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PERFORMANCE OF BOVINE TUBERCULIN SKIN TESTS AND
FACTORS AFFECTING THE PROPORTION OF FALSE POSITIVE
SKIN TEST RESULTS IN MICHIGAN

presented by
Bo Norby

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PERFORMANCE OF BOVINE TUBERCULIN SKIN TESTS AND
FACTORS AFFECTING THE PROPORTION OF FALSE POSITIVE
SKIN TEST RESULTS IN MICHIGAN

By

Bo Norby

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Large Animal Clinical Sciences
(Epidemiology)

2003

ABSTRACT

PERFORMANCE OF BOVINE TUBERCULIN SKIN TESTS AND
FACTORS AFFECTING THE PROPORTION OF FALSE POSITIVE
SKIN TEST RESULTS IN MICHIGAN
By

Bo Norby

Dairy and beef cattle (n=494) from seven Michigan farms located in the
northeastern part of the lower peninsula in Michigan were used to estimate the sensitivity
(Se) of the caudal fold tuberculin test (CFT), the CFT and comparative cervical test used
in serial interpretation (CFTCCTSER), and gross necropsy using a ‘gold standard’
approach. Using all seven herds, the sensitivities of the CFT, the CFTCCTSER , and gross
necropsy were 93.0% (95% CI: 80.9% to 98.5%), 88.4% (95% CI: 74.9% to 96.1%), and
86.1% (95% CI: 72.1% to 94.7%), respectively. The Se of the two skin tests was slightly
higher when two or more gross lesions were present, and the Se Of gross necropsy was
significantly higher (P = 0.049). In addition, four two-population-two test Simulation-
based Bayesian models allowing for correlation between the two tests were used to
estimated Se and specificity (Sp) of the CFT and CFTCCTSER, assuming that a gold
standard was not available. Sensitivity and Sp of both the CFT and CFTCCTSER were
estimated with results of mycobacterial culture (CULT). There were no significant
correlations between CFT and CULT, but a significant negative correlation (0.218 [PCI:
0.005 to 0.731]) between CFTCCTSER and CULT. The estimates for Se and Sp of the
CFT, CFI'CCTSER, and CULT were 85.4% (PCI: 56.3 to 97.5), 75.8% (PCI: 47.5% to

93.0%), and 62.3% (PCI: 40.1% to 89.9%), respectively. Herd-level sensitivity (HSe)

and specificity (HSp) and predictive values for l) CFl‘CCT 513R, 2) the overall sensitivity
and specificity of serial use of CFI‘CCTSER, histologic exam, CULT and PCR, 3) where
specificity of 2) was assumed to be 100%, and 4) which was as 3) but increasing
sensitivity to 90%. An empirical distribution of number of herds and herd sizes for the
northeastern lower peninsula was used for these simulations. Point estimates of HSe and
HSp for the four scenarios were 75.0% and 94.0%, 71.2% and 100%, 78.3%, and 100%,
and 83.3% and 100%. All the HSe estimates ranged from 0 to 100% and between 0.023
to 100% for HSp. Herd-level predictive values positive and negative were 14.3% and
99.6%, 100 and 99.5%, 100 and 99.6%, and 100 and 98.9% for the four scenarios,
respectively. Increasing the sensitivity of scenario 4 to 90% only increased the HSe from
78.3% to 83.3%. Results from 4,989 bovine tuberculosis (bTb) negative herds tested
with the CFT between 1996 and 2001 were used to investigate the association between
the proportion of false positive (PFP) results on the CFI‘ by herd and herd, geographic,
and ecologic factors using multiple negative binomial regression. The final multiple
negative binomial model contained herd type (beef vs. dairy), agricultural region, and the
testing veterinarian as a random effect. The number of cases of PFP per 100 tested
animals was 2.25 for beef and 4.38 for dairy cattle. Cattle located in agricultural regions
1, 2, 3, 5, and 6 had significantly higher PFP as compared to region 9. Using 3,301
records with spatial coordinates, one primary and 32 secondary clusters of herds with
high PFP were identified. Additionally, PFP was not significant associated with the

elevation Of the herd and whether or not a wetland area was located close to the farm.

This work is dedicated to the memory of my father

who passed away at a much too early age.

iv

ACKNOWLEDGEMENTS

It would like to acknowledge the people whose contributions have made this work
possible:

First and foremost, I would like to thank my major professor, Dr. Paul Bartlett,
who has been an outstanding mentor and who gave me the freedom to pursue work
relating to my special interests and to whom I will always be in great debt.

Dr. John Kaneene, whose door was always open, and who has made me
appreciate epidemiology even more.

The other members of my committee: Drs. Daniel Grooms, Fitzgerald, and
Templeman who, beyond their duty, made an important contribution to my education.

Michigan Department of Agriculture (MDA) and United States Department of
Agriculture (USDA) for providing the data for this project. In particular, I would like to
thank Drs. Larry Granger and Colleen Bruning-Fann who helped me gather data, allowed
me free access to test records in their possession, and helped me understand all aspects of
the bovine tuberculosis eradication effort in Michigan.

My fellow graduate students at the Population Medicine Center who tolerated my
questions and who always had time to listen. I wish you the very best in your future
endeavors.

Also a special thank to Dr. Tim Hanson whose help was instrumental in
development of Bayesian models, and to my external examiner Dr. Ian Gardner, who first

sparked my interest the epidemiology of diagnostic tests.

My mother Inger, my brother Steen, and my wife Lauren without whose
unconditional support, this endeavor would not have been possible.

Finally for financial support of this research, a special thanks to the USDA, the
College of Veterinary Medicine, and Department of Large Animal Clinical Sciences at

MSU.

vi

TABLE OF CONTENTS

LIST OF TABLES xii
LIST OF FIGURES xiv
LIST OF ABBREVIATIONS xv

CHAPTER 1: Introduction, Rationale, Problem Statement,
General Methods, and Overview.

Introduction 1
Rationale 2
Problem Statement 4
Study objectives 5
General methods 6
Overview 9
References 10

CHAPTER 2: Literature Review.

Tuberculins 12
Tuberculin skin tests 13
Sensitivity and specificity of the CFT and CCT in the United States 15
Factors affecting the sensitivity and

specificity of the tuberculin skin tests 19
Herd-level estimates of sensitivity and specificity 21

References 23

vii

CHAPTER 3: The sensitivity of gross necropsy, caudal fold and comparative
cervical tests for the diagnosis of bovine tuberculosis.

Abstract
Introduction
Materials and Methods
Summary of state-wide testing procedure
CFT
CCT
Data selection
Gross necropsy
Histopathology
Mycobacterial culture and identification
Polymerase chain reaction
Statistical analysis
Results
Discussion

References

viii

26

28

30

30

30

31

31

32

32

33

33

34

34

4o

45

CHAPTER 4: Estimation of sensitivity and specificity
of bovine tuberculosis skin tests in Michigan

when a perfect reference test is not available.

Abstract

Introduction

Materials and Methods
Animals
Diagnostic tests and testing procedure
Latent-class models
Prior elicitation
Sensitivity analysis

Results

Discussion

References

Appendix A

ix

48

50

53

53

54

55

57

59

60

65

70

74

CHAPTER 5: Herd-level sensitivity, specificity, and predictive values
of bovine tuberculosis skin tests in Michigan.
Abstract
Introduction
Materials and Methods
Diagnostic tests and testing procedure
Analyses
Input distributions for Se, Sp, TP, and HTP
Herd size distributions and sampling technique
Results
Discussion
The ‘HerdTest’ model

Comments and recommendations to the eradication program
In Michigan

References

83

85

87

87

89

90

92

95

98

101

103

105

CHAPTER 6: Herd and spatial factors affecting the proportion of false positive
results on the caudal fold tuberculin test in Michigan cattle

Abstract 107
Introduction 109
Materials and Methods 110
Diagnostic tests and testing procedure 110

Statistical analysis 1 12

Spatial analysis 115

Ecological associations 117

Results 117
Descriptive statistics 117

Negative binomial regression model 122

Spatial analysis 125

Ecological associations 127

Discussion 128
References 1 33
SUMMARY 136
CONCLUSIONS 139
APPENDD( B 145
BIBLIOGRAPHY 170

xi

LIST OF TABLES

TABLE

Table 2-1. Calculation of sensitivity and specificity when a gold standard
is available.

Table 3-1. Relationship between mycobacterial isolates from cattle and
skin tests, gross necropsy, and the reference test (positive on either
mycobacterial isolation or PCR).

Table 3-2. Apparent bTb prevalence in seven herds using the caudal fold,
comparative cervical and reference tests (positive on culture and/or PCR).

Table 3-3. Sensitivity of CFI‘, CFTCCTSER, and gross necropsy using
bacteriologic culture and PCR as the reference test.

Table 3-4. Sensitivity Of CFT, CFI‘CCTSBR, and gross necropsy in
animals with lesions in one, or two or more lymph nodes.

Table 4-1. Apparent prevalence (APP; %) in old and young
subpopulations based upon the caudal fold tuberculin test (CFT) and
Mycobacterial culture (CULT).

Table 4-2. Testing Scenario #1: 2 x 2 contingency table showing the
observed counts for the caudal fold tuberculin test (CFT) and
Mycobacterial culture (CULT) in populations 1 and 2.

Table 4-3. Testing Scenario #2: 2 x 2 contingency table showing the
observed counts for the caudal fold and comparative cervical tuberculin

tests used in serial interpretation (CFTCCTSER) and Mycobacterial culture
(CULT) in populations 1 and 2.

Table 4-4. Prevalences (7:1,7P2),sensitivities (Se) and specificities (Sp) for
the caudal fold tuberculin test (CFT) and mycobacterial culture (CULT).
Point estimates for all parameters are presented as the median of the
posterior densities and their respective 95% PCI.

Table 4-5. Prevalences (7:1,7t2),sensitivities (Se) and specificities (Sp) for
the caudal fold tuberculin test and comparative cervical tuberculin tests
used in serial interpretation (CFTCCT 313R) and mycobacterial culture
(CULT) for all four models. Point estimates for all parameters are

presented as the median of the posterior densities and their respective 95%
PCI.

xii

PAGE

16

37

38

39

4O

59

60

60

63

TABLE

Table 4-6. Two 2 X 2 contingency tables showing responses of two binary
diagnostic tests.

Table 4-7. Four 2 x 2 contingency tables showing responses of two binary
tests classified by true disease status.

Table 4-8. Classification of probabilities as explained by sensitivities and
specificities.

Table 5-1. Input variables for sensitivity (Se) Specificity (Sp), and within
herd prevalence (T P) and herd prevalence (HTP) used for the shareware
program ‘HerdTest’.(Jordan and McEwen, 1998).

Table 5-2. Distributions of herds in 10 counties and all of Michigan in
1997.

Table 5-3. Herd-level sensitivity (HSe) and specificity (HSp) for four
different scenarios with individual animal sensitivity (Se) and Specificin
(Sp) used in 10 counties in the northern part of the lower peninsula in
Michigan.

Table 5-4. Herd-level predictive value positive (HPVP) and negative
(HPVN) for four different scenarios with individual animal sensitivity (Se)

and Specificity (Sp) used in 10 counties in the northern part of the lower
peninsula in Michigan.

Table 5-5. Spearman’s rank correlation between herd-level input variables
and herd-level output variables for Scenario 3. p-values are shown in
brackets (Ho: rs=0).

Table 6-1. Proportion of false positive (PFP) on caudal fold tuberculin test
(CFT) in Michigan, by herd type and agricultural region.

Table 6—2. Herd size by herd type and agricultural region.

Table 6—3. Univariate analysis of factors associated with the proportion of
false positive (PFP) on caudal fold tuberculin test (CFT) in Michigan.

Table 6-4. Multivariable analysis of factors associated with number of
CFT suspect results.

Table 6-5. Univariate analysis of ecological factors associated with the

proportion of false positive (PFP) on caudal fold tuberculin test (CFT) in
Michigan.

xiii

PAGE

74

75

76/77

93

94

95

96

96

119

120

124

125

127

LIST OF FIGURES

FIGURE

Figure 5-1. Geographical location of the lO—county-area in northern
Michigan.

Figure 5-2. Scenario 2 - Medians for herd level sensitivity (HSe),
specificity (HSp), predictive value positive (HPVP), and negative (HPVN)
for different fixed herd sizes using input values from scenario 2.

Figure 5-3. Scenario 3 - Medians for herd level sensitivity (HSe),
specificity (HSP), predictive value positive (HPVP), and negative (HPVN)
for different fixed herd sizes in scenario 3.

Figure 6-1. Observed and expected frequencies of false positive test results
per farm. Neg-Bin: Negative Binomial.

Figure 6-2. Nine agricultural regions in Michigan.

Figure 6-3. Distribution of proportion of CFT false positive (PFP) by herd
size.

Figure 6-4. Distribution of the mean proportion of CFT false positive
test results (PFP) by veterinarian.

Figure 6-5. Spatial distribution of herds tested for bovine tuberculosis with
the caudal fold tuberculin test in Michigan, including Spatial clusters of

herds with a high proportion of CFI‘ false positive test results. 0 Individual
herds. 0 Spatial clusters.

xiv

PAGE

90

97

98

113

114

121

122

126

ABBREVIATION
APHIS

bTb

CCT

CFT
CFTCCTSER
CW P

CW P-PG
EM

GGE
HCSM
HPVN
HPVP

HSe

HSp

M. bovis
MDA

MLE

NR

OT

PCR

LIST OF ABBREVIATIONS

MEANING

Animal and Plant Health Inspection Service
Bovine tuberculosis, caused by Mycobacterium bovis
Comparative cervical tuberculin test

Caudal fold tuberculin test

CFT and CCT used in serial interpretation

Cell wall protein

Cell wall protein peptoglycan

Expectation maximization

Generalized estimation equations

Heat concentrated synthetic medium (tuberculin)
Herd-level predictive value negative

Herd-level predictive value positive

Herd-level sensitivity

Herd-level specificity

Mycobacterium bovis

Michigan Department of Agriculture

Maximum likelihood estimation
Newton-Raphson

Koch’s old tuberculin

Polymerase chain reaction

XV

PPD
PVN
PVP
Se
SICTT
SIT
SP

SP
USDA

VS

Purified protein derivative

Predictive value Negative

Predictive value positive

Sensitivity

Single intradermal comparative tuberculin test
Single intradermal test

Synthetic peptide

Specificity

United States Department of Agriculture

Veterinary Services

xvi

CHAPTER ONE
INTRODUCTION, RATIONALE, PROBLEM STATEMENT,
GENERAL METHODS, and OVERVIEW

INTRODUCTION

In 1979, Michigan was declared free of bovine tuberculosis (bTb) caused by
Mycobacterium bovis.(Corso et al., 1996) In 1994, bTb was identified in a single white-
tailed deer,(Corso et al., 1996) and a bTb positive bovine was diagnosed in 1995. As of
June, 2003, bTb has been diagnosed in 30 cattle herds, primarily in the Northeast comer
of Michigan’s lower peninsula. Bovine tuberculosis has furthermore been diagnosed in
approximately 400 white-tailed deer, two elk, one domestic cat, four bobcats, 13 coyotes,
two opossums, two raccoons, and two red foxes.(C. Bruning-Fann, personal
communication 2002)

Bovine tuberculosis is an infection with Mycobacterium bovis, which affects a
wide range of domestic animals, particularly cattle, goats, farmed and wild deer and
several wildlife species.(Bruning-Fann et al., 2001) Bovine tuberculosis is also a concern
to public health because humans may become infected by inhaling infected droplets or
ingesting contaminated meat or milk. The disease is of substantial economic concern to
livestock producers, because infected herds most commonly are depopulated for disease
control purposes and national and international markets may be lost due to the
quarantines and importation limitation. In addition, movement bans and rigorous testing

schemes may be posed on herds in areas where bTb is present in the cattle population.

According to the United States Department of Agriculture (USDA), bTb is a
reportable disease and a plan was implemented for testing all domestic cattle herds in
Michigan with the caudal fold tuberculin test (CFT).(October 31, 2000, Amendment to
the Animal Industry Act 466, State of Michigan.) Cattle with “suspect” responses on the
CFI‘ were retested with the comparative cervical tuberculin test (CCT). Animals
classified as “reactors” on one CCT (or “suspect” on two successive CCT) were
submitted to the Diagnostic Center for Population and Animal Health, Michigan State
University, for euthanasia and necropsy. Diagnosis of bTb-infected animals was based on

mycobacterial isolation and/or identification by polymerase chain reaction (PCR).
RATIONALE

The bovine tuberculosis (bTb) skin tests have been used successfully for control
and eradication of bTb in the United States since the eradication program was begun in
1917.(Anonymous, 1992) In 1992, there were only 10 states that had not achieved bTb-
free status.(Frey, 1995) Nevertheless, bTb has become endemic in the cattle population
in certain areas in the United States, including the northern part of Michigan’s lower
peninsula.(Kaneene et al., 2002) Two tuberculin skin tests are still being used in series to
detect individual animals and herds that are infected with bTb. The caudal fold
tuberculin test (CFT) is used to screen herds, and animals that respond to the CFT are
retested with the comparative cervical test (CCT).(USDA and APHIS, 1999) Both the

CFT and the CCT form the core of the bTb eradication program in Michigan.

It is important that state and federal veterinarians have knowledge of how well the
tests they use for bTb eradication perform when a testing strategy is outlined, and it has
been recommended that accuracy of the tuberculin skin tests be evaluated in the
geographic area in which they are used and that the sensitivity and specificity should be
evaluated in populations naturally infected with bTb.(Greiner and Gardner, 2000;
O'Reilly, 1995) Furthermore, it may be helpful to regulatory veterinarians if they know
of certain herd or ecologic/geographic factors that systematically alter the results on the
tuberculin skin tests so that such factors can be taken into consideration when a herd has
been tested for bTb and the status of the herd is being evaluated.

Several authors have reported estimates of the sensitivity (Se) and specificity (Sp)
of these two skin tests (CFT and CCT) used in cattle.(Francis and Seller, 1978; Gaboric
et al., 1996; Lepper et al., 1977; Leslie and Hebert, 1975; Leslie et al., 1975a; Leslie et
al., 1975b; Pollock et al., 2000; Roswurm and Konyha, 1973; Whipple et al., 1995; Wood
et al., 1991; Wood et al., 1992) However, the estimates vary considerably, and the
variation in estimates of Se and Sp is most likely due to one or a combination of the
following factors: 1) Differences in the concentration of the tuberculin used for the CFT,
2) different (“gold”) standards used for estimation of Se and Sp of the CFT, 3) bTb
prevalence, 4) the amount of purified protein derivative (PPD) used for the skin tests, and
5) regional variation in cross reacting mycobacteria that cause false positive results on the
CFT,(Cooney et al., 1997; Comer and Pearson, 1978a, 1978b), and 6) variation in the
interpretation of the CFT by the testing veterinarians.(Kleeberg, 1960). In Michigan,
mycobacterial culture (CULT) and polymerase chain reaction (PCR) performed on

histologic suspect samples were considered to be the definitive test for diagnosis of bTb.

Although the performance of the skin tests have been estimated in the United
States(Gaboric et al., 1996; Roswurm and Konyha, 1973; Whipple et al., 1995), it has not
been determined exactly how the tests have performed during the current bTb outbreak in
northeastern Michigan.

It has been stated that the tuberculin tests should be considered as herd tests rather
than individual animals tests, because in an eradication program it is more important to
detect infected herds than infected individual animals. Hence, the herd-level estimates of
sensitivity (HSe) and specificity (HSp) of the serial testing program in Michigan may be
of more relevance to regulatory veterinarians managing the eradication effort than Se and

Sp. The herd-level performance of the tuberculin tests have not been estimated before.

PROBLEM STATEMENT

It should be clear that working estimates of both individual animal and herd-level
estimates of the skin-tests as used in the eradication effort in Michigan would be of value
to regulatory veterinarians both in evaluation of the current program and in planning for
adjustments or evaluation of use of new tests used alone or in combination with the CFI‘
and CCT in the future. Furthermore, factors affecting the outcome of the CFT and CCT

may help guide regulatory veterinarians when such programs are developed and

implemented.

STUDY OBJECTIVES

The overall Objective of this dissertation is to procure tools that may be used by

regulatory veterinarians to help better understand results Obtained by the caudal fold and

comparative cervical tuberculin tests. In order to accomplish this aim several research

objectives needed to be addressed. They are:

1)

2)

3)

4)

Determine the sensitivity of the caudal fold tuberculin test (CFT) and the CFT

and comparative cervical tuberculin tests used in serial interpretation

(CFI‘CCTSER) as well as gross necropsy using a gold standard approach.

