39

20

29

.9921

11

.9429

15

.8424

19

.71 52

.5874 2 7

.4725

31

.3 766

35

.2995

30

1 .0000

10

.9667

14

.8848

18

.7697 2 2

.6448

26

.5275

30

.4256

34

.341 8

38

31

.98 1 0

13

. 9 1 82

17

. 8 1 62

21

.6979

25

.5804

29

.4747

33

.3852

37

32

.9905

12

.9455

16

.8586

20

.7483

24

.6334

28

.5253

32

.4308

36

33

.9952

11

.9636

15

.8929

19

.7930 23

.6823

27

.5744

31

.4764

35

34

1 .0000

10

.9788

14

.9232

18

.8350 22

.7303

26

.6234

30

.5236

34

n=7

23

Cu

n= 1 0

Cu

15

.0040

40

.0022

45

. 00 1 3

50

.0008

55

.0005

60

.0003

65

16

.0079

39

.0043

44

.0025

49

.00 1 6

54

.00 1 0

59

.0007

64

17

.01 59

38

.0087

43

. 00 5 1

48

.003 1

53

.0020

58

.001 3

63

18

.0278

37

.01 52

42

.0088

47

.0054

52

.0035

57

.0023

62

19

.0476

36

41

.01 52

46

.0093

51

.0060

56

.0040

61

20

.0754

35

.0260 . 04 1 1

40

.0240

45

.01 48

50

.0095

55

.0063

60

21

.1 1 1 1

34

.0628

39

.0366

44

.0225

49

.01 45

54

.0097

59

22

. 1 548

33

.0887

38

.0530

43

.0326

48

.02 1 0

53

.01 40

58

23

. 2 1 03

32

. 1 234

37

.0745

42

.0466

47

.0300

52

.0200

57

24

.2738

31

. 1 645

36

.1010

41

.0637

46

.04 1 5

51

.0276

56

25

.3452

30

. 2 1 43

35

.1 3 3 8

40

.0855

45

.0559

50

.0376

55

26

.4206

29

.2684

34

.1 71 7

39

.1 1 1 1

44

.0734

49

.0496

27

.5000

28

.33 1 2

33

. 2 1 59

38

. 1 422

43

.0949

48

.0646

54 53

28

.5 794

27

.3961

32

.2652

37

. 1 772

42

.1 1 99

47

.0823

52

29

.6548

26

.4654

31

. 3 1 94

36

. 2 1 76

41

.1 489

46

. 1 032

51

30

.7262

25

.5346

30

. 3 775

35

.261 8

40

.1 8 1 8

45

. 1 2 72

50

31

.7897

24

.6039

29

.43 8 1

34

. 3 1 08

39

.2 1 88

44

. 1 548

49

32

.8452

23

.6688

28

.5000

33

.3621

38

.2592

43

. 1 855

48

33

.8889

22

. 73 1 6

27

.561 9

32

.41 65

37

.3032

42

.2 1 98

47

34

.9246

21

.7857

26

.6225

31

.4 7 1 6

36

.3497

41

.2567

46

35

.9524

20

.8355

25

.6806

30

.5284

35

.3986

40

.2970

45

36

.9722

.8766

24

.7348

29

.5835

34

.4491

39

.3393

44

37

.9841

19 18

.91 1 3

23

.7841

28

.6379

33

.5000

38

.3839

43

38

.99 2 1

17

.9372

22

.8283

27

.6892

32

.5509

37

.4296

42

39 40

.9960

16

.9589

21

.8662

26

.7382

31

.60 1 4

36

.4765

41

1 .0000

15

.9740

20

.8990

25

.7824

30

.6503

35

.5235

40

Appendix XVI

,I, I

m=6

21

.00 1 1

57

.0006

63

.0003

69

.0002

75

.0001

81

22

.0022

56

. 00 1 2

62

.0007

68

.0004

74

.0002

80

23

.0043

55

.0023

61

.001 3

67