Determine the sensitivity and specificity of the caudal fold tuberculin test

(CFT) and the CFT and comparative cervical tuberculin tests used in serial
interpretation (CFTCCTSER) using methods that do not require the assumption

of a gold standard.

Estimate the herd-level sensitivity and specificity of the of the caudal fold
tuberculin test (CFT) and the CFT and comparative cervical tuberculin test

when used in the bovine tuberculosis infected region of Michigan.

Determine herd, geographic, and ecologic factors that may affect the outcome

of the CFT.

5) Determine if spatial clustering of herds with a high proportion of false positive

results on the CFT were present in Michigan.

GENERAL METHODS

The objectives in this study were addressed using two data sets. The first two
objectives were addressed using test results from 494 cattle in seven conveniently
selected herds. The third objective was addressed by a simulation study, and the fourth
and fifth Objectives were addressed using CFT test results from 4,989 and 3,301 herds,

respectively obtained from the Michigan Department of Agriculture.

The first dataset was a subset of 22 herds (2 dairy and 20 beef) that were
identified as having at least one animal positive by bacterial isolation or PCR. Of these 22
herds, our study was limited to the 7 herds for which cattle were individually evaluated
by each of six diagnostic tests: CFT, CCT, necropsy, histopathologic exam, PCR and
bacteriologic culture. In the remaining 15 herds, only cattle that were suspects or reactors
on the CCT were submitted for a full necropsy, histopathologic exam, PCR or culture,
and hence they could not be used in this study. Of 516 cattle from the seven herds, 22
cattle had missing or erroneous laboratory records and were therefore excluded.
Therefore, 494 cattle were included in this study.

The following information was available on all 494 individual animals: Herd ID,

test results for all tests described above, testing veterinarian, age, and gender.

Mycobacterial isolation and PCR were used in parallel as the reference or
definitive test for bTb. As such, cattle were designated as being truly infected with bTb if

they were found positive either by culture or PCR assay.

The sensitivity of the CFT and CFTCCTSER and gross necropsy was estimated
using a gold standard method. Furthermore, the sensitivity and specificity of the CFI‘
and CFTCCTSER were estimated using latent-class models and Bayesian inference,

assuming that a gold standard was not available.

The second data set consisted of all cattle herds that had a whole herd test for bTb
between January 1996 and November 2001. During this period, 8,260 bTb negative
cattle herds (4,223 beef and 4,037 dairy) underwent a ‘whole herd test’ with the CFI‘.
Some herds were tested more than once during this period. These herds were all judged
to have been negative for bTb because all cows were negative on the CFT or the CCT or
cows positive on CCT were later concluded to be negative by necropsy, culture and PCR.
For a herd to be included in this study, the testing private veterinary practitioner had to
have tested at least 3 herds. Furthermore, the herd size in this study was limited to beef
herds > 12 cattle and dairy herds > 22 cattle. After deletion of herds that did not fulfill
these criteria, 4,989 herds were left over for analysis of associations between the
proportion of false positive test results on the CFT in herds and herd factors and
geographical location.

For the spatial analysis, a spatial coordinate was need for each farm. The exact
spatial coordinates (latitude and longitude) of the tested herds were not available, so the

geographic location of herds was obtained by mapping (geocoding) the address of the

herd to spatial data on roads in Michigan using ArcINfO (ESRI, Redlands, CA). The

spatial reference data on roads in Michigan were obtained from the 2000 Census

(http://wwwmichigan.gov/cgil). Herds that had an address match 280% to the reference
address were considered an acceptable match. After geocoding, spatial coordinates (x,y
coordinates, Michigan GeORef) were Obtained for 1,039 beef and 2,262 dairy herds,
respectively. These herds (n = 3,301) were used in the spatial analysis, as well as to
investigate associations between the proportion of false positive test results on the CFT in
herds and elevation of the herd and whether a wetland area was located within a certain
radius from the farm.

Associations between the proportion of false positive test results on the CFT in
herds and herd factors, geographic, and ecologic factors were tested using a multiple
factor negative binomial regression model treating the testing veterinarian as a random
effect. The spatial scan statistic was used to identify possible clusters of herds with an

unusually high proportion of false positive test results on the CFT.

OVERVIEW

A literature review focusing on the sensitivity and specificity of the caudal fold
and comparative cervical tuberculin tests is presented in chapter two. Chapter three
addresses Objective 1 and presents estimates of the CFT, and CFT and CCT used in serial
interpretation, and of gross necropsy using a gold standard approach. Similarly, chapter
four addresses objective 3, and presents sensitivity and specificity estimates of the two
skin tests using a novel Bayesian approach accounting for possible dependence between
the tests. Objective 4 is addressed in chapter five presenting herd—level estimates for the
two skin tests. Chapter six addresses objectives 4 and 5 by evaluating factors associated

with the herd-level proportion of false positive results on the CFT.

REFERENCES

Anonymous 1992. Assessment of risk factors for Mycobacterium bovis in the United
States (Fort Collins, CO, USDA, APHIS, VS).

Bruning-Fann, C.S., Schmitt, S.M., Fitzgerald, S.D., Fierke, J.S., Friedrich, P.D.,
Kaneene, J .B., Clarke, K.A., Butler, K.L., Payeur, J .B., Whipple, D.L., Cooley, T.M.,

Miller, J .M., Muzo, DP, 2001, Bovine tuberculosis in free-ranging carnivores from
Michigan. J. of Wildlife Dis. 37, 58-64.

Cooney, R., Kazda, J ., Quinn, J ., Cook, B., Miiller, K., Monaghan, M., 1997,
Environmental mycobacteria in Ireland as a source of non-specific sensitization to
tuberculins. Irish Vet. J. 50, 370-373.

Corner, L.A., Pearson, C.W., 1978a, Pathogenicity in cattle of atypical mycobacteria
isolated from feral pigs and cattle and the correlation of lesions with tuberculin
sensitivity. Austr. Vet. J. 54, 280-286.

Comer, L.A., Pearson, C.W., 1978b, Response of cattle to inoculation with atypical
mycobacteria of bovine origin. Austr. Vet. J. 54, 379-382.

Corso, B., Wagner, B., Norden, D. 1996. Assessing the risks associated with M. bovis in
Michigan free-ranging deer. (Fort Collins, CO, Centers for Epidemiology and Animal
Health, USDA, APHIS). PP. 1-2.

Francis, J., Seller, R.J., 1978, The sensitivity and specificity of various tuberculin tests
using bovine PPD and other tuberculins. Vet. Rec. 103, 420-425.

Frey, G.H., 1995, Bovine tuberculosis eradication: The program in the United States, In:
Thoen, C.O., Steele, J.H. (Eds.) Mycobacterium bovis infection in animals and humans.

Iowa State University Press, Ames, IA, pp. 119-129.

Gaboric, C.M., Salman, M.D., Ellis, R.P., Triantis, J ., 1996, Evaluation of five-antigen
ELISA for diagnosis of tuberculosis in cattle and Cervidae. J AVMA 209, 962-966.

Greiner, M., Gardner, LA, 2000, Epidemiologic issues in the validation of veterinary
diagnostic tests. Prev. Vet. Med. 45, 3-22.

Kaneene, J .B., Bruning-Fann, C.S., Granger, L.M., Miller, R., Porter-Spalding, BA,
2002, Environmental and farm management factors associated with tuberculosis on cattle
farms in northeastern Michigan. J AVMA 221, 837-842.

Kleeberg, H.H., 1960, The tuberculin test in cattle. JSAVMA 31, 213-225.

10

Lepper, A.W.D., Pearson, C.W., Comer, L.A., 1977, Anergy to tuberculin in beef cattle.
Aust.. Vet. J. 53, 214-216.

Leslie, I.W., Hebert, C.N., 1975, Comparison of the specificity of human and bovine
tuberculin PPD for testing cattle. 3 - National trial in Great Britain. Vet Rec 96, 338-341.

Leslie, I.W., Hebert, C.N., Barnett, D.N., 1975a, Comparison of the specificity of human
and bovine tuberculin PPD for testing cattle. 2 - Southeastern England. Vet Rec 96, 335-
338.

Leslie, I.W., Hebert, C.N., Burn, K.J., MacClancy, B.N., Donnelly, W.J.C., 1975b,
Comparison Of the specificity of human and bovine tuberculin PPD for testing cattle. 1 -
Republic of Ireland. Vet Rec 96, 332-334.

O'Reilly, L., 1995, Tuberculin Skin Tests: Sensitivity and Specificity, First Edition. Iowa
State Press, Ames, 355 p.

Pollock, J .M., Girvin, R.M., Lightbody, K.A., Clements, R.A., Neill, S.D., Buddle, B.M.,
Andersen, P., 2000, Assessment of defined antigens for the diagnosis of bovine
tuberculosis in skin test-reactor cattle. Vet Rec 146, 659-665.

Roswurm, J.D., Konyha, 1973, The comparative cervical tuberculin test as an aid to
diagnosing bovine tuberculosis. Proc. Annu. Meet. U.S. Anim. Health Assoc. 77, 368-
389.

USDA, APHIS 1999. Bovine tuberculosis eradication. Uniform methods and rules,
effective January 22, 1999, (United States Department of Agriculture), pp. 1-34.

Whipple, D.L., Bolin, C.A., Davis, A.J., Jamagin, J .L., Johnson, D.C., Payer, J.B., Saari,
D.A., Wilson, A.J., Wolf, M.M., 1995, Comparison of the sensitivity of the caudal fold

skin test and a commercial gamma-interferon assay for diagnosis of bovine tuberculosis.
AJVR 56, 415-419.

Wood, P.R., Corner, L.A., Rothel, J.S., Baldock, C., Jones, S.L., Cousins, D.B.,
McCormick, B.S., Francis, B.R., Creeper, J., Tweddle, N .E., 1991, Field comparison of
the interferon-gamma assay and the intradermal tuberculin test for the diagnosis of
bovine tuberculosis. Austr. Vet. J. 68, 286-290.

Wood, P.R., Comer, L.A., Rothel, J .S., Ripper, J .L., Fifis, T., McCormick, B.S., Francis,
B., Melville, L., Small, K., Witte, K.D., Tolson, J ., Ryan, T.J., Lisle, G.W., Cox, J.C.,
Jones, S.L., 1992, A field evaluation of serological and cellular diagnostic tests for
bovine tuberculosis. Vet. Microbiol. 31, 71-79.

11

CHAPTER TWO

LITERATURE REVIEW

The tuberculin skin tests have been used around the world for over a century in
control and eradication of bovine tuberculosis (bTb) in cattle. Although changes in the
production of tuberculins and in the implementation of the tests have occurred over the
years, the tuberculin skin tests are still used with success today. The tuberculin skin tests
have been reviewed recently by Monaghan et al. (1994). A review by Francis et al.
(1978) focused in particular on the bovine purified protein derivative (PPD) and its use
with the skin tests. A broader review of both in vivo and in vitro diagnostic tests for

detection of Mycobacterium bovis infections in cattle was published by Adams (2001).

Tuberculins

Purified protein derivative (PPD) is the most commonly used tuberculin today,
including in the United States, however heat concentrated synthetic medium (HCSM)
tuberculin may be used in some countries. Originally Koch’s old tuberculin (OT) was
use in tuberculin tests. In the US. bovine tuberculin (PPD-B) is derived from M. bovis
strain ANS and avian tuberculin (PPD-A) is derived form M. avium strain D4.(Angus,
1978) The PPD tuberculins are a mixture of sugars, lipids, proteins, and nucleic acids
and contain a variety of antigens that are common to several mycobacteria,(Monaghan et
al., 1994), hence cross reaction may occur to other mycobacteria when the skin test is

performed. (Affronti, 1988) reviewed various attempts to isolate fractions from different

12

cellular components of the mycobacterium and their use as antigens in skin tests. Angus
et al (1989) tested the use of M. bovis cell wall protein (CW P), a cell wall protein
peptoglycan complex (CW P-PG) and a 13 amino acid synthetic peptide (SP) as potential
test tuberculins. They found that the SP lacked sufficient tuberculin reactivity for use in
cattle, and there was considerable response to cattle sensitized with M. bovis and M.

avium for both CW P and CWP-PG. However, further research in this field is needed.

Tuberculin skin tests

Hypersensitivity to tuberculin usually occurs within 30 to 50 days after infection
with tubercle bacilli.(Francis, 1947) The reaction to tuberculin injected intraderrnally is a
delayed-type hypersensitivity reaction, which induces messenger RNA (mRNA)
expression of gamma interferon (‘y-INF), interleukin (IL) 2, 1L4, ILlO, and tumor necrosis
factor-alpha (TNFOt), and the reaction is maximal after approximately 72 hours.(Francis
and Seller, 1978; Ng et al., 1995)

Two types of tuberculin skin tests are used in cattle; the single intradermal test
(SIT) where bovine PPD (PPD-B) is injected intraderrnally and the Single intradermal
comparative tuberculin test (SICTT) using both avian PPD (PPD-A) and PPD-B. In the
United States, the SIT is performed in the caudal fold of the tail and is referred to as the
caudal fold tuberculin test (CFT). The SIC'I'I‘ is used as a follow up test on animal that
were positive (suspect) on the CFT, and it is referred to as the comparative cervical
tuberculin test (CCT).(USDA, 1999)

In the United States, the CFT is performed by USDA/APHISN S accredited

veterinarians or public veterinarians by intradermal injection of 0.1 m1 of USDA bovine

I3

purified protein derivative (1 mg/ml PPD-B) into either side of the caudal fold. The
injection site is read by visual observation and palpation 72 hours (plus or minus 6 hours)
following injection. Cattle may not be subjected to CFT retest at intervals less than 60
dayS.(USDA, 1999) Suspects in herds containing only CFT suspects must be retested
with the CCT within 10 days of the CFT injection, retested with the CFT after 60 days, or
shipped to slaughter. The CCT may only be administered by state or federal
veterinarians. Intradennal injection of biologically balanced PPD-B and PPD-A are
performed at separate sites approximately 12.5 cm apart on the midcervical region. The
skin thicknesses of the areas for injection of bovine and avian PPD are measured to the
nearest 0.5 mm before the injection and again approximately 72 hours (plus or minus 6
hours) later. Comparative cervical test responses must be recorded on the CCT
scattergrarn (VS FORM 6-22d), and the animal is classified as negative, suspect, or
reactor.(USDA, 1999) Suspects on the CCT must be retested negative by the CCT after
60 days or shipped directly to slaughter. Reactors on the CCT must be shipped to
slaughter and post mortem examination.(USDA, 1999)

When a whole herd is tested for bTb, all animals over the age of 24 months must
be tested with the CFT.(USDA, 1999) However, in Michigan all animals 12 months or
older were tested. A post mortem exam is performed on all animals that are reactors or
suspects on two consecutive CCT tests. Animals receive humane euthanasia and all
organs including medial retropharyngeal, submandibular, tracheobronchial, mediastinal,
mesentary, ileocolic, and hepatic lymph nodes are examined for gross lesions consistent
with bTb. Selected tissues are subject to histological exam and mycobacterial

culture.(Schmitt et al., 1997) Tissues from animals that are suspect on histological exam

l4

are tested with polymerase chain reaction (PCR).(Miller et al., 1997) If tissues are
positive on PCR or mycobacterial culture, the animal is concluded to be infected with M.
bovis. All other animals are considered to be negative for bTb. If an animal in a herd is
positive for bTb, the herd is considered infected with bTb, and in most instances the herd

is depopulated.

Sensitivity and specificity estimates for the CFT and C C T in the United States

Diagnostic, screening, and other tests are often evaluated by their sensitivity (Se)
and specificity (Sp). However, the predictive values are of equal importance when the
results of an individual test are evaluated. The sensitivity [P(T+ID+)] of a diagnostic test
is defined as the conditional probability that a test positive animals (T+) is in fact truly
infected (D+), i.e. the proportion of T+ animals that are truly infected. Likewise the
probability that a test negative animal (T-) is in fact truly negative (D-), is termed the
specificity [P(T-ID-)], i.e. the proportion of T- animals that are truly disease negative. On
the other hand, the predictive values are the ‘post test’ probabilities. The predictive
values are the probabilities that a disease positive (negative) animal is positive (negative)
on a given test. Hence the predictive value positive (PVP) is the conditional probability
of P(D+IT+), and the predictive value negative (PVN) is the conditional probability of
P(D-lT-).(Greiner and Gardner, 2000)

If a perfect reference test, or a series of tests, (i.e. ‘gold standard’) correctly
identifies all tested animals, the Se, Sp, PVP, and PVN of a new test or test with
unknown accuracy, may be estimated as shown in Table 2-1. Sensitivity = ala+c, Sp =

d/b+d, PVP=a/a+b, and PVN = d/c+d

15

Table 2-1. Calculation of sensitivity and specificity when a gold standard is
available.

 

 

‘Gold Standard’
D+ D-
T+ a b a+b
New test
T- c d c+d

 

 

 

 

a+c b+d N=a+b+c+d

Often a gold standard is not available, which is the case when evaluating the true
infection Status of cattle in a population where infection with Mycobacterium bovis is
present. However, the Se and Sp of a new test may also be evaluated against a test with
known sensitivity and specificity, or the Se may be estimated if the reference test has a
perfect specificity.(Gart and Buck, 1966; Staquet et al., 1981) New statistical methods,
including maximum likelihood estimation (MLE),(Georgiadis et al., 1998; Hui and
Walter, 1980; Singer et al., 1998; Walter and Irwig, 1988; Weng, 1996) and simulation
based Bayesian inference(Johnson et al., 2001; Joseph et al., 1995) offer the researcher a
way to estimate Se and Sp of two or more tests when a gold standard is not available. A
review of these methods has been published by En¢e et al. (2000). Furthermore, these
simulation based methods also allow the investigator to account for dependency between
tests.(Black and B.A.Craig, 2002; Dendukuri and Joseph, 2001; En¢e et al., 2001;

Georgiadis et al., 2003)

16

In the following review of published estimates of Se and Sp of tuberculin Skin
tests performed in the US, a direct comparison of these studies is not possible because
the skin tests are evaluated against different ‘levels’ of gold standards. I was only able to
identify two recent studies from 1995 and 1996, that estimate the sensitivity and
specificity of the CFT,(Gaboric et al., 1996; Whipple et al., 1995) and an additional study
estimating the Sc and Sp of the CFT and CCT from 1973.(Roswurm and Konyha, 1973)
The study by Whipple et al. (1995) also estimated the accuracy of a y-INF assay and
Gaboric et al (1996) additionally estimated the Sc and Sp of a five-antigen enzyme-
linked immuno sorbent assay (ELISA). The study by Roswurm et al. (1973) is
particularly interesting because it is the only study performed in the US. that also
estimates Se and Sp of the CCT.

Although the source is unknown, the USDA published estimates of the Se and Sp
of the CFT and CCT in cattle.(Anonymous, 1992) The Se and Sp of the CFT and CCT
were 82% and 96%, and 74% and 96%, respectively. It is likely that these results are
partially derived from the work of Roswurm and Konyha (1973).

In the study by Whipple er al. (1995), 610 cattle from one dairy herd were tested
with the CFT. They used four different reference test scenarios to determine the ‘true’
infection status of the cattle; 1) cattle positive by bacteriologic culture only, 2) histologic
examination only, 3) bacteriologic culture and histologic examination (serial
interpretation), and 4) bacteriologic culture or histologic examination (parallel

interpretation). Using these four reference standards the Se of the CFT ranged from 80.4

to 84.4%.

17

Gaboric et al. (1996) used a sample of 4,504 cattle from 23 herds of which 4 dairy
and 2 beef herds were considered infected with M. bovis. Of the 4,504 cattle, 4,167
(93%) were considered not to be infected. An animal was considered to be positive for
bTb if it was from an infected herd and was positive on either bacteriologic culture or
histologic examination. They estimated the Se and Sp of the CFT to be 84.9% and
89.2%, respectively. The Se and Sp of the 5-antigen ELISA are 65.6% and 56.4%,
respectively. More interestingly, when the two tests were interpreted in parallel (i.e. an
animal was positive on one or both of the tests) the Se and Sp were 95% and 50%,
respectively. In serial interpretation (an animal was positive on both tests), the Se and Sp
were 55.5% and 95.7%, respectively. This particular study shows that even though the
sensitivity of the 5-antigen ELISA is fairly low (65.6%), use of the ELISA and CFT in
parallel increases the combined Se dramatically.(Gaboric et al., 1996)

In both of the above studies, the CFT consisted of an intradermal injection of 0.1
ml USDA PPD-B (1 mg/ml).

Roswurm and Konyha (1973) estimated the Se and Sp of the CCT and Sp of the
CFT in 3 bTb positive and 27 bTb negative publicly owned cattle herds from the US.
The negative herds had at least a seven year history Of being bTb free. For an animal to
be considered positive for bTb, it had to originate from a herd in which M. bovis had
recently been cultured, and have either 1) gross pathologic lesions typical of bTb, 2)
histopathologic evidence of mycobacterial infection, or 3) have M. bovis cultured from
infected body tissues. The Se of the CCT when administered 7 days after the CFT, was
74.4% and 88.5% when using CCT reactors only, and CCT reactors and CCT suspects in

parallel to represent a positive test result, respectively. The Sp Of the CFT was estimated

18

to be 94.1%. The Sp of the CCT performed on CFT suspect animals was 92% when
using only CCT negative animals. If both CCT negative and suspect animals were
considered to be test negative, the Sp of the CCT was 99.1%. The volume of PPD-B and
PPD-A used for the testing is this study is somewhat unclear, however the PPD
tuberculins were biologically balanced so they were of equal potency with PPD-B and
PPD-A containing 0.996 mg and 1.128 mg of protein per ml, respectively.

These three studies used similar criteria to characterize a bTb positive animal and
the Sc and Sp estimates were very similar. However, it is likely that for all three Studies
some animals truly infected with M. bovis were not discovered. It is not possible to
predict how this would have affected the Se estimates.

It is commonly considered that Se and Sp of diagnostic tests are constant
parameters of a test. However, empirical evidence suggests that both Se and Sp may vary
within and among populations of animals.(Greiner and Gardner, 2000) In cattle infected
with bTb, it is known that the Se is lower in animals in the pre-allergic, inactive, and
anergic stages.(Francis, 1947; Lepper et al., 1977) Hence in a population with a large
proportion of such animals, the Se will be estimated lower than in a population with a
low proportion of such animals. Whether this affected the estimates and uncertainty of

Se and Sp presented above is unknown.
Factors affecting the sensitivity and specificity of the tuberculin skin tests

A logical question to ask is why do some bTb negative animals react positively on

the CFT and CCT and why do some bTb positive animals react negatively on the skin

19

tests while others do not? Different factors may affect the test including: 1) the tester, 2)
the tuberculin used, 3) the instrumentation, and 4) the animal.(Kleeberg, 1960)

Firstly, it takes 30-50 days from when an animal is infected until it will react to
injected tuberculin.(Francis, 1947) Furthermore, some cattle may not react to tuberculin
injection, including many cattle with generalized infection.(Lepper et al., 1977) This
condition is known as anergy and is poorly understood.

A large area for variation in the outcome of a skin test lies with the testing
veterinarian. Mistakes can be made in both injecting the PPD and reading the test. For
example, the veterinarian performing the test may consistently inject the tuberculin
subcutaneously rather than intraderrnally. The outcome of such incorrect injection of
PPD, however, has not been documented.

Incorrect storage and handling of PPD may lead to a decrease in potency and
hence an increase in false negative test results. Furthermore, bacterial contamination of
the PPD may have a negative effect on the potency of the PPD.

Successful testing also relies on the choice of suitable instruments.(Kleeberg,
1960) It has been shown that multiple dose syringes may administer varying
volumes.(Monaghan et al., 1994) For the CCT, it is imperative to use good calipers and
thoroughly palpate the skin for nodules and other abnormalities where the PPD is
injected. Furthermore, it is recommended to use coil Spring activated calipers thus
ensuring uniform pressure on the skin at each measurement.(Kleeberg, 1960)

Radunz and Lepper (1985) showed that repeat testing with a single comparative
tuberculin test within 4 and 7 days of initial testing with the CFI‘ decreased the response

to the CCT in tuberculin-sensitized cattle. However, the sensitivity had returned to

20

sufficient level when re-tested at 60 days. Hence it is important that re-testing with the
CCT is not performed too close in time to the CFT.

Furthermore, immunosuppression (i.e. in postpartum cows) may affect the
animals ability to mount an effective immune response and react to the tuberculin
injection. Malnutrition may also affect the immune response however, a study on 20
bullocks did not support this claim.(Monaghan et al., 1994)

False positive reaction to the tuberculin Skin tests also occur, and are most likely
caused by cross-reacting mycobacteria other than M. bovis. However, because the

specificity of the skin tests already is high, the hope for improvement is low.

Herd-level estimates of sensitivity and specificity

The Se and Sp of the tuberculin Skin tests have been estimated in various studies
around the world.(Gaboric et al., 1996; Lepper et al., 1977; Leslie and Hebert, 1975;
Leslie et al., 1975a; Leslie et al., 1975b; Roswurm and Konyha, 1973; Whipple et al.,
1995; Wood et al., 1991) However, it is to my knowledge unknown how the skin tests
perform on the herd-level, i.e. herd-level sensitivity (HSe) and specificity (HSp). Herd-
level test interpretation has recently been reviewed by Christensen and Gardner (2000).
Factors influencing estimates HSe and HSp include animal-level Se and Sp, the sample
size, the true prevalence of the disease within positive herds (TP), and the number of test-
positive animals used to define a positive herd (cutoff).(Martin et al., 1992) Because Se,
Sp and prevalence within a herd changes during a bTb eradication program, HSe and Hsp
will likely change too. During an eradication program, the within herd prevalence

usually decreases, which leads to a decrease in HSe.(Christensen and Gardner, 2000)

21

However, the HSp should remain unchanged unless Sp changes, in which case HSp

decreases with decreasing Sp and vice versa.

22

REFERENCES

Adams, LG, 2001, In vivo and in vitro diagnosis of Mycobacterium bovis infection. Rev.
sci. tech. int. Epiz. 20, 304-324.

Affronti, L.F., 1988, Mycobacterial antigens: reagents for tuberculin skin testing and
serodiagnosis of tuberculosis. Plenum Press, New York, 1-37 pp.

Angus, RD, 1978, Production of reference PPD tuberculins for veterinary use in the
United States. J. of Biol. Standard. 6, 221-227.

Angus, R.D., Payeur, J.B., Elksen, L.A., 1989, Preliminary evaluation of an intradermal
tuberculin test utilizing cell wall protein extracted from M. bovis. Proceedings of the US.
Animal Health Association 93, 111-124.

Anonymous 1992. Assessment of risk factors for Mycobacterium bovis in the United
States (Fort Collins, CO, USDA, APHIS, VS).

Black, M.A., B.A.Craig, 2002, Estimating disease prevalence in the absence of a gold
standard. Statist. Med. 21, 2653-2669.

Christensen, J., Gardner, I.A., 2000, Herd-level interpretation of test results for
epidemiologic studies of animal diseases. Prev. Vet. Med. 45, 83-106.

Dendukuri, N., Joseph, L., 2001, Bayesian approach to modeling the conditional
dependence between multiple diagnostic tests. Biometrics 57, 158-167.

Enee, C., Andersen, S., Sorensen, V., Willeberg, P., 2001, Estimation of sensitivity,
specificity and predictive values of two serologic tests for the detection of antibodies

against Actinobacillus pleuropneumoniae serotype 2 in the absence of a reference test
(gold standard). Prev. Vet. Med. 51, 227-243.

Enpe, C., Georgiadis, M.P., Johnson, W.O., 2000, Estimation of sensitivity and
specificity of diagnostic tests and disease prevalence when the true disease status is
unknown. Prev. Vet. Med. 45, 61-81.

Francis, J ., 1947, Bovine tuberculosis, Including a contrast with human tuberculosis.
Staple Press, London, 220 p.

Francis, J ., Seller, R.J., 1978, The sensitivity and specificity of various tuberculin tests
using bovine PPD and other tuberculins. Vet. Rec. 103, 420-425.

Gaboric, C.M., Salman, M.D., Ellis, R.P., Triantis, J ., 1996, Evaluation of five-antigen
ELISA for diagnosis of tuberculosis in cattle and Cervidae. JAVMA 209, 962-966.

23

Gart, J., Buck, A., 1966, Comparison of a screening test and a reference test in
epidemiologic studies. Am J Epidemiology 83, 593-602.

Georgiadis, M.P., Gardner, I.A., Hedrick, RP, 1998, Field evaluation of sensitivity and
specificity of a polymerase chain reaction (PCR) for detection of N. salmonis in rainbow
trout. J. Aquat. Anim. Health 10, 372-380.

Georgiadis, M.P., Johnson, W.O., Gardner, I.A., Singh, R., 2003, Correlation-adjusted
estimation of sensitivity of two diagnostic tests. Appl. Statist 52, 1-14.

Greiner, M., Gardner, I.A., 2000, Epidemiologic issues in the validation of veterinary
diagnostic tests. Prev. Vet. Med. 45, 3-22.

Hui, S.L., Walter, S.D., 1980, Estimating the error rates of diagnostic tests. Biometrics
36, 167-171.

Johnson, W.O., Gastwirth, J .L., Pearson, M., 2001, Screening without a "gold standard":
The Hui-Walter Paradigm revisited. Am. J. Epidemiol. 153, 921-924.

Joseph, L., Gyorkos, T., Coupal, L., 1995, Bayesian estimation of disease prevalence and
the parameters of diagnostic tests in the absence of a gold standard. Am. J. Epidemiol.
153, 921-924.

Kleeberg, H.H., 1960, The tuberculin test in cattle. JSAVMA 31, 213-225.

Lepper, A.W.D., Pearson, C.W., Comer, L.A., 1977, Anergy to tuberculin in beef cattle.
Aust. Vet. J. 53, 214-216.

Leslie, I.W., Hebert, C.N., 1975, Comparison of the specificity of human and bovine
tuberculin PPD for testing cattle. 3 - National trial in Great Britain. Vet Rec 96, 338-341.

Leslie, I.W., Hebert, C.N., Barnett, D.N., 1975a, Comparison of the specificity of human
and bovine tuberculin PPD for testing cattle. 2 - Southeastern England. Vet Rec 96, 335-
338.

Leslie, I.W., Hebert, C.N., Burn, K.J., MacClancy, B.N., Donnelly, W.J.C., 1975b,
Comparison of the specificity of human and bovine tuberculin PPD for testing cattle. l -
Republic of Ireland. Vet Rec 96, 332-334.

Martin, S.W., Shoukri, M., Thorbum, M.A., 1992, Evaluating the health status of herds
based on tests applied to individuals. Prev. Vet. Med. 14, 3343.

Miller, J ., Jenny, A., Rhyan, J ., Saari, D., Suarez, D., 1997, Detection of Mycobacterium
bovis in formalin-fixed, paraffin-embedded tissues of cattle and elk by PCR amplification
of an IS6110 sequence specific for Mycobacterium tuberculosis complex organisms. J
Vet Diagn Invest 9, 244-249.

24

Monaghan, M.L., Doherty, M.L., Collins, J .D., Kazda, J.F., Quinn, P.J., 1994, The
tuberculin test. Vet Micro 40, 1 11-124.

Ng, K.H., Watson, J.D., Prestidge, R., Buddle, B.M., 1995, Cytokine mRNA expressed in
tuberculin skin test biopsies from BCG -vaccinated and Mycobacterium bovis innoculated
cattle. Irnmunol. Cell. Biol. 73, 362-368.

Radunz, B.L., Lepper, A.W.D., 1985, Suppression of skin reactivity to bovine tuberculin
in repeat tests. Aust. Vet. J. 62, 191-194.

Roswurm, J .D., Konyha, 1973, The comparative cervical tuberculin test as an aid to
diagnosinf bovine tuberculosis. Proc. Annu. Meet. U.S. Anim. Health Assoc. 77, 368-
389.

Schmitt, S., Fitzgerald S., Cooley, T., Bruning-Fann, C., Berry, D., ,, T., Minnis, R.,
Payer, J ., Sikarskie, J, 1997, Bovine tuberculosis in free-ranging white-tail deer in
Michigan. J Wildlife Dis 33, 749-758.

Singer, R.S., Boyce, W.M., Gardner, I.A., Johnson, W.O., Fisher, AS, 1998, Evaluation

of bluetongue virus diagnostic tests in free-ranging bighom sheep. Prev. Vet. Med. 35,
265-282.

Staquet, M., Rozencweig, M., Lee, M., Muggai, F.M., 1981, Methodology for assessment
of new dichotomous diagnostic tests. J. Chronic Dis. 34, 599-610.

USDA, APHIS. 1999. Bovine Tuberculosis Eradication: Uniform Methods and Rules,
Effective January 22, 1999, (United States Department of Agriculture), pp. 1-34.

Walter, S.D., Irwig, L.M., 1988, Estimation of error rates, disease prevaelnce and relative
risk from misclassified data: a review. J. Clin. Epidemiol 41, 923-937.

Weng, T.S., 1996, Evaluation of a new diagnostic test against a reference test less than
perfect in accuracy. Commun. Statist. Simul. Comput. 35, 533-555.

Whipple, D.L., Bolin, C.A., Davis, A.J., Jamagin, J.L., Johnson, D.C., Payer, J.B., Saari,
D.A., Wilson, A.J., Wolf, M.M., 1995, Comparison of the sensitivity of the caudal fold

skin test and a commercial gamma-interferon assay for diagnosis of bovine tuberculosis.
Am J Vet Res 56, 415-419.

Wood, P.R., Comer, L.A., Rothel, J .S., Baldock, C., Jones, S.L., Cousins, D.B.,
McCormick, B.S., Francis, B.R., Creeper, J ., Tweddle, N.E., 1991, Field comparison of
the interferon-gamma assay and the intradermal tuberculin test for the diagnosis of
bovine tuberculosis. Austr Vet J 68, 286-290.

25

CHAPTER THREE
THE SENSITIVITY OF GROSS NECROPSY, CAUDAL FOLD AND
COMPARATIVE CERVICAL TESTS FOR THE DIAGNOSIS OF BOVINE
TUBERCULOSIS.
ABSTRACT
Bovine tuberculosis was diagnosed in 22 cattle herds in the Northeast corner of

Michigan’s lower peninsula. Of these 22 herds, 494 animals in 7 herds were examined by
gross necropsy, histopathologic exam, mycobacterial culture, and polymerase chain
reaction assay performed only on samples that were histologically compatible for bTb.
Results of culture and polymerase chain reaction assay interpreted in parallel were used
as the reference test for calculation of the sensitivity of 1) the caudal fold test, 2) the
caudal fold and comparative cervical skin tests used in series, and 3) gross necropsy.
Mycobacterium bovis was isolated from 43 animals. Using all seven herds, the
sensitivities of the caudal fold test, the caudal fold and comparative cervical tests used in
series, and gross necropsy were 93.02%, 88.37%, and 86.05%, respectively. When the
data were stratified by low and moderate prevalence herds, the sensitivities were 83.33%,
75.0%, and 83.33 in low prevalence herds and 96.77%, 93.55%, and 87.10% in moderate
prevalence herds. The sensitivities Of the two skin tests were slightly higher when 2 or
more gross lesions were present, and the sensitivity Of gross necropsy was significantly
higher (P = 0.049) than when one gross lesion was present. The sensitivity of the caudal
fold test was found to be notably higher than most estimates in other studies, however a
direct comparison was not possible because the amount of purified protein derivative and
the reference methods were different in this study as compared to other published studies.

Though the sensitivities are high, two of the seven herds (29%) would have had one or

26

more positive animals left in the herd if a test-and-removal program had been used. This
suggests that when positive herds are identified, selective culling of skin test reactors is a

less acceptable disease control strategy than is complete depopulation.

27

INTRODUCTION

In 1979, Michigan was declared free of bovine tuberculosis (bTb) caused by
Mycobacterium bovis.(Corso et al., 1996) In 1994, bTb was identified in a single white-
tailed deer,(Corso et al., 1996; Schmitt et al., 1997) and a bTb positive bovine was
identified in 1995. As of June, 2002, bTb has been diagnosed in 22 cattle herds, primarily
in the Northeast corner of Michigan’s lower peninsula. Bovine tuberculosis has
furthermore been diagnosed in approximately 400 white-tailed deer, two elk, one
domestic cat, four bobcats, 13 coyotes, two opossums, two raccoons, and two red foxes
(C. Bruning-Fann, personal communication 2002).

Up until January 2002, 732,661 cattle in 13,689 herds have been tested with a serial
skin testing protocol involving the caudal fold test (CFT) of all cattle and re-testing of
suspects with the comparative cervical test (CCT). Tuberculin tests have been used
successfully in the United States since the bovine tuberculosis control program was
introduced in 1917.(Anonymous, 1992) In the US, “The caudal fold test is the official
tuberculin test for routine use in individual cattle, bison or goats and herds of such
animals where the tuberculosis status of the animals is unknown”.(USDA and APHIS,
1999; USDA, 1999)) In Michigan, the CFT was used as the screening test and a program
was undertaken in1998-2002 to test all cattle in the state over the age of 12 months. In
herds that had one or more CCT reactor(s) after the initial herd test, the CCT reactors(s)
were removed and the remaining herd retested with the CFT. With herds that had any
epidemiologic association with cattle from bTb positive herds, all cattle present in the

bTb exposed herd were tested with the CFT after removal of the bTb exposed cattle.

28

Cattle that responded to the CFT and were from herds of unknown bTb status were
retested with the CCT. Cattle that responded to the CFT and were from herds of positive
bTB status were classified as reactors and removed from the herd.

Several authors have reported estimates of sensitivity and/or specificin for the CFT
.(Francis and Seiler, 1978; Lepper et al., 1977; Leslie and Hebert, 1975; Leslie et al.,
1975a; Leslie et al., 1975b; Pollock et al., 2000; Roswurm and Konyha, 1973a; Roswurm
and Konyha, 1973b; Whipple et al., 1995; Wood et al., 1991; Wood et al., 1992) These
estimates range from 41.7% to 94.9%. However, it was not possible to use these reports
from the literature to estimate how the CFT would perform in MI, because of the wide
variation in: 1) background mycobacterial fauna present in various geographic location,
2) bTb prevalence, and 3) the amount of purified protein derivative (PPD) used for the
skin testing in different studies. It has therefore been recommended that the accuracy of
tuberculin tests should be evaluated in the geographic area intended for its use, and that
the sensitivity and specificity should be evaluated in populations naturally infected with
bTb and in similar populations free from disease, respectively.(O'Reilly, 1995)

The objectives of this study were to estimate the sensitivities of the CFT, the CFT
and the CCT used in series (CFTCCTSER), and gross necropsy (necropsy) as used under
Michigan conditions. The apparent individual-animal prevalence (AP) using CFT,
CFTCCTSER, and gross necropsy in affected herds were also compared. Results from this

study will hopefully aid USDA, foreign countries and the state departments of agriculture
in evaluating the risk of bTb infection in exported Michigan cattle as well as evaluating

the effectiveness of the current bTb eradication effort in Michigan.

29

MATERIALS AND METHODS

Summary of state-wide testing procedure.

A plan was implemented for testing all domestic cattle herds in Michigan with the
CFT (October 31, 2000, Amendment to the Animal Industry Act 466, State of
Michigan.) Cattle with “suspect” responses on the CFT, as described below, were
retested with the CCT. Animals classified as “reactors” on one CCT (or “suspect” on two
successive CCT) were submitted to the Michigan State University, Diagnostic Center for
Population and Animal Health for euthanasia and necropsy. Diagnosis of bTb-infected
animals was based on mycobacterial isolation and/or identification by polymerase chain

reaction (PCR).

CF T.

Public or private practicing veterinarians performed the CFT using an intradermal
injection of 0.1 ml of USDA bovine PPD(1 mg/ml PPD)(Angus, 1978; USDA, 1999) in
the caudal fold on either side of the base of the tail. Approximately 72 hours after initial
injection, the injection site was palpated and examined visually by the same veterinarian
who gave the injection 72 hr previously. The test was considered positive (“suspect”) if

any sign of inflammation was detected (C. Bruning-Fann, personal communication

2002).

30

CCT.

Within 7 days of the reading of a suspect CFI' result, a USDA or state
veterinarian administered the CCT. The skin thicknesses of the areas for injection of
bovine and avian PPD were measured to the nearest 0.5 mm before the injection and
again approximately 72 hours later. The CCT utilized cervical intradermal injections of
0.1 ml of USDA bovine PPD and 0.1 ml of USDA avian PPD (biologically balanced,
1mg/ml PPD) approximately 12.5 cm apart from each other. The difference (‘after’ minus
‘before’) in skin-thickness was plotted on a scattergram used to interpret the CCT results
as “negative”, “suspect” or “reactor” (USDA, VS Form 6-22D). The underlying principle
of test interpretation is that bTb-infected cattle have a greater response to bovine PPD in
comparison to their response to avian PPD. For our analyses, we considered CCT
suspects and reactors as both having a positive CCT result. Individual animals positive on
both CFT and CCT were euthanized and necropsied for further testing as described

below.