.0008

73

.0005

79

24

.0076

54

.0041

60

.0023

66

.001 4

25

.01 30

53

.0070

59

.0040

65

.0024

72 71

.0009 .001 5

26

.0206

52

.01 1 1

.0063

64

.0038

70

.0024

27

.0325

51

.0 1 75

58 57

77 76

.01 00

63

.0060

69

.0037

75

28

.0465

50

.0256

56

.01 4 7

62

68

.0055

74

29

.0660

49

.0367

55

.02 1 3

61

.0088 .01 2 8

67

.0080

73

30

.0898

48

.0507

54

.0296

60

.01 80

66

.01 1 2

72

78

31

. 1 201

47

.0688

53

.0406

59

.0248

65

.01 5 6

71

32

. 1 548

46

.0903

52

.0539

58

.0332

64

.02 1 0

70

33

.1 970

45

.1 1 7 1

51

.0709

57

.0440

63

.0280

69

34

.2424

44

. 1 474

50

.0906

56

.0567

62

.0363

68

35

.2944

43

. 1 830

49

. 1 1 42

55

.0723

61

.0467

67

36

.3496

42

.2226

48

.1412

54

.0905

60

.0589

66

37

.4091

41

.2669

47

. 1 725

53

.1 1 1 9

59

.0736

65

38

.4686

40

. 3 1 41

46

.2068

. 1 361

58

.0903

64 63

39

.53 1 4

39

. 3 654

45

.2454

52 51

. 1 638

57

. 1 099

40

.5909

38

.41 78

44

.2864

50

. 1 942

56

.1 3 1 7

62

41

.6504

37

.4726

43

.3 3 1 0

49

.2280

55

.1 566

61 60

42

.7056

36

.5274

42

.3773

48

.2643

54

. 1 838

43

.7576

35

.5822

41

.4259

47

.3035

53

.2 1 39

59

44

.8030

34

.6346

40

.4749

46

.3445

52

.2461

58

45

.8452

33

.6859

39

.5251

45

.3878

51

.2 8 1 1

46

.8799

32

.7331

38

. 5 74 1

44

.4320

50

.3 1 7 7

57 56

47

.9 1 02

31

.7774

37

.6227

43

.4773

49

. 3 564

55

48

.9340

30

. 8 1 70

36

.6690

42

.5227

48

.3962

54

49

.9535

29

.8526

35

. 7 1 36

.5680

47

.4374

53

50

.9675

28

.8829

34

.7546

41 40

.61 22

46

.4789

52

51

.9794

27

.9097

33

.7932

39

.6555

45

.52 1 1

51

m=8

m=7 n :;:: 8

n=lO

n=9

28

.0003

77

.0002

84

.0001

91

.0001

98

36

.0001

1 00

.0000

1 08

.0000

1 16

29

.0006

76

.0003

83

.0002 9 0

.0001

97

37

.0002

99

.0001

1 07

.0000

115

30

.001 2

75

.0006

82

.0003

89

.0002

96

38

.0003

98

.0002

1 06

.0001

114

31

.0020 74

.001 1

81

.0006 88

.0004

95

39

.0005

97

.0003

1 05

.0002

113

32

.0035

73

.00 1 9

80

.00 1 0 8 7

.0006

94

40

.0009

96

.0005

1 04

.0003

112

33

.0055

72

.0030

79

.00 1 7

86

.001 0

93

41

.001 5

95

.0008

1 03

.0004

111

34

.0087

71

.0047

78

.0026 85

.001 5

92

42

.0023

94

. 001 2

1 02

.0007

110

35

.01 3 1

70

.0070

77

.0039 84

.0023

91

43

.0035

93

. 001 9

1 01

.001 0

1 09

36 37

.01 89

69

.0 1 03

76

.0058 83

.0034

90

44

.0052

92

.0028

1 00

.001 5

1 08

.0265

68

. 0 1 45

75

.0082

82

.0048

89

45

.0074

91