Data selection.

As of December 31, 2001, 732,661 cattle in 13,689 herds in Michigan had been
tested with the CFT and CCT. Twenty-two of these herds (2 dairy and 20 beef) were
identified as having at least one animal positive by bacterial isolation or PCR. Of these 22
herds, our study was limited to the 7 herds for which cattle were individually evaluated
by each of four diagnostic tests: necropsy, histopathologic exam, PCR and bacteriologic
culture. In the remaining 15 herds, only cattle that were suspects or reactors on the CCT

were submitted for a full necropsy, histopathologic exam, PCR or culture, and hence they

31

could not be used in this study. Of 22 herds, 20 were depopulated, and two herds elected

a quarantine and testing program.

Gross necropsy.

For animals in the seven herds with complete data, a pathologist performed
necropsy and histological examination on all cattle submitted to the Diagnostic Center for
Population and Animal Health (DCPAH), Michigan State University. Animals received
humane euthanasia and all organs including medial retropharyngeal, submandibular,
tracheobronchial, mediastinal, mesentary, ileocolic, and hepatic lymph nodes were
examined for gross lesions consistent with bTb. In this study, an animal was considered
positive on necropsy if 1 or more lymph nodes or other tissues contained focal or

multifocal abscesses or granulomas.

Histopathology.

Lymph nodes were separated into three groups; head, chest and abdomen.
Samples for histopathologic exam were examined by DCPAH and the National
Veterinary Services Laboratories (NVSL), Ames, Iowa. Formalin fixed tissues were
embedded in paraffin and cut into 6 pm sections. Histopathologic slides were prepared
using standard Hematoxylin eosin (HE) staining methods.(Prophet et al., 1992) Ziehl-
Neelson staining for the detection of acid fast bacteria was performed on tissue that was
suspect for bTb on regular HE stained samples. A sample was considered positive for

bTb if there was evidence of granulomatous inflammation associated with focal necrosis

32

or mineralization or if identification of acid-fast bacteria was made on the Ziehl-Neelson

stain.

Mycobacterial culture and identification.

Fresh samples were collected from all animals and cultured at NVSL. For six
animals, tissues were also cultured at the Michigan Department of Community Health
(MDCH). The culture procedures used at both laboratories have been described
previously.(Schmitt et al., 1997) After a series of biochemical tests used for the
identification of mycobacterial isolates, a genetic probe (Genetic probe, Accuprobes,
Gen-probe, San Diego, CA) was applied to cultures of Mycobacterium spp. as soon as
growth was evident on weekly examinations.(Fitzgerald et al., 2000) The genetic probe is
specific tO the M. tuberculosis complex in that it will react to M. tuberculosis, M.
africanum, M. microti, and M. bovis, but will not react to M. avium spp. or environmental

mycobacterial species.(Reisner et al., 1994)

Polymerase chain reaction assay.

Samples that were suspect of bTb on histological examinations were submitted
for testing by polymerase chain reaction assay (PCR) as previously described.(Miller et
al., 1997) In summary, formalin-fixed, paraffin-embedded tissue was used for DNA
extraction. To identify M. tuberculosis complex mycobacteria, the primers amplified a
123-bp fragment of insertion sequence IS6110.(Eisenach et al., 1990) Positive samples

had a band of the expected size as compared with control DNA.

33

Statistical analysis.

Mycobacterial isolation and PCR (Isol-PCR) were used in parallel as the
reference or definitive test for bTb. As such, cattle were designated as being truly
infected with bTb if they were found positive by culture, PCR examination, or both. The
apparent individual animal prevalence P(T+) was calculated as the proportion of tested
animals that were test positive (T+). The AP for all seven herds was estimated for CFT,

CFTCCTSER, necropsy and Isol-PCR (reference). The sensitivity was calculated as the

conditional probability of a test positive result given that the animal was truly bTb-
infected (P(T+lD+)). Apparent prevalence and sensitivity were reported as point
estimates with exact 95% confidence interval for binomial proportions. The chi-square
test or Fisher’s exact test was used to compare apparent prevalence among tests, and
prevalence and sensitivity between high and low prevalence herds. The Fisher exact test
was used if an observed cell value was lower than five (5). The McNemar test was used
tO compare sensitivity between tests within strata (all, moderate and low prevalence
herds). Results are shown in aggregate and stratified by factors such as moderate/low
prevalence, and number of gross lesions. Commercial software (Proc Freq, SAS Institute,

Cary, NC) was used for data analyses.

RESULTS

Of 516 cattle from the seven herds, 22 cattle had missing or erroneous laboratory

records and were therefore excluded. Therefore, 494 cattle were included in this study.

Forty-three animals were infected according to the reference test (Isol-PCR), which was

34

used as the definitive test in the calculation Of sensitivity. Of the 43 infected animals,
seven were positive by culture only, five by PCR only and 31 were positive on both
culture and PCR.

Table 3-1 Shows the relationship between test results on the CFT, CFTCCTSER,

necropsy and the isolation of different mycobacterial species. Mycobacterium spp. were
isolated from 47 of the 494 animals included in the study. Mycobacterium bovis was
isolated from 38 animals of which two animals also had Runyon Group IV
mycobacterium isolated (Table 3-1). In addition, M. fortuitum, M. smegmatis and
mycobacteria from the M. avium and M. terrae complexes were isolated (Table 3-1).

The apparent prevalence based on the CFT, CFTCCTSER, and necropsy is shown
in Table 3-2. The overall apparent prevalence based on the reference test, CFT,
CFTCCTSER, and necropsy were 8.70%, 15.8 %, 9.11%, and 8.70, respectively. Overall
for all seven herds, the prevalence by CFT was significantly higher (P < 0.005) than for
the other three tests. Herds 2 and 7 had significantly higher bTb prevalence than did the
other five herds, as measured by all three tests (P< 0.001) (Table 3-2).

The caudal fold test had the highest sensitivity (93.02%) of the three tests (Table
3-3). When Stratified by low and moderate prevalence herds, the sensitivity for the CFT
and gross necropsy were lower for the low prevalence herds than for the high prevalence
herds, although this difference was not statistically significant. Likewise, the sensitivity
of CFTCCTSER was lower (75.0%) in low prevalence herds than it was in high
prevalence herds (93.55%). When the sensitivities of the three tests were stratified by the

number of affected lymph nodes in the animal, the sensitivity of the CFI’, CFI‘CCTSER

were slightly higher when two or more affected lymph nodes were detected, and the

35

sensitivity Of gross necropsy was significantly higher (P = 0.049) when two or more

lesions were present (Table 3-4).
Herds 4, 6, and 7 each had one animal with an apparent false-negative test result

on the CFT and herds 4 and 7 each had one apparent false-negative animal on the

CFTCCTSER.

36

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Table 3-3. Sensitivity of CFT, CFI‘CCTSER, and gross necropsy using bacteriologic

culture and PCR as the reference test.

 

 

 

 

 

 

 

 

All herds

Test (T +,D+) (T-,D+) Sensitivity (%) Exact 95% CI
CFI‘ 40 93.02 80.94-98.54
CFTCCTSER 38 88.37 74.92-96.11
Necropsy 37 86.05 72.07-94.70
Low prevalence herds

Test (T+,D+) (T-,D+) Sensitivity (%) Exact 95% CI
CFT 10 83.33 51.59-97.91
CFTCCTSER 9 75.00 4281-945 1
Necropsy 10 83.33 51.59-97.91
Moderate prevalence herds

Test (T+,D+) (T-,D+) Sensitivity (%) Exact 95% CI
CFT 30 96.77 83.30-99.92
CFTCCTSER 29 93.55 78.58-99.21
Necropsy 27 87.10 70.17-96.37

 

T+, T-, D+, and D- denotes test (T +, T-) and infection (D+, D-) positive and negative out
come, respectively. (T+,D+), (T -,D+), and (D+) represent true positive, false negative,

and the total number of true positive animals, respectively.
None of the sensitivity estimates within any of the three strata (All herds, low and
moderate prevalence) were significantly different.

The estimates of sensitivity for CFI‘, CFI‘CCTSER, and necropsy were not significantly
different between the low and high prevalence herds.

39

Table 3-4. Sensitivity of CFT, CFI‘CCTSER, and gross necropsy in animals with
lesions in one, or two or more lymph nodes.

 

Screening Number of

 

tests lesions (T+,D+) ('I‘-,D-1j (D+) Sensitivity (%) Exact 95% CI
CFT 1 25 2 27 92.59 75-71-99.09
>1 15 1 16 93.75 69.77-99.84
CFI‘CCTsER 1 23 4 27 85.19 66.27-95.81
>1 15 1 16 93.75 69.77-99.84
Necropsy l 21 6 27 77.78“ 57.74-91.38
>1 16 o 16 100" 7941-100

 

Values with different superscript are significantly different.

DISCUSSION

In this study, bacteriologic culture and/or PCR were used as the reference test (i.e.
definitive test) to detect animals truly infected with bovine tuberculosis. Both of these
tests ultimately use a genetic probe that is specific to the Mycobacterium tuberculosis
complex,(Eisenach et al., 1990; Reisner et al., 1994) which includes M. tuberculosis, M.
africanum, M. microti, and M. bovis. Barring laboratory error, mycobacterial isolation
and PCR are widely accepted as 100% specific tests.(Eisenach et al., 1990; Reisner et al.,
1994) It was therefore assumed that all animals positive on the reference test (Isol-PCR)
were truly bTb-infected animals; i.e. the specificity of Isol-PCR was assumed to be

100%. This assumption allowed us to calculate unbiased estimates of sensitivity for the

40

three screening tests; necropsy, CFT and CFI‘CCTSER.(Staquet et al., 1981) Furthermore,

it was assumed that the proportion of false negative animals on the screening test(s) were
the same for truly infected animals that were positive or negative on the reference test.
This assumption was necessary to presume that sensitivity estimates were unbiased. Both
mycobacterial isolation and PCR examination may expectedly fail to detect infected
animals if lesions were not present (early infection) or lesions were present in tissues that
were not collected.(Miller et al., 1997; O'Reilly, 1995) Likewise, this may explain why
some animals were positive on culture and negative on PCR and vice versa. Even though
the reference test is assumed to have perfect specificity, the sensitivity of Isol-PCR was
probably less than perfect and false negative results were likely to have occurred.
Therefore specificity and predictive values were not calculated for the screening tests
being evaluated in this study.

The bTb infected herds were stratified into moderate prevalence herds (235%;
herds 2 and 7) and low prevalence herds ((35%; herds 1, 3, 4, 5, and 6) and these two
strata presented two distinct epidemiologic patterns. Herds with bTb low prevalence had
few lesions per infected animal. This may indicate recent transmission of the disease to a
small number of cattle, most likely from the wild deer reservoir. Herds with moderate
bTb prevalence suggest that some cattle had been infected for a long period of time
thereby allowing time and opportunity for cow-to-cow transmission to occur.

The sensitivity [P(T+|D+)]of a diagnostic test is defined as the conditional
probability that a test positive animals (T +) is in fact truly infected (D+), i.e. the
proportion of T+ animals that are truly infected. It is commonly assumed that sensitivity

and specificity of diagnostic tests are unchanging properties of the diagnostic test itself

41

and thus are independent of the circumstances of its application (i.e. the sensitivity and
/or specificity do not change among different groups of animals). This may not always
hold true, as animals in different stages of a disease or under different circumstances may
yield different test results.(Donald, 1993; Donald et al., 1994; Greiner and Gardner,
2000) This may explain what was observed in comparing the test sensitivities in the low
prevalence herds to the moderate prevalence herds. Also, the prevalence of cross-
reacting organisms may vary greatly across different ecological environments. For these
reasons, it is important that the performance of the various diagnostic tests for bTb be
evaluated under the conditions that the tests will be used under.(O'Reilly, 1995)

Though not statistically significant, this study suggests that the sensitivity of the

CFT might be higher than that of the CFTCCTSER and gross necropsy (Table 3-3). Since

the same amount of bovine PPD was used for both the CFT and CFI‘CCTSER it would be

expected that the sensitivity would be almost the same for the two test scenarios. This
trend of higher sensitivity for the CFT may be a function of the location on body on
which the test is performed, but more likely is due to the CCT being a function of the
difference in reaction between the bovine and avian antigens, rather than just a function
of the bovine antigen alone. Also, the CCT as performed by federal and state
veterinarians, may be read much more carefully and quantitatively than is the CFT
applied by private practitioners screening large numbers of cattle. However, further
studies would be needed to investigate this phenomenon.

The sensitivity of the CFT in this study is notably higher than most estimates in
other studies.(Francis and Seiler, 1978; Lepper et al., 1977; Pollock et al., 2000; Whipple

et al., 1995; Wood et al., 1991; Wood et al., 1992) However, a direct comparison among

42

studies reported in the literature is not possible because different reference tests and
preparations and concentrations of PPD were used. A study of the CCT(Roswurm and
Konyha, 1973a; Roswurm and Konyha, 1973b) estimated the sensitivity of the CCT to be
74.36% and 88.46% when using ‘reactor’ and ‘reactors’ and ‘suspects’ as test positives,

respectively. That protocol was similar to the protocol used in this study, as was their

estimate of CFTCCTSER sensitivity.

The sensitivity of gross necropsy is often used (together with other tests) as part
of a reference test.(Lepper et al., 1977; Pollock et al., 2000) In this study, the reference
test was assessed independently from gross necropsy findings, which allowed us to

estimate the sensitivity of gross necropsy as a diagnostic assay. The sensitivity of
necropsy (86.05%) was almost as high as CFTCCTSER (88.37%). Furthermore, the

sensitivity of gross necropsy increased to 100% when 2 or more lesions were present.
Such animals with multiple lesion sites would expectedly shed greater numbers of
infective Mycobacterium bovis and thus would be a more important source of disease
transmission. The gross post-mortem necropsy exam can perhaps be viewed as the “upper
detection limit” of any practical slaughter-based system for bTb.

False negative results were most infrequently found with the CFI‘, followed by
the CFTCCTSER and then by gross necropsy. Several explanations have been suggested

for this inability of the skin tests to detect infected animals, including anergic cattle,
poorly injected PPD, variance in potency of PPD, loss of potency of PPD over time,
mistaken animal identification, and operator error.(Lepper et al., 1977; Monaghan et al.,

1994)

43

The focus of our study was not to investigate the specificity (or proportion of
false-positive results) of the screening tests, however it is worth noting that only one
animal out of 11 animals infected with atypical mycobacteria reacted to the CFT (Table

3-1, column 3). This animal was infected with M. fortuitum. No false positive results

were observed on the CFTCCTSER. Possible explanations for why the CFT was positive
and the CFI‘CCTSER was negative on an animal infected with M. fortuitum might relate

to a higher specificity of the CFTCCTSER or the animal being co-infected with M. bovis.

Also, a greater reaction on the avian component of the CCT (including cross-reactions)
tend to make the CCT yield negative results. Six bTb-infected animals had no detectable
lesions on necropsy. This may be due to early infection (insufficient time for lesion
development) or inhibition of lesion growth by the hosts’ immune system.

It is well accepted that the CFT and CFTCCTSER are more suited to the detection

of infected herds rather than the detection of infected cattle, i.e. some bTb-infected
animals will escape detection when the skin tests are used to assess the infection status of
individual animals. In this study, bTb positive animal would have been undetected in two

of the seven infected herds (29%) if only the CFI‘CCTSER reactor animals were culled

rather than depopulating the entire herd. This finding supports a disease control policy of
total herd depopulation over a test and slaughter approach, because findings in this study
suggest the test and slaughter approach would fail to detect all infected animals in

approximately 29% of the herds.

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Microbiol 32, 2995-2998.

Roswurm, J .D., Konyha, 1973, The comparative cervical tuberculin test as an aid to
diagnosinf bovine tuberculosis. Proc. Annu. Meet. U.S. Anim. Health Assoc. 77, 368-
389.

Schmitt, S., Fitzgerald, S., Cooley, T., Bruning-Fann, C., Berry, D., Carlson, T., Minnis,
R., Payer, J ., Sikarskie, J, 1997, Bovine tuberculosis in free-ranging white-tail deer in
Michigan. J Wildlife Dis 33, 749-758.

Staquet, M., Rozencweig, M., Lee, M., Muggai, F.M., 1981, Methodology for assessment
of new dichotomous diagnostic tests. J. Chronic Dis. 34, 599-610.

USDA, A. 1999. Bovine Tuberculosis Eradication: Uniform Methods and Rules,
Effective January 22, 1999, (United States Department of Agriculture), pp. 1-34.

Whipple, D.L., Bolin, C.A., Davis, A.J., Jamagin, J .L., Johnson, D.C., Payer, J .B., Saari,
D.A., Wilson, A.J., Wolf, M.M., 1995, Comparison of the sensitivity of the caudal fold

skin test and a commercial gamma-interferon assay for diagnosis of bovine tuberculosis.
Am J Vet Res 56, 415-419.

46

Wood, P.R., Comer, L.A., Rothel, J .S., Baldock, C., Jones, S.L., Cousins, D.B.,
McCormick, B.S., Francis, B.R., Creeper, J ., Tweddle, N.E., 1991, Field comparison of
the interferon-gamma assay and the intradermal tuberculin test for the diagnosis of
bovine tuberculosis. Austr Vet J 68, 286-290.

Wood, P.R., Comer, L.A., Rothel, J .S., Ripper, J .L., Fifis, T., McCormick, B.S., Francis,
B., Melville, L., Small, K., De Witte, K., Tolson, J ., Ryan, T.J., de Lisle, G.W., Cox, J .C.,
Jones, S.L., 1992, A field evaluation of serological and cellular diagnostic tests for
bovine tuberculosis. Vet Micro 31, 71-79.

47

CHAPTER FOUR

ESTIMATION OF SENSITIVITY AND SPECIFICITY OF BOVINE TUBERCULOSIS

SKIN TESTS IN MICHIGAN WHEN A PERFECT REFERENCE TEST IS NOT

AVAILABLE.
ABSTRACT
Four-hundred-and-ninety-four cattle from seven herds were tested with the caudal

fold and comparative cervical tuberculin tests to detect infection with Mycobacterium
bovis as part of the bovine tuberculosis eradication program in Michigan. Bayesian
inference was used to estimate the sensitivity and specificity of the caudal fold tuberculin
test and the comparative cervical tuberculin test in four different ‘two-population-two-
tests’ latent-class models. The two tuberculin skin tests could not be used in the same
model, hence the sensitivities and specificities of the two tuberculin skin tests were
evaluated against results of mycobacterial culture. Possible dependence between the
caudal fold and comparative cervical tests, and mycobacterial culture was investigated
using a conditionally independence model and three models allowing for dependence
between sensitivities and specificities. One of the dependence models assumed perfect
specificity for mycobacterial culture. There was a statistically significant negative
correlation between the comparative cervical tests and mycobacterial culture, however
the dependence between the caudal fold test and mycobacterial culture was not
significant. Assuming conditional dependence between both skin tests and mycobacterial
culture, the Bayesian estimates and posterior 95% credible intervals of the sensitivity and
specificity of the caudal fold and comparative cervical tests were 0.854 (0563-0975) and

0.939 (0899-0982), and 0.758 (0475-0930) and 0.986 (0962-0999), respectively. The

48

estimates of sensitivity and specificity obtained in this study generally agree with those

reported from other studies in the United States.

49

INTRODUCTION

Bovine tuberculosis (bTb) is an infection with Mycobacterium bovis, which
affects a wide range of domestic animals, particularly cattle, goats, farmed and wild deer
and several wildlife species.(Bruning-Fann et al., 2001) Bovine tuberculosis is also a
concern to public health because humans may become infected by inhaling infected
droplets or ingesting contaminated meat or milk. The disease is of substantial economic
concern to livestock producers, because infected herds most commonly are depopulated
for disease control purposes and national and international markets may be lost due to
quarantines and importation limitation. In addition, movement bans and rigorous testing
schemes may be imposed on herds in areas where bTb is present in the cattle population.

Begun in 1917, the US bovine tuberculosis eradication program has successfully
used the tuberculin skin tests to eradicate bTb from most areas of the United States.(Frey
1995) In 1995, a bovine with bTb was identified in Michigan, whereupon it was decided
to test all cattle in Michigan with the caudal fold tuberculin test (CFT) (October 31, 2000,
Amendment to the Animal Industry Act 466, State of Michigan). Up until January 2002,

732,661 cattle in 13,689 herds have been tested with a serial skin testing protocol
(CFI‘CCTSER) using the CFT as a screening test for all animals over the age of 12

months, with CFT-positive animals (‘suspects’) being re-tested with the comparative
cervical tuberculin test (CCT).(Norby etal., 2003)

Several authors have reported estimates of the sensitivity (Se) and specificity (Sp)
of these two skin tests (CFT and CCT) used in cattle.(Francis and Seller, 1978; Gaboric

et al., 1996; Lepper et al., 1977; Leslie and Hebert, 1975; Leslie et al.,t 1975; Leslie et al.,

50

1975; Pollock et al. 2000; Roswurm and Konyha, 1973; Whipple et al., 1995; Wood et
al., 1991; Wood et al., 1992) However, the estimates vary considerably, most likely
because of the difference in 1) geographic location of the cattle and hence the background
mycobacterial fauna present, 2) bTb prevalence, 3) the amount of purified protein
derivative (PPD) used for the skin tests, and 4) the reference tests (‘gold standards’) the
skin tests were evaluated against, and whether or not the tests were used independently,
in series, or in parallel. Most laboratories consider mycobacterial culture (CULT) to be
the definitive test for diagnosis of bTb, although polymerase chain reaction (PCR) is
gaining rapid acceptance.

Both CULT and PCR are considered to have almost perfect specificity (very close
to 1.0) because they use a genetic probe for final identification.(Miller et al., 1997;
Schmitt et al., 1997) Using CULT and/or PCR allows for estimation of Se of the skin
tests, but not the Sp of the skin tests.(Gart and Buck 1996; Staquet et al., 1981) In this
scenario, it is not possible to obtain estimates of Sp of the skin tests.

Using, novel statistical methodologies, it possible to estimate the disease
prevalences, Se, and Sp when each animal’s true disease status is unknown.(En¢e, et al.,
2000) Prevalence, Se, and Sp may be estimated using a latent-class analysis, such as
maximum likelihood estimation using the Newton-Raphson algorithm(Georgiadis et al.,
1998; Hui and Walter, 1980; Tanner 1996), the expectation-maximization
algorithm(Dempster et al., 1977; Singer et al., 1998; Weng, 1996) or simulation-based
Bayesian inference.(Dendukuri and Joseph, 2001; Enoe et al., 2001; Georgiadis et al.,

2003; Johnson et al., 2001; Joseph et al., 1995)

51

If animals in one population are tested with two conditionally independent
dichotomous tests, there are three independent cells (3 degrees of freedom) available to
estimate five parameters (prevalence, Se and Sp of test 1, and Se and Sp of test 2 based
on a likelihood estimation approach. Hence the model is unidentifiable, i.e. there are an
infinite number of possible solutions to the model. However, data on two populations are
available, there are six independent cells and, with the addition of another prevalence
parameter, there are now six parameters to estimate, and hence a unique solution is
possible.(En¢e et al., 2000; Hui and Walter, 1980; Johnson et al., 2001; Singer et al.,
1998; Walter and Irwig, 1988; Weng 1996)

However, if a ‘conditional independence model’ is used when the diagnostic tests
are correlated, biased estimates of prevalence, sensitivity and specificity are to be
expected.(Black and Craig, 2002; Dendukuri and Joseph, 2001; Gardner et al., 2000;
Georgiadis et al., 2003; Torrance-Rynard and Walter, 1997; Vacek, 1985) Several
authors have proposed models allowing for pairwise dependence between tests using a
classical frequentist approach.(Qu and Hadgu, 1998; Qu et al., 1996; Yang and Becker,
1997) In these models, at least four diagnostic tests are required to model pairwise
dependence for Se and Sp.(W alter and Irwig, 1988) Bayesian approaches to estimate Se
and Sp of two dependent tests applied to subjects in one population have been
described.(Black and Craig, 2002; Dendukuri and Joseph, 2001). Bayesian models using
test results from two dependent tests applied to two populations have also been
proposed.(Georgiadis et al., 2003). Again, all parameters in the likelihood functions for
these models are generally unidentifiable, i.e. there are eight parameters to estimate, but

only six degrees of freedom. However, this dilemma can be overcome by assigning

52

informative prior information to some of the parameters when such information is
available.(Black and Craig, 2002; Dendukuri and Joseph, 2001; Georgiadis et al., 2003)
The objectives of this study were to estimate Se and Sp of the CFT (scenario 1)

and the CFI‘ and CCT used in serial interpretation (CFTCCTSER) (scenario 2). Bayesian

models were used to estimate Se and Sp of the two testing scenarios applying CULT as
the second test for both scenarios. An expansion of the model proposed by Black and
Craig (2002) was used to model possible dependence between tests. Results from this
model were compared to a conditional independence model, a model assuming perfect

specificity for CULT, and a model proposed by Georgiadis et al., (2003).

MATERIALS AND METHODS.

Animals

As of June 2003, 30 cattle herds in Michigan had been diagnosed with bovine
tuberculosis since the start of the current outbreak in 1995. Cattle in seven of these herds
were used in this study because all cattle in these herds were individually and

independently evaluated by both CFTCCTSER and CULT.(Norby et al., 2003) In the

remaining 23 bTb positive cattle herds, only cattle that were ‘suspects’ or ‘reactors’ on

the CCT were submitted for full necropsy and CULT; hence they were not eligible for

this study.

53

Diagnostic tests and testing procedure.

The statewide testing procedure and implementation of the CFT and CCT, and
CULT has been described elsewhere.(Norby et al., 2003) In short, the CFI‘ was
performed by public or private practicing veterinarians, using an intradermal injection of
0.1 ml of USDA bovine PPD (1mg/ml) in the caudal fold on either side of the base of the
tail.(USDA and APHIS, 1999) The injection site was palpated approximately 72 hours
later, and the test was considered positive (“suspect”) if there was any sign of
inflammation.(Bruning-Fann, personal communication, 2002) If the CFI‘ was “suspect”,
a USDA or state veterinarian administered the CCT within 7 days of when the CFT was
read. For the CCT, 0.1 ml of USDA bovine PPD and 0.1 ml of USDA avian PPD
(biologically balanced, 1mg/ml) were injected intradermally on the neck approximate
12.5 cm apart. The thickness of the skin was measured before injection and approximate
72 hours after injections. The difference (‘after’ minus ‘before’) in skin-thickness was
plotted on a scattergram (USDA, VS, Form 6-22D) used to interpret the CCT results as
“negative”, “suspect”, or “reactor”. In practice and in this study, both “suspect” and
“reactors” were classified into one group considered “positive” on the CCT. Because the
CCT was only performed on animals that were suspects on the CFT, it was not possible
to estimate Se and Sp of the CCT used as an independent test. Necropsy was conducted
at the Diagnostic Center for Population and Animal Health at Michigan State University,
and mycobacterial culture and identification was performed on fresh samples at the
National Veterinary Services Laboratories, Ames, Iowa. For six animals, tissues were
also cultured at the Michigan Department of Community Health.(Norby et al., 2003) The

necropsy and culture procedure has been described elsewhere.(Norby et al., 2003;

54

Schmitt et al., 1997) A very specific genetic probe is used with CULT to classify
mycobacterial species into isolates belonging to the Mycobacterium complex, which
include M. bovis, tuberculosis, africanuum, and microtii.(Schmitt etal., 1997) Since it
was unlikely that cattle in Michigan were infected with mycobacteria belonging to the
Mycobacterium complex other than M. bovis, we assume that all isolates that were

positive on culture are in fact M. bovis.

Latent-class models
The parameters of interest were the Sc and Sp of the CFT and CFTCCI‘SER. The

technique used in this study was a two-population, two-test approach in which it was
assumed that the disease prevalence was different in the two populations, but Se and Sp
remained constant in both populations.(Georgiadis et al., 2003) As argued by Georgiadis
et al. (2003), a two-population-two test scenario was employed because addition of a
“second population” in the fixed effects model increases the degrees of freedom to 6 as
compared to three degrees of freedom in a one-population-two test model. If the two
tests are assumed to be conditionally independent, the model is then identifiable because
there are six degrees of freedom available to estimated 6 parameters, i.e. 2 prevalences,
two sensitivities and two specificities. If the two tests are not conditionally independent
then two extra parameters (a total of eight) needs to be estimated, resulting in eight
parameters.(Georgiadis et al., 2003) Even though the model is no longer identifiable, the
two-population-two-test model decreases the reliance upon additional prior

information.(Georgiadis et al., 2003)

55

The cattle in the seven herds were divided into two subpopulations(En¢e et al.,
2001; En¢e et al., 2000; Willeberg et al., 1997) based on the age of the cattle; cattle 2
four years of age comprised population 1 and population 2 was < four years of age. Se

and Sp were evaluated using the test results of CULT as the second test following CFT
(Scenario 1) and following CFTCCTSER (Scenario 2). Originally, the seven herds were

‘naturally’ divided into two herds with moderately high and five with moderately low
apparent prevalences(Norby et al., 2003), and the analyses were also performed on this
dataset. Four different Bayesian models were used to estimate these parameters: 1) a
conditional independence model using non-informative (uniform) prior information all
parameters (M1a)(En¢e et al., 2000) and a conditional independence model using
informative priors on prevalences and Sp of CULT (M1b)(Johnson et al., 2001), 2) an
extension of a conditional dependence model as described by Black and Craig (2002)
(M2), 3) a conditional dependence model assuming that Sp of CULT was perfect (M3),
and 4) a conditional dependence model as described by Georgiadis et al. (2003) (M4).
The models proposed by Black and Craig (2003) and Georgiadis et al. (2003),
respectively, are based on estimation of the latent cell counts in two two-by-two tables
representing a cross classification of the results on the two tests in the two populations
(see Table 4-7 in the appendix). In essence, the two models are identical, however, the
model by Georgiadis et al. (2003) is a reparameterization of the model proposed by Black
and Craig (2003), using a one-to-one transformation of four parameters (pl 111, poo“), and
the sensitivity and specificity of test 1) (appendix A). Hence, all the full conditionals
were recognizable and could be sampled using Gibbs sampler(Gelfand and Smith, 1990;

Tanner 1996). In contrast the full conditional densities, two parameters in M2 and one

56

parameter in M3 were unrecognizable and were sampled using Metropolis-Hastings
(MH) algorithm(Chib and Greenberg, 1995). The remaining six parameters were
sampled using Gibbs sampler (Appendix A). Bayesian inference was performed using
Markov-Chain Monte Carlo (MCMC) simulation.

Posterior point estimates and 95% credible intervals (PCI) for the six parameters
were defined as the median, lower 2.5% and upper 97.5% percentiles of the posterior
distribution, respectively.(Gelman et al., 2000) The PCI is a 95% Bayesian (probability)
interval where parameters have a 95% probability of being included in the PCI.(Gelman
et al., 2000) A more detailed description of the models and Bayesian sampling methods
are presented in Appendix A.

A ‘bum-in’ of 2000 MCMC cycles were used to assure that the models had
reached convergence.(Tanner, 1996) This was monitored by plotting the parameter
estimates for each cycle. Then, 10,000 MCMC cycles were used to estimate the posterior

densities for prevalences, Se’s, and Sp’s.

All four models were coded in the IML procedure in SAS (SAS Institute, Cary,

NC) (Appendix B).

Prior elicitation
Prior information was elicited as beta distributions (Beta(a; ,6» for the

prevalences, sensitivities, and specificities.(Joseph et al., 1995; Mendoza-Blanco et al.,
1996) Beta distributions were chosen because they are highly flexible and the full
conditional distributions of the parameters are also then beta distributions, facilitating

easy sampling and involve relatively simple calculations.(En¢e et al., 2000)

57

The conditional dependence models require specification of prior information on
at least some of the six parameters, in contrast to the conditional independence model
where no a priori knowledge is necessary about the parameters (the model is fully
identifiable). Use of priors effectively places restrictions on the parameter space by only
including regions where the parameter values are likely to be concentrated. We chose to
place prior information on prevalences, and the Sp of CULT, because we believed that
we had relatively good information regarding these parameters. Choosing a ‘most likely’
value (prior mean) and a value for the lower 5th percentile of the prior density for the
parameter of interest, it was then possible to specify the hyperparameters for a beta
distribution that fits those specifications.

The mycobacterial culture method uses a very specific genetic probe, and it was
therefore assumed that the specificity of CULT was 1.0, or very close to 1.0. The most
likely value for Sp of CULT was set to 0.999 and the 5th percentile to 99 providing
Beta(360.4, 1.36) for M2 and M4. The priors on Se and Sp of either CFT or CFTCCTSER
were always non-informative [Beta( 1 ,1 )].

We did not have exact prior knowledge on the bTb prevalence in the two populations.
Hence the most likely value was assumed to lie between the apparent prevalence (APP)
as obtained by CULT and the CFT (Table 1). The most likely value was determined as
the mean of the APP for CFT and CULT, and the lower 5th percentile was set at the APP
for CULT, because the specificity of CULT is close to one and false positive results were
unlikely. The priors for prevalence were Beta(l3.63, 57.94) for the young animals and

Beta(5.98, 66.68) for the older animals (T able 4-1).

58

Table 4-1. Apparent prevalence (APP; %) in old and young subpopulations based
upon the caudal fold tuberculin test (CFT) and Mycobacterial culture (CULT).

 

 

 

Age 2 4 years Age < 4 years
APP (%) C1I APP (%)s CII
CFT 22.5 16.8, 28.9 10.4 7.2, 14.4
CULT 13.8 9.3, 19.4 3.7 1.9, 6.5
Mean 18.15 7.05

 

I95% Confidence interval.

Sensitivity analysis

A sensitivity analysis was performed to investigate how sensitive the posterior
inference was to the priors that were placed on prevalences and the Sp of CULT.(Enoe et
al., 2003) Altemately, 1) non-informative priors were placed in succession on one of
these three parameters, while the other two were held at their original beta distribution
(constant). 2) Diffuse, but correctly specified priors were placed on Sp of CULT, by
gradually lowering the 5’h percentile to 0.85, and the priors on prevalence were held
constant. 3) Mis-specified priors were placed on Sp of CULT_ i.e., the prior median of
this new prior was centered at 0.95, 0.90, and 0.85, and the priors on prevalence were
held constant. 4) Diffuse, but correctly specified priors were placed on the two
prevalences. The median of the prevalence in population one held at 0.1815 and the 5th
percentile was lowered to 0.1 and 0.05 and increased to 0.25. For population 2, the
median was held at 0.0705 and the 5th percentile lowered to 0.01 and 0.005 and increased
to 0.14. 5) Mis-specified priors were placed on prevalences in the same manner as
described for the specificity, hence the medians were 0.1 and 0.25, and 0.05 and 0.14 for

populations 1 and 2, respectively.

59

RESULTS

Twenty-two of 516 cattle in the seven herds had erroneous records and were
excluded from the dataset. Therefore, 494 cattle were included in the study. The mean
age in population 1 was 70.6 months (std =19.0) and 15.7 months (std = 11.1) in
population 2. The apparent prevalences (APP) based upon CFT and CULT are shown in

Table 4-1. Cross-classification of observed counts for scenario 1 (CFT and CULT) and

scenario 2 (CFTCCTSER and CULT) are shown in tables 2 and 3, respectively.

Table 4-2. Testing Scenario #1: 2 x 2 contingency table showing the observed
counts for the caudal fold tuberculin test (CFT) and Mycobacterial culture (CULT) in
populations 1 and 2.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Population 1 Population 2
CULT CULT
+ - + -
+ 24 20 44 + 11 20 31
CFT - 3 149 152 CFT - 0 267 267
27 169 196 11 287 298

 

Table 4-3. Testing Scenario #2: 2 x 2 contingency table showing the observed
counts for the caudal fold and comparative cervical tuberculin tests used in serial

interpretation (CPTCCTSER) and Mycobacterial culture (CULT) in populations 1 and 2.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Population 1 Population 2
CULT CULT
+ - + -
CFT- + 23 7 30 CFT- + 10 5 15
CCTSER - 4 162 166 CC’I‘SER - 1 282 283
27 169 196 11 287 298

 

The overall observed agreement for the 494 animals were measured as the
proportion of cattle with concordant test results (451/494=0.913 and 477/494=0.966) and

by the Kappa statistic (1c=0.576 and K = 0.777) for scenario 1 and 2, respectively. The

60

proportion with concordant results for populations 1 and 2 were 173/196 = 0.883, K =
0.609 and 278/298=0.933, K = 0.496 for scenario 1 and 185/ 196:0.944, K=0.774 and
283/298:0.950, K=0.759 and for scenario 2.

The estimated prevalences, Se’s and Sp’s from all four Bayesian models for both
testing scenarios are presented as posterior medians (point estimates) and PCI’s in tables
4 and 5. For example, for M2 in scenario 1 (CFT and CULT), the point estimate for Se
of the CFT was 0.854 and the 95% PCI was (0.563,0.975). There was no significant
correlation between disease-positive animals for models M2, M3, or M4 in either of the
two scenarios, as the 95 % PCI’s for correlation between disease positive animals

included 0. However, the correlation between disease negative animals was significant
for CFTCCTSER and CULT and very close to being significant for CFT and CULT

because the 95% CI almost included 0; the lower 25‘” percentile was —0.004 and -0.005
for models 2 and 4, respectively. Hence, for this study, the estimates of the conditional
dependence model (M2) were selected as being the preferred method of analysis.

Sensitivity analyses were performed on M1 and M2 to assess the effect of less
informative prior information on the Sp of CULT and the two estimates of
subpopulations prevalence. First, the prior information on Sp2 was made more diffuse by
gradually lowering the 5th percentile to 0.85, and by using a non-informative prior. The
resulting point estimates for all parameters were within the range on the original 95 % PCI
for the model using original priors for all analyses in both scenarios, except when using a
non-informative prior for scenario 2, in which case the point estimate using the flat prior
was 0.001 outside of the original 95% PCI. All point estimates obtained with the

sensitivity analyses were within 0.016 of the parameters estimates obtained by the

61

original prior for Sp of CULT only when the point estimate was changed from 0.999 to
0.95 and the 5th percentile was lowered to 0.80, did the point estimate of the sensitivity
analyses fall outside the original 95% PCI. Similar results were seen when analogous
adjustments were made to the priors of the two prevalence estimates. Changing the prior
for the prevalence in either of the two populations had the greatest effect on the
sensitivity estimates. Making the prior more diffuse had less effect on the sensitivity
estimated than did changing the location of the peak of the prior. The largest differences
in sensitivity estimates were most commonly seen when a non-informative prior was used
or when the prior’s peak was changed considerably for the two prevalence estimates
(results not shown).

Originally, the seven herds were ‘naturally’ divided into two populations based on
the herd apparent prevalence. Two herds had moderately high prevalence and 5 herds had
low prevalence.(Norby et al., 2003) The two prevalence estimates, Se’s, and Sp’s were
also estimated using this scenario. New priors for the prevalences were created as

described before and the same prior for Sp2 was used. The sensitivity estimates were
0.896 and 0.843 for CFT and CFI‘CCTSER, and 0.806 and 0.789 for CULT in the two

populations. Estimates of posterior medians of specificity estimates were 0.862 and 0.969

for CFT and CFTCCTSER, and 0.997 and 0.996 for CULT in the two scenarios

respectively.

62

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20>:0::2 032603 823006 003 0.0230600: :35 6:0 00:20:06 86003 022: .:0 :02608 022: 00 60::000:6 0:0 0338806 220 :0: 00:08:00
8206 020608 80.2 220 :0: 2.2.2206 0:82:20 20233030928 6:0 2302.00.21.28 :02:0:0:6:0::2 202.200 :2 600: 0:00: 8200:0322: 2003.200
0>2:0:06800 6:0 :00: 8208038 620.: 206000 022: :0: 68 0062021220060 6:0 208 0063628003325 000:020>0:6 6-0 030 .2.

DISCUSSION

In this study, we estimated the sensitivity and specificity of the CFI‘ and
CFTCCTSER as they were applied to cattle in seven herds in the northeastern pan of the

lower peninsula in Michigan. We used CULT as the second test in our two-population,
two-tests scenarios to accomplish that goal. Because the correlation between the disease
negative animals was significant for scenario 2 and very close to being significant for
scenario 1, we decided that the results from the conditional dependence model (M2)
generally produced the best estimates.

Our estimates of the Se of the CFT were very similar to other US estimates.
(range:0.804-O.849).(Anonymous, 1992; Gaboric et al., 1996; Whipple et al., 1995) The
estimates of Sp of the CFT are similar to estimates reported by the USDA(Anonymous,

1992), and higher than reported by Gaboric et al., (1996). However, the Sc estimates for
CFI‘ and CFI‘CCTSER are lower than estimated reported by Norby et al., (2003) in which
independence between the skin tests was assumed and the CULT was assumed to be the
definitive test.