.0039

99

.0022

1 07

38

.0364

67

.0200 74

.01 1 5

81

.0068

88

46

.01 03

90

.0056

98

.0031

1 06

39

.0487

66

.0270

73

.01 5 6 80

.0093

87

47

. 0 1 41

89

.0076

97

.0043

1 05

40

.0641

65

.0361

72

.0209

79

.01 25

86

48

. 0 1 90

88

. 0 1 03

96

.0658

1 04

41

.0825

64

.0469

71

.0274

78

. 0 1 65

85

49

.0249

87

. 0 1 37

95

.0078

1 03

42

. 1 043

63

.0603

70

.0356

77

.02 1 5

84

50

.0325

86

. 0 1 80

94

.01 03

1 02

43

. 1 297

62

.0760

69

.0454 76

.0277

83

51

.041 5

85

.0232

93

. 0 1 33

1 01

44

. 1 588

61

.0946

68

.05 7 1

75

.03 5 1

82

52

.0524

84

.0296

92

.01 7 1

1 00

45

.1914

60

. 1 1 59

67

.0708

74

.0439

81

53

.0652

83

.0372

91

.02 1 7

99

46

.2279

59

. 1 405

66

.0869

73

.0544

80

54

.0803

82

.0464

90

.02 73

98

47

.2675

58

. 1 678

65

. 1 052

72

.0665

79

55

.0974

81

.0570

89

.0338

97

48

. 3 1 00

57

. 1 984

64

. 1 261

71

.0806

78

56

. 1 1 72

80

.0694

88

.04 1 6

96

49

.3552

56

. 23 1 7

63

. 1 496

70

.0966

77

57

. 1 393

79

.0836

87

.0506

95

50

.4024

55

.2679

62

. 1 755

69

. 1 1 48

76

58

. 1 64 1

78

.0998

86

.06 1 0

94

51

.4508 5 4

.3063

61

.2039

68

. 1 349

75

59

.191 1

77

. 1 1 79

85

.0729

93

52

. 5000 5 3

.3472

60

.2 349

67

. 1 5 74

74

60

.2209

76

. 1 383

84

.0864

92

53

.5492

52

. 3894

59

.2680 66

.1819

73

61

.2527

75

. 1 606

83

.1015

91

54

.5976

51

.43 3 3

58

.3032

65

.2087

72

62

.2869

74

. 1 852

82

. 1 1 85

90

55

.6448

50

.4775

57

.3403

64

. 2 3 74

71

63

.3227

73

.21 1 7

81

. 1 371

89

56

.6900 49

.5225

56

. 3 788 63

.2681

70

64

.3605

72

.2404

80

. 1 577

88

57

. 73 2 5

48

. 5667

55

. 4 1 85

62

.3004

69

65

.3992

71

.2707

79

. 1 800

87

58

.7721

47

. 6 1 06

54

.45 9 1

61

.3 345

68

66

.4392

70

.3029

78

.204 1

86

59

.8086 4 6

.6528

53

.5000 60

.3698

67

67

.4796

69

.3365

77

.2299

85

60

.841 2

45

.69 3 7

52

.5409 59

.4063

66

68

.5204

68

.371 5

76

.2574

84 83

61

.8703 44

.7321

51

.581 5

58

.4434

65

69

.5608

67

.4074

75

.2863

62

.8957 43

.7683

50

.62 1 2

57

.481 1

64

70

.6008

66

.4442

74

. 3 1 67

82

63

.9 1 75

. 80 1 6

49

.6597

56

.5 1 89

63

71

.6395

65

.48 1 3

73

.3482

81

42

72

.6773

64

. 5 1 87

72

.3809

80

73

.71 31

63

.5558

71

. 4 1 43

79

74

.7473

62

.5926

70

.4484

78

75

.7791

61

.6285

69

.4827

77

76

.8089

60

.6635

68

. 5 1 73

76

Apli>enldix XVI

m=' n=9

n== 10

Cu

n=9 (cont.)

n",, 10

cu

(COOt.)