The three dependence models performed similarly, with the largest variability

observed between Se estimates for CFT and CFI‘CCTSER. The point estimates for each

of the parameters were within the 95% PCI of the other models for all the estimable
parameters, for both scenarios. In general, the Se estimates were slightly lower for the
dependence models as compared to the estimates from the independence model.
However, the parameter estimates for prevalence and Sp’s were very similar for all the

models. Since the correlation between disease negative animals was very low (0.096) for

65

the CFT and CULT scenario and moderately low (0.218) for the CFTCCTSER and CULT

scenario, we would not expect that there would be a large difference between parameter
estimates for the independence and dependence models. Similar observations were made
in simulation studies by Georgiadis et al., (2003). The 95% PCIs for Se’s in the three
dependence models were as expectedly wider than for the independence model, reflecting
the additional uncertainty of estimating more parameters with the same
information.(Georgiadis et al., 2003)

For all four models, we also observed that the 95% PCI’s were wider for the Se
than for the Sp estimates. This was most likely explained by the low ‘overall’ disease
prevalence, and consequently less information on which to base the Se estimates as
compared to Sp estimates. Using prevalence estimates from M2 in scenario 1, there were
only approximately (0.204*196+0.063*298) 58 disease positive animals in our total
sample. A larger sample size or higher prevalence would most likely have produced
more stable parameter estimates with narrower PCI’s.

The 95% PCIs for the prevalence estimates were of approximately equal width for
all four models, and were virtually identical for the 3 dependence models. In both of the
two scenarios, Se and Sp estimates for CULT were under our assumptions expected to be
equal. However, the point estimates for Se of CULT was between 0.072 and 0.088 for
the four models in scenario 1 as compared to scenario 2. This discrepancy may in part be
explained by the uncertainty in the data and the low disease prevalence. The specificity
estimates for CULT were similar for the two scenarios.

Se and Sp estimates of a diagnostic test may vary within herds or

populations.(Donald et al., 1994; Greiner and Gardner, 2000) In our analyses, it was

66

possible that the performance of the skin tests and CULT may have varied within herds
based on the infection status of the animals. Perhaps animals that are heavily infected
react more readily to the skin tests than animals with more recent or less severe infection.
The Se estimates of CFT were slightly lower and Se estimates were slightly higher for the

CFI‘CCTSER when the population was divided based on age rather than upon herd

apparent prevalence. The Sp estimates were significantly higher (based on the 95% PCI)
for the CFT and slightly higher for the CFTCCTSER when comparing the results based on
the two methods we used to obtain two populations. This suggests that Se and Sp may
not be constant within subpopulations. Hence, the Se and Sp estimates were overall
estimates for all the populations in the study, and extrapolation between populations
should be done with caution.(En¢e et al., 2000)

Because a perfect reference test (gold standard) was unavailable in this study, we

estimated Se and Sp of the CFT and CFTCCTSER using Bayesian inference.(Enoe et al.,

2000) In the two-population, two-test scenario proposed here, it is possible to estimate
the six parameter (two prevalences, two Se’s, and two Sp’s) without prior knowledge on
any of the parameters, if it is assumed that the tests are independent and that the Se’s and
Sp’s are constant across populations, i.e. the model is identifiable. However, it was not
certain that the skin tests and CULT were conditionally independent, and model(s) that

accounted for possible dependence were needed. Therefore, two extra parameters
needed, p11” and poop, respectively(Black and Craig, 2002), and hence the two-

population, two-test scenario was unidentifiable. Additional degrees of freedom can be
acquired by increasing the number of populations under the assumption that Ses and Sps

are constant across populations. However, it was not feasible to divide our initial

67

population of 494 cattle into more than two subpopulations because of the low number of
truly infected animals. Furthermore, it is questionable whether an addition of degrees of
freedom will improve the model.(Georgiadis et al., 2003)

We chose to use a Bayesian approach as compared to a maximum likelihood
approach because the problem of an unidentifiable model could be overcome by using
prior information on some of the parameters.(Black and Craig, 2002; Georgiadis et al.,
2003) Our independence and dependence models performed well, and converged within a
few hundred MCMC cycles. We preferred the approach described by Black and Craig
(2002), because it is easily extended to multiple populations and tests. Model M3 can
also be used in scenarios where it is reasonable to assume that one of the tests have
perfect specificity.

Several factors may affect the estimates of Se and Sp, including the stage of
disease, length of exposure, animal age, prevalence of infection in the herd, and ksdjfk

immune status of the host.(Greiner and Gardner, 2000) For bTB, the Sc of the skin tests
may be lower for pre-allergic, inactive, and anergic stages of the infection.(Greiner and
Gardner, 2000) When we divided our sample according to the age of animals, prevalence
(as determined by M2-M4) was almost 0.15 higher in older cattle as compared to younger
cattle. This may be attributed to the fact that older animals are more likely to have
generalized and more active infections, whereas younger animals will be more likely to
have acquired their infection more recently, and hence not showing as imminent reactions
to the skin tests.(Norby et al., 2003) It is likely that animals from herds with a high
prevalence may have older and more established infections because such herds may have

been infected for a longer period of time. Our analysis does not account for either of

68

these biological factors, and it is hence possible that our sensitivity estimates for both
skin tests and CULT maybe slightly overestimated, and specificity estimates slightly

underestimated.

The sample of animals used in this study was not a random and blinded sample
of bTb positive and negative animals.(Greiner and Gardner, 2000) However, the CFT
and CCT were performed before it was known if these herds would be deemed to be truly
infected. Because all our models performed very uniformly, the internal validity of our
study was likely high. This does not automatically signify that the external validity of the
study also is high. However, our estimates of Se and Sp of the skin tests are close to
previously published results from the U.S.(Anonymous 1992; Gaboric et al., 1996;
Whipple et al., 1995) It should be noted, however, that when disease prevalence
decreases when an eradication program progresses, it is likely to negatively affect

‘working’ estimates of Se and Sp of the skin tests.(Greiner and Gardner, 2000)

69

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73

APPENDIX A

For all the models, let m, i = {1,2} represent the true prevalence in populations 1
and 2, and let S 1, 52, represent the sensitivities, and C1 and C2 represent the specificities
of tests 1 and 2, respectively. The results of the two tests, submitted to all animals in the
two population, are presented as counts {"ijk} in two 2x2 tables (T able 4-6), where the
first subscript 1', denote the population, the subscript j denote the results of test 1 (T1: CFT
or CFTCCTSER), and k denoting the result of test 2 (T2: CULT), (i = {1,2} and j,k =
{0,1 }). If the true disease status of each tested animal was known, the count in each cell
in the two 2 x 2 tables can be divided into two counts, where nil-k = aijk + bijk. Here, ail-k
and bijk represent animals that are truly disease positive and disease negative,

respectively. The data can then be summarized in four separate 2 x 2 tables (Table 4-7).

Table 4-6. Two 2 x 2 contingency tables showing responses of two binary
diagnostic tests.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Population 1 Population 2
Test 2 Test 2
+ - + -
Test 1 + "111 "110 nll- Test 1 + "211 "210 "21-
' "101 "100 "to ' "201 "200 "20-
111.] nm 111.. "2.1 112.0 n2..

 

74

Table 4-7. Four 2 x 2 contingency tables showing responses of two binary tests
classified by true disease status.

Disease positive animals

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Population 1 Population 2
Test 2 Test 2
+ - + -
Test 1 + 0111 0110 011- Test 1 + ‘1211 0210 021-
' 0101 0100 010- ' 0201 0200 020-
01.1 (11.0 al.. 02.] (12.0 02..

 

Disease negative animals

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Population 1 Population 2
Test 2 Test 2
+ - + -
Test 1 + bin bno bu. Test 1 + b211 bzio 521-
‘ bim bloc b10- ‘ bzm bzoo b20-
b1.1 b1.0 b1” b2.] b2.0 172..

 

The prevalence in the two populations, Se’s and Sp’s of the two tests may be
estimated if the true disease status is known. However, in this study, the true disease

status is unknown (because a perfect reference test was not available), and it is only
possible to observe the sums of disease positive and negative animals (nil-k = aijk + bijk)-
Hence the 2 x 2 table for each of the two populations (Table 4-6) is the result of
collapsing the two tables of latent data for each population (Table 4-7). The use of latent

data is a key component of algorithms that rely upon data augmentation such as the

expectation-maximization algorithm as well as some forms of Monte Carlo inference,

including Gibbs sampler.(Tanner, 1996)

Conditional independence model (M I ).
Let p101: P(T1 = j, T2 = kl D = I), where l={0,l }, represent the corresponding joint

classification probabilities for the latent data of disease positive and negative animals in

75

the two populations, where the subscript I denotes the true disease status of an animal (0

= negative, and 1 = positive).(Black and Craig, 2002; Singer et al., 1998) The

classification probabilities were assumed to be equal across populations. As the two tests

were considered to be independent

ij1I=P(T1 =13 T2 = kID = 1)

=p(T. = 110 = mm = le = I)

= Pj-11P-k11

Hence, the classification probabilities are the product of the conditional probabilities

(Table 4-8)
P1111 =5152 P1110: (1-C1)(1-C2)
P1011 =Sl(1-Sz) P1010= (1-C1)C2
P0111 = (1-51)52 P0110=(1-C2)
P0011 = (1-SI)(1-Sz) P0010 = C1C2

Table 4-8. Classification of probabilities as explained by sensitivities and
specificities.
Disease positive animals

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Population 1 Population 2
Test 2 Test 2
+ - + -
Test 1 + P11111 P11011 Sl Test 1 + P21111 P21011 51
' Prom 1”10011 1-51 ' P2010 P20011 1-51
52 l-Sz 1 S2 l-Sz I

 

76

Table 4-8 (continued).Classification of probabilities as explained by sensitivities and

specificities.

Population 1

Disease negative animals

 

 

 

 

 

 

 

 

Population 2

 

 

 

 

 

 

 

 

Test 2 Test 2
+ - + -
Test 1 + P1100 P11010 1-C1 Test 1 p2mo P21010 l-Cl
' P1000 P10010 C1 ' P20110 P20010 C1
1-C2 C2 1 1-C2 C2 1

 

Ses and Sps are computed using the law of total probability(Casella and Berger, 2001)

51= P(7'1|D=1) = P(T1=1. T2=llD) + P(T1=1, T2=OID) = P1111 +P1011

52 = P(T2lD=1) = P(T1=1. T2=llD) + P(T1=0, T2=OlD) = P1111 + P0111

C1 = P(T1|D=0) = P(T1=0. T2=OlD) + P(T1=0. T2=1lD) = P0010 4' P0110

C2 = P(Tle=0) = P(T1=0. Tz=0|D) + P(T1=1. T2=OID) = P0010 + P1010

The parameters 7!], 7:2, S 1, 82, C1, and C; were estimated using simulation-based

Bayesian inference. In Bayesian inference all the parameters are treated as random

variables conditioned on the observed data. Hence, the joint posterior inference is

determined by the combined input of prior information and the likelihood, where the

priors express preceding uncertainty about the parameter estimates. Finally, the marginal

densities for the six parameters can be obtained using Gibbs sampler. In short, the Gibbs

sampler works as follows. First, the latent data (aijk) are sampled from independently

distributed binomial distributions, where the latent data are two 2 x 2 tables of the

subjects that are disease positive (D=l), i.e. ail-k. The latent counts are sampled

77

independent from their conditional distributions given the observed counts {nil-k} , the

classification probabilities {ijII} and the prevalence {m},(Johnson et al., 2001) hence

 

. . ”'P °
aijk "' Bmoml nil-k , [Flu] ) , NOIC that ijII = 31.92, and SO
Irink11+l'7Fink10

forth.

The values for the latent counts in the disease negative tables are simply

bijk = nijk — aijk (Black and Craig, 2002)

Second, the full conditional distributions for the six parameters are sampled successively.

M~Beta( 1~+a7t1 “bl +flm)
m~Beta(az. +am.b2..+ 2:2)
”Beta(anl +aS1b“1 +flS1)
SZ~Beta(a.1+a52’~-b1+fl$2)
ClBeta(b 0.+aC1'b-0-+fl C1)

CB~eta(b 0+afl.2.b.0.+ fly”).

78

where d s and ,3s represent a priori information. The Gibbs sampler is then iterated to

convergence.

Conditional dependence model (M2 )

For the dependence model, we extended the approach of Black and Craig (2002)
to include test results from two populations However, we limited our model to the full

conditional dependence model, and no restrictions were placed on the relationship
between pl 111 and S152, and p000 and CICZ. Hence, we allowed for the correlation

between disease positive and negative animals to range between —1 and 1. The

restrictions placed on the parameter space by introducing pl 111 and pomo makes it difficult
to sample from the full conditionals {S 1, S2, pl 111} and/or {C1, C2, p000}. However, this is

resolved by jointly updating the sets of parameters using the Metropolis-Hastings (MH)

algorithm.(Black and Craig, 2002) In their model, Craig and Black, (2002) placed
uniform priors on p111] and p000, respectively, given S1, 52, C1, and C2, thereby forcing
positive correlation between Se and Sp. Hence, the classification probabilities in the
disease positive and negative table are the function of Se’s and P1111. and Sp’s and p001),

respectively.(Black and Craig, 2002)

Using a Dirichlet( 1 ,1,1,1) prior for the four cells in the disease positive and

negative tables, then

79

 

 

 

P1111 Pa.11+17 F151 11o —b.11+1-
' +1 ° +1
‘1.) 10“ ~ Dirichlet “"0 1.710") ~ Dirichlet [“0
P0111 a.01+1 P0110 b-01+1
_I'7001id .000 +14 1P0010_ PM +1-

 

 

 

 

 

$1=P1111+P10119 $2: p1111+p0111’C1=p0110+l7001wand C2=P1011+P0011

For the disease positive table, the cycle move from the previous MCMC cycle to the next

cycle with the probability (acceptance rate)

‘ a -1 fl -1
(m). 1, H 1% (a) 5" 1:5,.) 3"

minGIaSZ)‘$132i=1 3k l—Sk

For the disease negative table

 

’ a -l '3 _1
P(HIOVG): m1n I’mln(C1’C2)—C1C2 121 (g) Ck [l—Ck) Ck

min(c1,c2)—c1c2,=1 ck 1-6,,

The prevalences and latent counts, (lg-k, can then be sampled directly from

 

. . 7n 1111
all] ~ Blnomla ”Ill, (1 X111) )
751101111+ ‘70 ‘C1-C2+P0010

80

 

, , 751(51—p11u) A
a110~Btnomi "110’

711(51- ‘P11|1)H( ”IXCZ—Poao)

 

mlSz- -p,ml 4]

”1(52" P11|1)+( +'1 ”IXCI P000)

. .{ ”Ill—SI SQ+Pnnl ]
a100~Bmom1 "100’

0101" Binomial{n10l ,

 

fill/IUSl-J'52+p11|1)"‘(1 7n)PO0Io

 

a Binomi n E21111 III A
211~ 211’
7’2 P11|1+(1—7IZX1—C1—C2+ p000)

22151- PH”) ]

 

~B'nom'al ,
0210 l l ["210 752(51- p11|1)+(+_1 ”ZXCZ“ P000)

 

222152-1111") ]

~Binomial ,
“2‘" ["20‘z2192-pn.1l+(1szCi-poaol

 

0200 ~ Binomia|[n200,7r 2(1

752(1— ”SI Sg‘l'le)
‘Sl $2+p11|1)+1+1-( 71'2)Poo|o

fl'] “' Beta(al..+ afll’bl..+ 751)

72'2 ~ Beta(a2.. + aflz2b2.. + fizz)

The correlations between S 1 and 52 (ds) and C1 and C2 (dc) were estimated and

sampled in each cycle of the MH algorithm, where

81

Pim'SISZ Pooo’CICZ
d = >O.andd = >0
S \l(51(1-32)52(1‘S1)) C JEl(l-C2)C2(1_Cl»

Conditional dependence model (M3)

For this model we assumed that the specificity of CULT (T2) was 1 (see prior
specification). Then P(T2=O|D=O)=1, which in turn implies that P(D=1|T2=l)=l as well.
In other words, if an animal was positive on T2, it was truly infected. This furthermore
implies that the vector of latent counts for disease positive animals a. = (all, a.10, am,
.aoo)T = (n.1 1, a.10, n01, a.00)T. Therefore, the vector for disease negative animals b. =
(1M 1. (Mo, b~012 boo)T =(02b-10.0. boo)T- In fact Pom= 0 and P1130 = 0- Sampling OfPI 1n.

51, and 52 was performed as described in model M2, however, pom =
C1 ~ BCIa(b.0. + “C1 ,b,0_ + 'BC1)’ and pom = l-Cl. ail-k were sampled in the same

manner as for M2. The prevalences are sampled as before, however they simplify to

71': " Beta("il 1+ ai10+ "£01 + aioo- + a,“ 'bi10+ bi00+ .531)

Conditional dependence model (M4)

As the last model, a ‘correlation-adjusted’-estimation-model using two tests was
used.(Georgiadis et al., 2003) This model uses a different parameterization of the
correlation between Se’s and Sp’s of the two tests than described for M2. We refer to the

paper by Georgiadis et a1. (2003) for further detail.

82

CHAPTER FIVE

HERD-LEVEL SENSITIVITY, SPECIFICITY, AND PREDICT IVE VALUES OF
BOVINE TUBERCULOSIS SKIN TESTS IN MICHIGAN.

ABSTRACT

In managing the statewide bovine tuberculosis eradication program in Michigan,
correct classification of infected herds is the most relevant actionable event for regulatory
intervention because, with few exceptions, the entire herd is depopulated if one or more
animals within a herd are diagnosed with bovine tuberculosis. A shareware program was
used to estimate herd-level sensitivity (HSe), specificity (HSp) and predictive value
positive (HPVP) and negative (HPVN) for the bovine tuberculosis tests as they were
implemented in Michigan. Four different scenarios were simulated. 1) serial
interpretation of the caudal fold and comparative cervical tuberculin tests, 2) serial
interpretation of the tuberculin tests, and mycobacterial culture and polymerase chain
reaction when the later two are used in parallel, 3) as for scenario 2, but specificity fixed
to 1.0, and 4) sensitivity was increased to 0.9 (4a) or 0.95 (4b) and Sp=1.0. Estimates of
test sensitivity (Se), specificity (Sp), true animal and herd prevalences were obtained
from the literature and in collaboration with regulatory veterinarians. An empirical
distribution of herd sizes in the northern part of the lower peninsula in Michigan was
used to simulate the variation in herd sizes in the area of Michigan where bovine
tuberculosis is most likely to occur. Furthermore, scenarios 2 and 3 were used to
investigate the effect of herd size on herd-level parameters. In general HSe estimates
were reasonably high, ranging between 0.712 and 0.840 for the four scenarios, however,
individual estimates all ranged between 0.0 and 1.0. Increasing Se only increased HSe

little. Herd-level specificity estimates were lowest for the two scenarios (0.693 and

83

0.940, respectively) where Sp was not assumed perfect (scenario 1 and 2). HPVP
estimates were very low (0.042 and 0.143, respectively) for the first two scenarios also,
but increased to 1.0 when perfect specificity was assumed. The HPVN remained high for
all four scenarios, ranging between 0.995 and 0.997 with very narrow confidence
intervals. The size of the tested herd has a major effect on HSe, which increases as the
herd size increases. Both HSp and HPVP decreased with increasing herd size. However,
when Sp was assumed perfect, only minor effect was seen on HSp and HPVN, but HSe
remained low at low herd size. It is apparent that the tests used in identifying herds that
are infected with bovine tuberculosis work fairly well on a herd basis. However, as the
herd size decreases so does the HPVN and HSe. Hence, it is advisable to test herds with

less than approximately 100 catlle more frequently and perhaps for an extended period of

time as compared to larger herds.

84

INTRODUCTION

Five years after the last confirmed case, the Michigan cattle population was
declared free from bovine tuberculosis (bTb) caused by Mycobacterium bovis in
1979.(Corso et al., 1996) The disease was not found in any animal species for 15 years,
with exception of a hunter-killed white—tailed deer in 1975.(Stuth and Fay, 1975) This
deer was considered to be an isolated case(Schmitt et al., 1997) and the disease was not
diagnosed again until 1994 when bTb was identified in a single white-tailed
deer.(Schmitt et al., 1997) The following year, bTb was diagnosed in a Michigan beef
cow. As of June 2003, bTb has been diagnosed in approximately 400 white-tailed deer,
two elk, one domestic cat, four bobcats, l3 coyotes, two opossums, two raccoons, and
two red foxes (C. Bruning~Fann and SD. Fitzgerald, personal communications 2002).
Further, 30 cattle herds in the northern part of Michigan’s lower peninsula have been
found to have at least one bTb-infected animal. A plan was implemented for testing of
all Michigan domestic cattle herds with the caudal fold tuberculin test (CFT) and the
comparative cervical test (CCT) used in series, with the CCT being applied only to
animals testing positive or “suspect” on the CFT (October 31, 2000, Amendment to the
Animal Industry Act 466, State of Michigan.)

In managing a statewide bTb eradication program, correct classification of
infected herds (herds with one or more infected animals) is the most relevant actionable
event for regulatory intervention because, with few exceptions, the entire herd is
depopulated if one or more animals are diagnosed with bTb. While the individual

animal-level sensitivity (Se) and specificity (Sp) of the tuberculin skin tests have been

85

estimated under local area conditions in Michigan(Norby et al., 2003a; Norby et al.,
2003b), the herd-level estimates of sensitivity (HSe) and specificity (HSp) of the serial
testing program are more relevant to the regulatory veterinarians managing the
eradication effort.

Factors influencing estimates of HSe and HSp include animal-level Se and Sp, the
size of the sample (n), the true prevalence of the disease within positive herds (TP), the
number of test-positive animals used to define a positive herd (cutoff)(Martin et al.,
1992), and among herd variation in the Sc, Sp and TP.(Donald et al., 1994) The herd-
level predictive value of a positive classification/designation (HPVP) and of a negative
classification/designation (HPVN) are furthermore dependent on the prevalence of herds
with the disease (HTP). Additional information regarding herd-level testing and factors
affecting herd-tests are reviewed by Christensen and Gardner (2000).

Martin et al. (1992) described a relatively simple way of estimating Hse, HSp,
HPVP, and HPVN. However, because the binomial distribution is used for estimating the
number of test positive animals in each sample, this method requires the assumption that
the sample size used for testing is S 20% of the herd size.(Christensen and Gardner,
2000; Jordan, 1996) Nonetheless, when testing for bTb in Michigan, all animals over the
age of 12 months in each herd were tested. This problem may be overcome by estimating
the number of test positive animals using the hypergeometric distribution.(Cameron and
Baldock, 1998). Jordan (1996) used this approach in a “shareware” program
(HERDACC version 3) that is used to estimate HSe and HSp, using point estimates for
Se, Sp, and TP, sampling from binomial or hypergeometric distributions. The results are

presented for five different prevalence estimates and up to 10 different cut-off values

86

used to define a “positive” herd. Though this software program simplifies the
calculations, it does not account for the uncertainty and variability in the input variables
and the clustering of disease positive animals e.g. within a herd. Clustering of disease
positive animals within a herd is plausible, and is the foundation for the utility of this
testing scheme to detect infected herds. The bTb eradication programs of the early 1900’s
recognized that the CFT and CCT used in serial interpretation detected infected herds
(not necessarily infected animals) and that this worked in practice, because the
infectiousness of the disease was such that it was exceedingly rare that only one animal in
a herd would be infected without the existence of multiple infected herdmates, i.e.,
clustering. The shareware program, ‘HerdTest’(Jordan and McEwen, 1998), permits the
user to include uncertainty about Se, Sp, and TP in the model, and furthermore allows for
a more complex sampling protocols. The objective of this study was to use the HerdTest

program to estimate HSe, HSp, HPVP, and HPVN for several different bTb testing

scenarios in Michigan.

MATERIALS AND METHODS

Diagnostic tests and testing procedure

The statewide testing procedure, and implementation of the CFT and CCT,
mycobacterial culture (CULT), and polymerase chain reaction (PCR) has been described
elsewhere.(Norby et al., 2003a) In short, the CFT was performed by public or private
practicing veterinarians, using an intradermal injection of 0.1 ml of USDA bovine PPD

(lmg/ml)(USDA and APHIS, 1999) in the caudal fold on either side of the base of the

87

tail. The injection site was palpated approximately 72 hours later, and the test was
considered positive (“suspect”) if there was any sign of inflammation (Bruning-Fann,
personal communication, 2002) If the CFT was “suspect”, a USDA or state veterinarian
administered the CCT within 7 days of when the CFT was read. For the CCT, 0.1 ml of
USDA bovine PPD and 0.1 ml of USDA avian PPD (biologically balanced, 1mg/ml)
were injected intradermally on the neck approximately 12.5 cm apart. The thickness of
the skin was measured before injection and approximately 72 hours after injections. The
difference (‘after’ minus ‘before’) in skin-thickness was plotted on a scattergram (USDA,
VS, Form 6-22D) used to interpret the CCT results as “negative”, “suspect”, or “reactor”.
Necropsy and histological exam was conducted on CCT positive animals at the
Diagnostic Center for Population and Animal Health at Michigan State University.
Histological exam and CULT was performed on fresh samples of select tissues from all
cattle that were necropsied. Samples that were suspect for M. bovis on histological exam
were tested with PCR at the National Animal Disease Center and CULT was performed
at the National Veterinary Services Laboratories, Ames, Iowa. For six animals, tissues
were also cultured at the Michigan Department of Community Health.(Norby et al.,
2003a) The necropsy, culture, and PCR procedure has been described elsewhere.(Miller
et al., 1997; Norby et al., 2003a; Schmitt et al., 1997) In the CULT procedure, a very
specific genetic probe was used to classify mycobacterial species into isolates belonging
to the Mycobacterium complex, which include M. bovis, tuberculosis, africanuum, and
microtii.(Schmitt et al., 1997) Since it was unlikely that cattle in Michigan were infected
with mycobacteria belonging to the Mycobacterium complex other than M. bovis, it is

assumed that all isolates that were positive on culture were M. bovis.

88

Analyses

The program ‘HerdTest’ as described by Jordan and McEwen (1998) was used to
estimate values for HSe, HSp, HPVP, HPVN for diagnostic tests used in the bTb
eradication program in Michigan. The input variables for this model included: Se, Sp,
TP, and HTP. Other inputs included a choice between binomial or hypergeometric
sampling, how many test-positive animals were needed to denote a positive herd, and a
selection of transmission mode (free-living—contagion or obligate-parasite). Input
variables may be either point estimates or frequency distributions. HSe, HSp, HPVP, and

HPVN were estimated for several different test scenarios: 1) serial interpretation of the
CFT and CCT(Norby et al., 2003b), 2) serial interpretation of the CFTCCTSER and
mycobacterial culture (CULT) and PCR used in parallel (SeMI and 8pm), 3) as for
scenario 2, but Sp fixed 1.0, and 4) Se increased to 0.9 (4a) or 0.95 (4b) and Sp=1.0. All
four scenarios were performed using the distribution of herd sizes in 10 counties (figure
5-1) in the northern part of the lower peninsula in Michigan, as reported by the National
Agricultural Statistics Service, USDA (Table 5-1). In addition, the herd-level parameters
were estimated for herd sizes fixed at 10, 25, 50, 100, 250, 500, and 1000 head of cattle,

using Se and Sp from scenarios 2 and 3. The results for HSe, HSp, HPVP, and HPVN

are reported as median, first and third quartiles, and the range.

89

Figure 5-1. Geographical location of the 10-county-area in northern Michigan.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Input distribution for Se, Sp, TP, and HT P
The input parameters for HerdTest were entered as frequency distributions to

account for the uncertainty and variability in parameter estimates.(Jordan and McEwen,
1998) The Se and Sp for CFTCCTSER (scenario 1) were estimated by Norby et al.

(2003a, b). However, there are no published estimates on the Sc and Sp of all the tests

(CFT, CCCT, CULT, and histologic exam and PCR) used in series in Michigan (Scenario
2 and 3). Hence, distributions for CFTCCTSER, CULT and PCR used in serial

interpretation were estimated in collaboration with veterinary epidemiologists at APHIS,

90

USDA (Lansing, Michigan). These distributions were created by selecting the most

likely values (median) and a range that was likely to cover 95% of all possible values.
For example, it was estimated that the most likely value for SeMI was 0.60 and the 5th and

95th percentiles were 0.50 and 0.70, respectively. These estimates were based on
empirical evidence and the Se estimate of CULT as reported by Norby et al. (2003b).
The Sp was assumed to be very close to one and for scenario 2, it was suggested to
follow a uniform distribution ranging between 0.995 and 1.0. For scenario 3, Sp was
fixed at 1.0. The true within-herd prevalence was based on estimates from Norby et al.
(2003b) and the median was judged to be 0.060 with 5m and 95th percentiles of 0.005 and
0.20, respectively. The input estimate of HTP was based on the number of herds that
were detected each year in the bTb ‘infected zone’, which consist of Alpena,
Montmorency, Alcona, and Oscoda counties. Approximate 8 new bTb herd diagnoses
are reported each year from this area, and the median and percentiles for HTP were hence
estimated to be 0.02, 0.005, and 0.05, respectively.

RISKview 4.0.4 (Palisades Corporation, Newfield, NY) was used to fit beta
distributions that followed the specifications for TP, HTP and sensitivities (Table 5-l).
For example, beta distribution for TP was Beta(1.7,22). The nature of the beta
distributions and RISKview made it impossible to fit beta distributions that exactly
followed the specifications for median and 5th and 95m percentiles for TP, HTP, and
sensitivities. However, both median, 5th and 95m percentiles as estimated by RISKview
were within 0.01 of the preferred values. The resulting distribution with median and 5‘h

and 95th percentiles are shown in Table 5-1.

91

Herd size distributions and sampling technique

The herd level parameters were estimated for different fixed herd sizes, as
describe earlier. Furthermore herd level parameters were estimated for a local area
containing 10 counties in the upper part of the lower peninsula (figure 5-1). The 10
county area was based on the current division into a ‘disease zone’, ‘surveillance zone’,
and ‘disease free zone’ in the area where bTb is present in Michigan. The 10 county area
consist of the ‘disease zone’ and the surrounding counties (the ‘surveillance zone’). It is
was considered unlikely that bTb is present outside this 10 county area, and using an
empirical herd distribution for the entire Michigan and a very low herd-level prevalence
could negatively bias the results of the herd-level performance of the tests in the area
where bTb is present. Empirical distributions of herds in all of Michigan and the 10
county area were reported for 1997 (Table 5-2) in ‘Michigan Agricultural Statistics’
(Michigan Agricultural Statistics Service, National Agricultural Statistics Service
(NASS), USDA, http://www.usda.gov/nass/mjl). The last category of herd sizes was
‘2500. It was assumed that all herds in this category were evenly distributed between

500 and 1,000 animals.

92

Table 5-1. Input variables for sensitivity (Se) Specificity (Sp), and within herd
prevalence (TP) and herd prevalence (HTP) used for the shareware program
‘HerdTest’.[Jordan and McEwen, 1998].

 

 

Input variables Distribution 5th percentile Median 95th percentile
“Se CFTCCTSER Beta(7. l ,2.5) 0.438 0.757 0.948

asp CFTCCTSER Beta(98.6,1.7) 0.950 0.986 0.998

b'cng, Beta(47,3 1) 0.493 0.603 0.708

”31,,“ Uni(0.995, 1) 0.995 0.998 1.0

Csp, Fixed at 1.0 1.0 1.0 1.0

d369,, Beta(90,10) 0.834 0.903 0.951

c5695 Beta(95,5) 0.900 0.953 0.983

TP Beta(1.7,22) 0.007 0.060 0.202

HTP Beta(3,l30) 0.0047 0.020 0.054

 

 

 

3Se and Sp as estimated when using only the caudal fold and comparative cervical
tuberculin tests in series (CFTCCTSER), scenario 1.

bSe and Sp as estimated for the serial use of the CFTCCT and mycobacterial culture
and/or histopathological exam and PCR(SeM1, Sle), scenario 2.

cSe and Sp used in scenario 3.

dSe set equal to 0.90, Sp set equal to 1.0, scenario 4a.

eSe set equal to 0.95, Sp set equal to 1.0, scenario 4b.

93

Table 5-2. Distributions of herds in 10 counties and all of Michigan in 1997.

 

Herd size No. of herds in No. of herds in
10 county area (%) Michigan (%)

 

1-9a 197 (19.4%) 3,913 (25.3%)
10.192. 168 (16.5%) 2,929 (18.9%)
20.49“ 315 (31.0%) 3,803 (24.6%)
50-993 163 (16.0%) 2,148 (13.9%)
100-1993 107 (10.5%) 1,497 (9.7%)
200.499“ 58 (5.7%) 955 (6.2%)

2 5009b 8 (0.8%) 223 (1.4%)
Total 1,016 (99.9%)c 15,468 (100%)

 

alCategories of herds sizes. It is assumed that the herd sizes within each category are
evenly distributed over the entire interval. The data are reported in agricultural statistics

for Michigan in 1997, (http://www.usda.gov/nass/miz). bIt was assumed that herd sizes
for the seventh category (2 500) was limited between 500 and 1,000. cThe discrepancy to

100% is due to round-off errors.

The hypergeometric distribution was selected as the sampling technique, because
all animals in the herds were sampled.(.lordan and McEwen, 1998) The free-living-
contagion mode where herds were allowed to have no infected animals was chosen,
because susceptible cattle may be infected with M. bovis from other sources than bTb
infected cattle within the same herd.(Kaneene et al., 2002)

Spearman’s correlation coefficient (rs) was used to investigate how input

variables affected the output variables.(Jordan and McEwen, 1998)

94

RESULTS

The results of the simulated herd-level parameters are shown in Tables 5-3 and 5-
4 for all four scenarios. For example, scenario 2 showed a median HSe of 0.75, quartiles
of 0.369, and 1.0 and a range of 0 - 1. HSe, HSp, HPVP, and HPVN for scenario 2 and 3
at different fixed herd sizes are shown in figure’s 5-2 and 5-3, respectively. Increasing
Se to 0.9 and 0.95 (scenario 4a and 4b) had only minor effects on HSe (0.783 and 0.833,
respectively) and HPVN (0.996 and 0.997, respectively), and no effect on HSp and
HPVN. When Sp was not fixed at 1.0 (scenario 1 and 2), the HPVP was very low (0.042
and 0.143, respectively).

Table 5-3. Herd-level sensitivity (HSe) and specificity (HSp) for four

different scenarios with individual animal sensitivity (Se) and Specificity (Sp) used in 10
counties in the northern part of the lower peninsula in Michigan.

 

 

 

HSe HSp
Median Q1, Q3 Range Median Q1, Q3 Range

Scenarioal

1 0.840 0.423,] 0.0, 1.0 0.693 0.372, 0.826 0.0, 1.0

2 0.750 0.369, 1.0 0.0, 1.0 0.940 0.838, 0.980 0.023, 1.0
3 0.712 0.302, 1.0 0.0, 1.0 1.0 1.0, 1.0 0.981, 1.0
4a 0.783 0.375, 1.0 0.0, 1.0 1.0 1.0, 1.0 1.0, 1.0
4b 0.833 0.412, 1.0 0.0, 1.0 1.0 1.0, 1.0 1.0, 1.0

 

aMedian and 5th and 95‘h for the input variables (Se, Sp, TP, and HTP) are shown in Table
5-1.

Spearman’s rank correlation coefficients were calculated for all scenarios to show
the extent of dependence between input parameters and herd-test performance. They are

shown specifically for scenario 3 in Table 5—4. The correlation between input variables

95

and herd-level test performance were similar for the other scenarios (results not shown).
When Sp was 1.0, there was no effect of herd size on the herd-level parameters, and

correlations between HSe and HPVP and the input variables were non—existent.

Table 5-4. Herd-level predictive value positive (HPVP) and negative (HPVN) for
four different scenarios with individual animal sensitivity (Se) and Specificity (Sp) used
in 10 counties in the northern part of the lower peninsula in Michigan.

 

 

 

HPVP HPVN
Median Q1, Q3 Range Median Q1, Q3 Range

Scenario“l
1 0.042 0.020, 0.0, 1.0 0.995 0.986, 1.0 0.922, 1.0

0.078
2 0.143 0.066, 0.0, 1.0 0.996 0.988, 1.0 0.935, 1

0.296
3 1.0 1.0, 1.0 1.0, 1.0 0.995 0.987, 1.0 0.942, 1.0
4a 1.0 1.0, 1.0 1.0, 1.0 0.996 0.988, 1.0 0.939, 1.0
4b 1.0 1.0, 1.0 1.0, 1.0 0.997 0.989, 1.0 0.935, 1.0

 

aMedian and 5‘h and 95‘h for the input variables (Se, Sp, TP, and HTP) are shown in Table
5-1.

Table 5-5. Spearman’s rank correlation between herd—level input variables and
herd-level outmit variables for Scenario 3. p-values are shown in brackets (Ho: rs=0).

 

 

Herd size Sensitivity Specificity eP(HD+) f15(1)...)
25156 +0.83 (0.00) +0.02 (0.63) -010 (0.002) -004 (0.21) +0.35 (0.00)
bHSp -0.83 (0.00) +0.03 (0.37) +0.51 (0.00) -0.06 (0.05) +0.03 (0.00)
CHPVP -0.38 (0.00) +0.00 (1.0) +0.43 (0.00) +0.55 (0.00) +0.20 (0.00)
dHPVN +0.69 (0.00) +0.04 (0.23) +0.03 (0.28) -0.32 (0.00) +0.41 (0.00)

 

aHerd-level sensitivity.

bHerd-level specificity.

cHerd-level predictive value positive.

dHerd-level predictive value negative.

eProbability that a randomly selected herd is disease positive.
fProbability that a randomly selected animal is disease positive.

96

Figure 5-2. Scenario 2 - Medians for herd level sensitivity (HSe), specificity

(HSp), predictive value positive (HPVP), and negative (HPVN) for different fixed herd
sizes using input values from scenario 2.

 

 

 

 

 

 

 

 

1 , t fl n
0.9]:(' nan-H89
0.8 - 3 ‘g —a- HSp
b 0.7 4‘ \\ —.— HPVP
E 0.6 ~ ' \\ —O—HPVN
8 0.5 — "\
.8 . x
a 0.4‘. \\\
0.3 “ \x“
0.2 ~~~~~~
4“ “‘~-..§
0.1" ‘0. _____ + ...... “I
0 I 1"-'°'”-¥""-"‘? ''''' ‘9
0 200 400 600 800 1000

Herd size

 

 

 

The following input variables were used for individual animal sensitivity (Se) and
specificity (Sp): Median and 5th and 95'h percentiles for Se and Sp were 0.603
(0493,0708), Sp=0.998 (0989,10), respectively. Medians and 5th and 95th percentiles
for within herd prevalence (P) and among herd prevalence (HP) were 0.060 (0007,0202)
and 0.020 (0005,0054), respectively. The cut point for disease positive animals was 1.

97

Figure 5-3. Scenario 3 - Medians for herd level sensitivity (HSe), specificity

(HSP), predictive value positive (HPVP), and negative (HPVN) for different fixed herd
sizes in scenario 3.

 

 

 

 

 

 

 

 

k I
0.99 :5 .'
0.97- "*"Hse
.' -+-HSp
3 0.95 - 5 -+- HPVP
n .
5°. 0.91 ~
0.89 .
0.87 — ?
0.85 1 + . . T .
0 200 400 600 800 1000
Herd size

 

 

 

The following input variables were used for individual animal sensitivity (Se) and
specificity (Sp): Median and 5th and 95th percentiles for Se and Sp were 0.603
(0493,0708), 1.0 (1.01.0), respectively. Medians and 5th and 95"I percentiles for within
herd prevalence (P) and among herd prevalence (HP) were 0.060 (0007,0202) and 0.020
(0005,0054), respectively. The cut point for disease positive animals was 1. The data

point for HSe for herd sizes 10 and 25 were 0.333 and 0.667. HSe and HPVP were 1.0
for all used herd sizes.

DISCUSSION

In this study we estimated the herd-level sensitivity, specificity, and predictive
values of bTb diagnostic tests as they are applied to cattle herds in Michigan. Results
from four different testing scenarios were investigated with different input values for
estimating HSe, HSp, HPVP, and HPVN. Scenario 3 (Se = 0.60, Sp = 1.0, TP = 0.06 and
HTP = 0.005) was considered to be most applicable to the situation in Michigan, because

all the tests are used in serial interpretation and because false positive results on CULT

98

and PCR are not likely.(Norby et al., 2003a) The other scenarios were investigated to
examine the effect of only using the CFTCCTSER in the eradication program as well as

investigating the effect of increasing the Se of the testing scheme.

For scenario 3, HSp and HPVP are both 1.0 with range (1.0-1.0), i.e. if a herd is
diagnosed positive for bTb, it is certain that the herd is truly infected (i.e., no false
positive herds). However, it is worth noting that unless Sp=1.0, then HPVP is very small
(scenarios 1 and 2).