45

.0000

1 26

.0000

1 35

68

.0680

1 03

.0394

1 12

46

.0000

1 25

.0000

1 34

69

.0807

1 02

.0474

47

.0001

1 24

.0000

1 33

70

.095 1

101

.0564

111 1 10

48

.0001

1 23

.0001

1 32

71

.1 1 1 2

1 00

.0667

1 09

49

.0002

1 22

.0001

1 31

72

. 1 290

99

1 03

50

.0004

121

.0002

1 30

73

. 1 48 7

98

.0782 .09 1 2

51

.0006

1 20

1 29

74

. 1 701

97

. 1 05 5

52

.0009

119

.0003 .0005

1 28

75

.1 933

96

.1214

1 06 1 05

1 07

53

.00 1 4

118

.0007

1 27

76

.2 1 8 1

95

. 1 388

1 04

54

.0020

117

.001 1

1 26

77

.2447

94

.1 577

1 03

55

.0028

116

.00 1 5

1 25

78

.2729

93

. 1 781

1 02

56

.0039

115

.002 1

1 24

79

.3024

92

.200 1

1 01

57

.0053

114

.0028

1 23

80

.3332

91

.2235

1 00

58

.0071

113

.0038

1 22

81

.3652

90

.2483

99

59

.0094

112

.00 5 1

121

82

.3981

89

. 2 745

98

60

.0 1 2 2

111

.0066

1 20

83

.43 1 7

88

.301 9

97

61

.01 5 7

110

.0086

119

84

.4657

87

.3304

62

.0200

1 09

.01 1 0

1 18

85

.5000

86

.3598

96 95

63

.0252

1 08

.01 40

1 17

86

.5343

85

.3901

94

64

.03 1 3

1 07

.01 75

116

87

.5683

84

.42 1 1

93

65

.0385

1 06

.02 1 7

1 15

88

.60 1 9

.4524

66

.0470

1 05

.0267

1 14

89

.6348

83 82

.4841

92 91

67

.0567

1 04

.0326

113

90

.6668

81

.6668

90

m==10 n",lO

Cu

81

.0376

1 29

82

.0446

1 28

83

.0526

1 27

1 52

84

.06 1 5

1 26

.0001

151

85

.07 1 6

1 25

60

.0001

1 50

86

.082 7

1 24

61

.0002

1 49

87

.0952

1 23

62

.0002

1 48

88

. 1 088

1 22

63

.0004

1 47

89

.1 237

121

64

.0005

1 45

90

. 1 399

1 20

65

1 45

91

. 1 575

1 19

66

.0008 .001 0

1 44

92

. 1 763

118

67

.00 1 4

1 43

93

. 1 965

1 17

68

.00 1 9

1 42

94

. 2 1 79

1 16

69

.0026

141

95

.2406

1 15

70

.0034

1 40

96

.2644

1 14

71

.0045

1 39

97

.2894

113

72

.0057

1 38

98

.3 1 5 3

1 12

73

.0073

1 37

99

.3421

111

74

1 36

1 00

.3697

1 10

75

.0093 .01 1 6

1 35

1 01

1 09

76

.0 1 44

1 34

1 02

.3980 .4267

77

.01 77

1 33

1 03

.4559

1 07

78

.02 1 6

1 32

1 04

.4853

1 06

79

.0262

131

1 05

.5 1 47

1 05

80

.03 1 5

1 30

n:;10

Cu

55

.0000

1 55

56

.0000

1 54

57

.0000

1 53

58

.0000

59

(cant.)

1 08

4.:))

r Appendix " ""

XVII c , , " ,, " , " " , " "

", " " ,

'" ',', ,,

"

�' '' '�

'' <J.) ....J

2

a Q)

o Fig. 1 0

�jU�----��---

Assessed

Acceptable

The relationship between assessed risk, acceptable level of risk, the appropriate level of protection, and Sanitary and Phytosanitary

measures, for import of a specific commodity. (From Pharo, 2004.)

unpublished sources, and ranged from verifiable objective data to guesses. Thus, the number of animals imported under the quarantine system was obtained from official government records, whereas the number of animals expected to be imported if control was changed to one based on vaccination without quaran­ tine was a guess. Taking account of the variability and the uncertainty in the risk assessment, modelled using the various triangular distributions, the results concluded that there would be very little increase in the risk of rabies being imported into Great Britain if quarantining of animals from the European Union was abandoned and was replaced by a control strategy based on animal identification, vaccination and serological testing. This risk assessment therefore provided evidence in favour of a policy change to the latter strategy.

What level of risk is acceptable? The results of risk assessments need to be meaning­ fully interpreted so that appropriate risk management strategies can be adopted. The latter implicitly depend on the level of risk that is deemed to be acceptable (more strictly, on the options that entail a specific level of risk). This is a major concern in the context of the international trade in animals and animal prod­ ucts, where epidemic diseases and zoonoses may be imported. The Sanitary and Phytosanitary (SPS) Agreement of the WTO (OlE, 1997) requires that each participating country specifies its appropriate level of protection or acceptable level of risk. Figure 10 depicts a conceptual framework for the acceptable level of risk in relation to SPS control mea­ sures (e.g., quarantine) for importation of animals or

their products. Noting that risk has two components­ the probability of an event's occurrence and the sever­ ity (impact) of its consequences - the risk units are best considered in economic terms, because probabil­ ity is dimensionless, but consequences of introduction of disease have an economic impact (e.g., in disease losses and control, and loss of trade). This framework assumes that risk can be estimated objectively and accurately (ideally quantitatively), and that each coun­ try can set its level of acceptable risk. Thus, if the cur­ rent level of disease risk is 10, and the acceptable level of disease risk is 4, Measure 4 comprises the optimum combination of control measures. Measures 1-3 are inadequate, whereas Measure 5 is excessive19. Note that the acceptable level of risk and the appropriate level of protection are subtly different. The former is about acceptable economic losses to the national economy, whereas the latter is the level of economic losses avoided by the application of safeguards. However, noting the steps in risk assessment (see above: 'Components of risk analysis'), Pharo (2004) concludes that neither the scientific assessment of risk nor the risk-reduction effect of safeguards can be estimated as objectively as the SPS framework antic­ ipates. Release assessment in import risk assessment, for example, usually computes the probability of an imported animal being affected. However, this is based on the prevalence of infection in the exporting countries, many of which may have poor surveil­ lance systems and consequently poor prevalence data. Additionally, predicting the volume of trade (and therefore the number of imported animals) may be 19 If the risk units are expressed in monetary terms, there is thus a clear similarity between risk analysis and cost-benefit analysis (see Chapter 20 and Lave, 1996).

Appendix XXIV

difficult. If the imported commodity is an animal prod­ uct rather than a live animal (e.g., hatching eggs), the exposure pathway and infectious dose may be com­ plex and difficult to ascertain. If bulk commodities such as animal feeds are being imported, the choice of trade-unit size is somewhat arbitrary and microbial inactivation curves for various stages of the produc­ tion process are usually unknown. Diagnostic tests may be used to estimate the risk of importing affected test-negative animals, but there is often a lack of preci­ sion attached to the estimate because of the attendant lack of precision associated with the relevant parame­ ter (sensitivity), reflected in the width of its confidence interval (see Chapter 17). The consequences of exposure may also be refrac­ tory to objective assessment, with the opinions of experts being no more than personal belief. Infections pose an additional problem when their zoonotic impact is uncertain (e.g., highly pathogenic avian influenza virus). Additionally, unknown factors may also confound prediction. For example, the magnitude of the foot-and-mouth disease epidemic in the UK in 2001 (Figure 4.1 ) was determined by widespread dis­ semination of the virus by subclinically infected sheep (Mansley et ai., 2003) - a feature that was impossible to predict before the epidemic. Moreover, economic impact is partly related to control policy, which may be modified unpredictably in the future. Thus, the traditional foot-and-mouth control procedures were modified in the UK in 2001 by a more aggressive culling policy only after the epidemic had begun, thereby incurring higher control costs than could be predicted (Kitching et ai., 2006)20. Market reaction also can be unpredictably extreme. A single case of bovine spongiform encephalopathy in Canada in 2003, for instance, resulted in cessation of exports, and the country's $7 billion per year cattle and beef industry suffered a 34% drop in value (Carter and Hule, 2004). Since Canada is a major exporter of beef to the US, the export ban also resulted in a substantial increase in the price of US beef (Hanrahan and Becker, 2004). In summary, there usually is a lack of quantitative data with which to assess precisely the probability and magnitude (severity) of the consequences of importa­ tion. Moreover, if acceptable risk is viewed monetarily, then it may be framed in terms of the level of economic losses that can be tolerated to optimize the benefits of international trade - but the perception and reaction of the public and politicians cannot be discounted. The

20 The full impact involved more than the cost of control. It also included losses to the leisure and tourist industry (Fawcett and Head, 2001a,b; Thompson et a/., 2002; Blake et aI., 2003), as well as psychological damage to individuals.

)()

determination o f acceptable levels o f risk i n import risk assessment is therefore complex, in common with acceptable risk in the wider context, which involves economic (Starr, 1969) and psychological (Fischhoff et ai., 1978) factors. This indicates that the final decision on the acceptable level of risk usually involves social, economic and political, rather than scientific, consid­ erations (Slovic, 2000; Sjoberg, 2001). Veterinarians need to be aware of the limitations of risk analysis, which may pose more questions than it answers. (Indeed, an important function of risk analy­ sis it to identify what is not known.) The results of risk analyses may be founded on invalid assumptions, and frequently there may be uncertainty attached to the hazards and processes for which risk is being assessed (Ballard, 1992). Moreover, it is often possible only to produce a relative ranking of the likelihood of events, rather than accurate assessments (Ansell, 1992), noting that numerical outputs are likely to be crude (Schneiderman, 1980). Nevertheless, risk analy­ sis has a valuable role to play in identifying and man­ aging risk in many areas of veterinary medicine, rather than attempting to prosecute a 'zero-risk' strategy, which is not amenable to changes in the light of new knowledge, economic circumstances, and political requirements.

Further Reading Ahl, A.S., Acree, J.A., Gibson, p.s., McDowell, RM., Miller, L. and McElvaine, M. (1993) Standardization of nomen­ clature for animal health risk analysis. Revue Scientifique et Technique, Office International des Epizooties, 12, 1045-1 053 Amass, S.F. (2005) Biosecurity: reducing the spread. The Pig Journal, 56, 78-87. (Guidelines for qualitative risk assessment

offarm biosecurity to prevent within-farm spread of infections) Amass, S.F. (2005) Biosecurity: stopping the bugs from getting in. The Pig Journal, 55, 104-1 14. (Guidelines for qualitative risk

assessment offarm biosecurity to prevent entry of pathogens) Codex Alimentarius Commission (1999) Principles and

Guidelines for the Conduct of Microbial Risk Assessment. CAC/GL-30. Food and Agriculture Organization of the United Nations, Rome Covello, V.T. and Merkhofer, M.W. (1993) Risk Assessment

Methods: Approaches for Assessing Health and Environmental Risks. Plenum Press, New York and London Covello, V.T., McCallum, D.B. and Pavlova, M.T. (Eds) (1989)

Effective Risk Communication: the Role and Responsibility of Government and Nongovernment Organizations. Plenum Press, New York ICMSF (1988) HACCP in Microbiological Safety and Quality.

Micro-organisms in Food, 4, Application of the hazard analysis critical control point (HACCP) system to ensure microbi­ ological safety and quality. The International Commission on Microbiological Specifications for Foods (ICMSF) of the International Union of Microbiological Societies. Blackwell Scientific Publications, Oxford

S())

Appendices

ICMSF (1998) Potential application of risk assessment techniques to microbiological issues related to inter­ national trade in food and food products. International Commission on Microbiological Specifications for Foods (ICMSF) Working Group on Microbial Risk Assessment. Journal of Food Protection, 61, 1 075-1086 Kindred, T.P. (1996) Risk assessment and its role in the safety of foods of animal origin. Journal of the American Veterinary Medical Association, 209, 2055-2056 MacDiarmid, S.C and Pharo, H-J. (2003) Risk analysis: assessment, management and communication. Revue

North, D.W. (1995) Limitations, definitions, principles and methods of risk analysis. Revue Scientifique et Technique, Office International des Epizooties, 14, 913-923 OIE (2006) Risk analysis. In: Terrestrial Animal Health Code, 15th edn. Section 1 .3. Office International des Epizooties, Paris O'Riordan, T., Cameron, J. and Jordan, A. (Eds) (2001) Reinterpreting the Precautionary Principle. Cameron May, London. ( A discussion of the current evolution of the pre­

Scientifique et Technique, Office International des Epizooties,

Pfeiffer, D.U. (2006) Communicating risk and uncertainty in relation to development and implementation of disease control policies. Veterinary Microbiology, 112, 259-264 Roberts, T., Ahl, A. and McDowell, R. (1995) Risk assessment for foodborne microbial hazards. In: Tracking Foodborne

22, 397-408 Moos, M. (1995) Models of risk assessments for biolog­ icals or related products in the European Union. Revue

Scientifique et Technique, Office International des Epizooties, 14, 1 009-1 020 Morley, R.S. (Coordinator) (1993) Risk analysis, animal health and trade. Revue Scientifique et Technique, Office International des Epizooties, 12, 1001-1362 Murray, N. (2002) Import Risk Analysis: Animals and Animal Products. Ministry of Agriculture and Forestry, Wellington Murray, N., MacDiarmid, S.C, Wooldridge, M., Gummow, B., Morley, R.S., Weber, S.E., Giovannini, A. and Wilson, D. (2004) Handbook on Import Risk Analysis for Animals &

Animal Products, Volume I. Introduction and Qualitative Risk Analysis. Office International des Epizooties, Paris Murray, N., MacDiarmid, S.C, Wooldridge, M., Gummow, B., Morley, R.S., Weber, S.E., Giovannini, A. and Wilson, D. (2004) Handbook on Import Risk Analysis for Animals &

Animal Products, Volume II. Quantitative Risk Analysis. Office International des Epizooties, Paris

cautionary principle in science, public affairs, the public under­ standing ofscience, and international law and trade)

Pathogens from Farm to Table: Data Needs to Evaluate Control Options. Conference Proceedings, January 9-10 1995, pp. 95 -115. United States Department of Agriculture Miscellaneous Publication Number 1532 Vose, D.J. (1997) Risk analysis in relation to the impor­ tation and exportation of animal products. Revue

Scientifique et Technique, Office International des Epizooties, 16, 1 7-29 Vose, D. (2000) Risk Analysis: A Quantitative Guide, 2nd edn. John Wiley, Chichester Wooldridge, M., Clifton-Hadley, R. and Richards, M. (1996)

'I don't want to be told what to do by a mathematical formula' ­ overcoming adverse perceptions of risk analysis. In: Society for Veterinary Epidemiology and Preventive Medicine, Proceedings, Glasgow, 27-29 March 1996. Eds Thrusfield, M.V. and Goodall, E.A., pp. 36-46

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