The HPVN is very high for all scenarios, with the median from 0.995 to 0.997.
Hence a negative herd test will almost always be correct (i.e. few false positive herds).

The effect of herd size on HSe, HSp, HPP, and HPVN was investigated by
keeping values for herd size fixed (figure 5-3 and 5-4) at 10, 25, 50, 100, 250, 500, and
1000, while all other input values were kept fixed as described for scenario 2 and 3.
Using inputs for Se, Sp, TP, and HTP from scenario 2 (figure 5-2), shows that the median
for HPVP drops quickly as herd size increased and slowly gravitates toward 0 when the
herd size is larger than 250. The HSp also decreases with increasing herd size, however
much slower than HPVP. Herd-level sensitivity increased with increasing herd size and
the median reached 1.0 at a herd size of approximately 100. However, it is important to
remember that both HSp, HPVP, and HSe in particular had wide ranges. When Sp=1
(scenario 3) (figure 5-3), changes in herd sizes only affected HSe and HPVN, and these
changes were virtually identical to the changes described above for scenario 2.

Using the empirical herd distribution from the 10 counties, the HSe was only
relatively high because the majority of herd (843 of 1,016) had less than 100 cattle. If the

herd distribution for all of Michigan was used, the results were only slightly higher for

99

HSe (0.667) and slightly lower for HPVN (0.931). This was done assuming that TP and
HTP are as high in the rest of Michigan as it is in the 10 county area. This is not a
reasonable assumption, and a simulation using a uniform distribution
(Uniform(0.00001,00001)) showed that Hsp, HPVP, and HPVN remained the same as in
the previous scenario, but HSe only took on values of 0 and 1 (median=l, Q1=0, and
Q3=1, simulation not shown).

Under the most likely scenario in Michigan (scenario 3), it was obvious that HSe
was low, in particular in smaller herds (figure 5-3). It was therefore investigated if an
increase in Se would increase HSe. If Se was increased to 0.90 (Beta(90,10)) or 0.95
(Beta(95,5)) there was none or only a slight increase in HSe, 0.783, and 0.833,
respectively. Hence using a test scenario with higher Se does not improve HSe
substantially (unless Se=l.0), because the average herd size is small. This is further
supported by the Spearman’s rank correlations between Se and herd-level parameters,
where the correlations are very small (Table 5-5) and not statistically significant.
However, herd size (=sample size) has a strong influence on all herd-level parameters
(Table 5-5). The correlation coefficients also show that Hse increase with increasing
P(D+), whereas only HPVP increase if P(HD+) increases. Increasing Se will have no or
very little effect on HPVN, HSp, and HPVP. Hence, the eradication program will only
gain minor improvement by increasing the Sc. Specificity has most influence on HSp
and HPVP.

We used 1997 census data of herd distributions in Michigan as reported by
Michigan Agricultural Statistics. Because only animals older than 12 months of age are

tested for bTb, the true number of animals tested will be lower than the used herd

100

distribution. However, since the testing has been ongoing for several years now, it is
likely that the distribution of herds used in this study is a fairly accurate estimate of the
situation in Michigan.

We chose to use the free-living contagion mode for simulations in this study,
allowing for cattle to get infected from other sources beside bTb-infected herdmates. In
Michigan, it was shown that there is a statistical significant association with a herd being
positive and the prevalence of bTB infected white-tailed deer(l(aneene et al., 2002),
hence white-tailed deer may serve as a reservoir for M. bovis and infect cattle directly or
contaminate pastures and feed for the cattle. Nevertheless, a simulation was conducted to
investigate the effect of using the obligate parasite mode. Using the obligate-parasite
mode had no effect on HSp and HPVP. However, HSe was increased (median=0933)
and the range was decreased to 025-1. There was only a slight increase of 0.03 in HPVN
and the range was virtually unchanged. This means that if our assumption about free-
living-contagion mode as compared to obligate contagion mode is wrong, only slight

errors in HSe and HPVN would have occurred, but estimates of HSe would be increased.

The ‘HerdTest' Model

We chose the model constructed by Jordan and McEwen (1998) (implemented in
the software program ‘HerdTest’ ) to estimate HSe, HSp, HPVP, and HVPN for the
series of tests used to diagnose cattle herds infected with bTb in Michigan. This model
has the advantage that uncertainty and variation in Se, Sp, TP, and HTP may be
accounted for using frequency distribution for these input variables. Another advantage

of this program is the estimation of Spearman’s rank correlation coefficient. The rs can

101

then be used to assess how changes in Se and Sp may influence the herd-level
parameters. In the bTb situation in Michigan, it is clear that an increase in Se will have
an advantageous effect on HSe, but only for smaller herds.

All the bTb tests used in Michigan are used in series, and hence the Se of these
tests can never be better than the Sc of the first test (CFT) used in the series of tests. The
Se of the skin test(s) could be improved by removing the CCT from the series of tests,
however, this also increases the number of cattle with false positive test results, and
hence increases the number and cost of animals sent to necropsy for further work up.
Another solution would be to use an additional test with high Se in parallel with the skin
tests. This would increase the overall Se, but most likely decrease Sp. If another test(s)
is used in parallel with the skin tests, it is important that this new test and the skin tests
are conditionally independent to obtain the optimal effect of using tests in
parallel.(Gaboric et al., 1996; Gardner et al., 2000) The gamma-interferon (‘y-TNF) has
received much attention as an alternative to (or for use in combination with) the skin tests
used in the United States.(Whipple et al., 1995) However, because both the skin tests and
the 'y-INF are measuring a cellular immune response(Wood et al., 1991) they may be
conditionally dependent and the gain of using these tests in parallel may be obsolete. If
the skin tests (or the y—INF) could be used in parallel with another test like for example an
ELISA detecting antibodies, then there may be a gain in Se sensitivity and hence HSe.
Gaboric et al. (1996) showed that the sensitivity of the CFT and ELISA used in parallel
(Se=95%) was higher than for the CFT (Se=84.9%) or ELISA (Se=65.6) used
individually. However, as stated earlier, this would signify a decrease in the Sp of the

test(s) and most likely affect HSp and HPVP in a negative sense.

102

Comments and recommendation to the eradication program in Michigan

It is apparent that the skin tests have been used very successfully in the United
States to eradicate bTb from most states,(Anonymous, 1992) and this simulation study
also shows that both HSp, and HSe are high in larger herds. The problem lies in
detection of disease positive animals in small herds if only one (or few) animals are
infected. This also reflects a characteristic of an eradication program where the number
of diseased herds and diseased animals within an infected herd tend to decrease as the
disease prevalence decreases.(Christensen and Gardner, 2000).

The tests used to eradicate bTb in Michigan work well on the herd-level. If the
tests are used in a test-and-removal scheme, i.e. removing only animals that were positive
on the bTb tests from the herd, it is likely that M. bovis infected animals will remain in a
herd after testing.(Norby et al., 2003a) Such animals are a source for new infections in
the herd, prolonging the eradication. Hence, it will take much longer for Michigan to
obtain bTb free status. It is pertinent that special attention is paid to small herds with less
than approximately 100 cattle, because the HSe and HPVN are low in small herds, and it
might be worthwhile to continue the testing of smaller herds more frequently or for a
longer period of time.

It is likely that a few herds may turn up bTb positive after the disease is
considered eradicated. This was for example seen in Denmark where three herds have
been diagnosed with bTb after the routine monitoring with tuberculin tests every three
years was discontinued in 1980(Flensburg, 1995) The three cases were in one instance

traced to the owner who had open kidney tuberculosis caused by M. bovis, the second

103

case was most likely caused by the owners father, and in the third herd, no evidence of
bTb could be found. If there truly is a non-bovine reservoir in Michigan as assumed in

our simulations, this may cause the eradication effort to prolong considerably.

104

REFERENCES

Anonymous 1992. Assessment of risk factors for Mycobacterium bovis in the United
States (Fort Collins, Colorado USA, USDA, APHIS, VS).

Cameron, A.R., Baldock, RC, 1998, A new probability formula for surveys to
substantiate freedom from disease. Prev. Vet. Med. 34, 1-17.

Christensen, J., Gardner, I.A., 2000, Herd-level interpretation of test results for
epidemiologic studies of animal diseases. Prev. Vet. Med. 45, 83-106.

Corso, B., Wagner, B., Norden, D. 1996. Assessing the risks associated with M. bovis in
Michigan free-ranging deer. (Fort Collins, Co, Centers for Epidemiology and Animal
Health, USDA, APHIS). PP. 1-2.

Donald, A.W., Gardner, I.A., Wiggins, AD, 1994, Cut-off points for aggregate herd

testing in the presence of disease clustering and correlation of test errors. Prev. Vet. Med.
19, 167-187.

Flensburg, J ., 1995, Regional and country status reports, Denmark, In: Thoen, C.O.,

Steele, J .H. (Eds.) Mycobacterium bovis in animals and humans. Iowa State University
Press, Ames, pp. 206-212.

Gaboric, C.M., Salman, M.D., Ellis, R.P., Triantis, J ., 1996, Evaluation of five-antigen
ELISA for diagnosis of tuberculosis in cattle and Cervidae. JAVMA 209, 962-966.

Gardner, I.A., Stryhn, H., Lind, P., Collins, M.T., 2000, Conditional dependence between

tests affects the diagnosis and surveillance of animal diseases. Prev. Vet. Med. 45, 107-
122.

Jordan, d., 1996, Aggregate testing for the evaluation of Johne's disease health status.
Aust. Vet. J. 73, 16-19.

Jordan, D., McEwen, SA, 1998, Herd-level test performance based on uncertain
estimates of individual test performance, individual true prevalence and herd true
prevalence. Prev. Vet. Med. 36, 187-209.

Kaneene, J .B., Bruning-Fann, C.S., Granger, L.M., Miller, R., Porter-Spalding, BA,
2002, Environmental and farm management factors associated with tuberculosis on cattle
farms in northeastern Michigan. JAVMA 221, 837-842.

Martin, S.W., Shoukri, M., Thorbum, M.A., 1992, Evaluating the health status of herds
based on tests applied to individuals. Prev. Vet. Med. 14, 33-43.

105

Miller, J ., Jenny, A., Rhyan, J ., Saari, D., Suarez, D., 1997, Detection of Mycobacterium
bovis in formalin-fixed, paraffin-embedded tissues of cattle and elk by PCR amplification

of an IS6110 sequence specific for Mycobacterium tuberculosis complex organisms.
J VDI 9, 244-249.

Norby, B., Bartlett, P.C., Fitzgerald, S.D., Granger, L., Bruning-Fann, C., Whipple, D.L.,
Payeur, J .B., 2003a, The sensitivity of gross necropsy, caudal fold and comparative
cervical tests for the diagnosis bovine tuberculosis. JVDI In Press.

Norby, B., Tempelman, R.J., Hanson, T., Kaneene, J .B., Bartlett, P.C., 2003b, Estimation
of sensitivity and specificity of bovine tuberculosis skin tesets in Michigan when a
perfect reference is not available, Dissertation, Michigan State University, MI

Schmitt, S., Fitzgerald, S., Cooley, T., Bruning-Fann, C., Berry, D., Carlson, T., Minnis,
R., Payer, J ., Sikarskie, J, 1997, Bovine tuberculosis in free-ranging white-tail deer in
Michigan. J Wildlife Dis 33, 749-758.

Stuth, J ., Fay, LB. 1975. Laboratory record for necropsy #76-50 (East Lansing,
Michigan: Wildlife Pathology Laboratory).

USDA, APHIS 1999. Bovine tuberculosis eradication. Uniform methods and rules,
effective January 22, 1999, (United States Department of Agriculture), pp. 1-34.

Whipple, D.L., Bolin, C.A., Davis, A.J., Jamagin, J .L., Johnson, D.C., Payer, J .B., Saari,
D.A., Wilson, A.J., Wolf, M.M., 1995, Comparison of the sensitivity of the caudal fold

skin test and a commercial gamma-interferon assay for diagnosis of bovine tuberculosis.
Am J Vet Res 56, 415-419.

Wood, P.R., Comer, L.A., Rothel, J .S., Baldock, C., Jones, S.L., Cousins, D.B.,
McCormick, B.S., Francis, B.R., Creeper, J ., Tweddle, N.E., 1991 , Field comparison of
the interferon-gamma assay and the intradermal tuberculin test for the diagnosis of
bovine tuberculosis. Austr Vet J 68, 286-290.

106

CHAPTER SIX
HERD AND SPATIAL FACTORS AFFECTING THE PROPORTION
OF FALSE POSITIVE RESULTS ON THE CAUDAL FOLD TUBERCULIN TEST
IN MICHIGAN CATTLE.
ABSTRACT
A survey of beef and dairy herds in Michigan tested with the caudal fold

tuberculin test was carried out to quantify herd, and ecologic factors associated with the
proportion of false positive tuberculin skin tests. Furthermore, a spatial analysis was
used to identify clusters of herds with unusually high proportion of false positive results
on the caudal fold tuberculin skin test. A total of 4,989 herds were included in the
analysis of herd factors and a subset of 3,301 herds that had reliable information on
geographical location were used to identify spatial clusters and analyze ecologic factors
associated with the proportion of false positive results on the caudal fold tuberculin test.
The overall proportion of false positive test results for beef and dairy was 4.82%, and
3.41% and 5.58% for beef and dairy herds individually. Negative binomial regression
with the testing veterinarian included as a random effect was used to assess statistically
significant factors associated with the proportion of false positive results on the caudal
fold tuberculin skin test. The proportion of false positive test results was higher in dairy
cattle than in beef cattle and considerably higher in areas of Michigan where bovine
tuberculosis is present. The adjusted proportion of false positive test results was 2.25 and
4.38 cases per 100 animals tested for beef and dairy herds, respectively. Thirty-two
clusters with a high proportion of false positive results on the caudal fold test were
detected. The primary cluster had a radius of 19.5 km and was located in the center of

one of the counties in the bovine tuberculosis infected area in Michigan. The study

107

identified factors that affect the proportion of false positive results on the caudal fold
tuberculin tests that could be used by regulatory veterinarians to assess the bovine
tuberculosis status of tested herds. Furthermore, regulatory veterinarians could use
results from this study to identify geographic areas and/or veterinarian that consistently

have high or low false positive test results.

108

INTRODUCTION

The bovine tuberculosis (bTb) skin tests have been used successfully for control
and eradication of bTb in the United States since the eradication program was begun in
1917.(Anonymous, 1992) In 1992, there were only 10 states that had not achieved bTb-
free status.(Frey, 1995) Nevertheless, bTb has become endemic in the cattle population
in certain areas in the United States, including the northern part of the Michigan’s lower
peninsula.(Kaneene et al., 2002; Norby et al., 2003a) Although the methods for
production of the tuberculin used in the skin tests have changed over time, tuberculin skin
tests are still being used in series to detect individual animals and herds that are infected
with bTb.(Angus, 1978) The caudal fold tuberculin test (CFT) is used to screen herds,
and animals suspect (positive) on the CFT are retested with the comparative cervical test
(CCT).(Norby et al., 2003a; USDA and APHIS, 1999)

When the prevalence of bTb infected animals is relatively high, e. g., 10%, the
ratio between true positives and false positives (FP) test results is also relatively high.
However, as the prevalence decreases, this ratio also decreases.(Frey, 1995) In other
words, the predictive value of a positive CFT result decreases as the prevalence
decreases.

The sensitivity (Se) and specificity (Sp) of the CFT has been estimated as used in
Michigan,(Norby et al., 2003a; Norby et al., 2003b) and in several other studies in the
United States(Gaboric et al., 1996; Whipple et al., 1995) and around the world.(Francis
and Seiler, 1978; Lepper et al., 1977; Leslie et al., 1975a; Leslie et al., 1975b; Pollock et

al., 2000; Wood et al., 1991; Wood et al., 1992) From these studies, it is evident that Sp

109

is not a constant parameter, hence neither is the proportion of false positive (PFP) as PFP
= l-Sp. Variation in Sp can be due to: l) differences in the amount and concentration of
the tuberculin used for the CFI‘, 2) different (gold) standards used for estimation of Se
and Sp of the CPT, 3) regional variation in cross-reacting mycobacteria that cause FP
results on the CFT.(Cooney et al., 1997; Corner and Pearson, 1978a, 1978b), and 4)
variation in the interpretation of the CFT by the testing veterinarians.

The objective of the current study was to use available data from bTb testing
performed in Michigan to describe possible associations between herd and
ecological/geographical factors and the proportion of FF results on the CFT (PFP), and to

describe PFP clustering within Michigan.

MATERIALS AND METHODS

Diagnostic tests and testing procedure.

The statewide testing procedure, and implementation of the CFT and CCT,
mycobacterial culture (CULT), and polymerase chain reaction (PCR) has been described
elsewhere.(Norby et al., 2003a) In short, the CFT was performed by public or private
practicing veterinarians, using an intradermal injection of 0.1 ml of USDA bovine PPD
(lmg/ml)(USDA and APHIS, 1999) in the caudal fold on either side of the base of the
tail. The injection site was palpated approximately 72 hours later, and the test was
considered positive (“suspect”) if there was any sign of inflammation (Bruning-Fann,
personal communication, 2002). If the CFT was “suspect”, a USDA or state veterinarian

administered the CCT within 7 days of when the CFT was read. For the CCT, 0.1 ml of

110

USDA bovine PPD and 0.1 ml of USDA avian PPD (biologically balanced, 1mg/ml)
were injected intradermally on the neck approximately 12.5 cm apart. The thickness of
the skin was measured before injection and approximately 72 hours after injections. The
difference (‘after’ minus ‘before’) in skin-thickness was plotted on a scattergram (USDA,
VS, Form 6-22D) used to interpret the CCT results as “negative”, “suspect”, or “reactor”.

Necropsy and histological exam were conducted on CCT positive animals at the
Diagnostic Center for Population and Animal Health at Michigan State University.
Culture and PCR were performed on fresh samples or paraffin embedded samples,
respectively, at the National Veterinary Services Laboratories, and National Animal
Disease Center, Ames, Iowa. For six animals, tissues were also cultured at the Michigan
Department of Community Health.(Norby et al., 2003a) The necropsy, culture, and PCR
procedure has been described elsewhere.(Miller et al., 1997; Schmitt et al., 1997)

The Michigan Department of Agriculture (MDA) maintains records of all cattle
and herds in Michigan tested with the bTb tuberculin skin tests. The records include a
herd ID, postal address, the date that testing was performed, the number of cattle that
were tested, the number of ‘suspect’ (positive) and negative on the CFT, an ID-number of
the veterinarian performing the testing, and whether or not the whole herd was tested
(‘whole herd test’).

Between January 15‘, 1996 and November 30‘", 2001, 8,260 bTb negative cattle
herds (4,223 beef and 4,037 dairy) underwent a ‘whole herd test’ with the CFT. Some
herds were tested more than once during this period. These herds were all judged to have
been negative for bTb because all cattle were negative on the CCT or cows positive on

CCT were later shown to be negative by necropsy, CULT and PCR.(Norby et al., 20038)

11]

For a herd to be included in this study, the testing private veterinary practitioner had to
have tested at least 3 herds.

Considering all herds with at least one CFI' suspect animal, the crude rate of FF
was 12% in beef herds and 7% in dairy herds. The minimum herd size for inclusion in
our study was determined as the herd size that would have at least one FP CFT result
with 95% confidence (C) when the proportion of false positive results (PFP) were 12%

for beef and 7% for dairy herds.

C O 2 log(1 — C)
log(l — PFP)

 

(Martin et al., 1992)

Therefore, the herd size in this study was limited to beef herds with > 12 cattle and dairy

herds with > 22 cattle.

Statistical analysis

The data were analyzed using SAS statistical software package (SAS Institute,

Cary, NC). Distributions of the observed data, the expected Poisson distribution (P(Y=y)

= e'” u’ly!)(Rice, 1995) and the expected negative binomial distribution

__ m'kr(k+m) my_ _f2 .
P(Y—y)—(l+-;) ( fink) )(m+k) ,m—mean,k—[a’2_i),(che,

1995) are shown in figure 6-1. The data were checked for errors and descriptive statistics

 

 

and frequency distributions were calculated.

112

Figure 6-1. Observed and expected frequencies of false positive test results per
farm. Neg-Bin: Negative Binomial.

 

 

2500

Number of herds

 

 

 

 

0 2 4 6 8 10 12 14 >=15
Number of CFI' suspects

 

 

 

Associations between PFP and herd factors were tested using a negative binomial
regression model(Wassink et al., 2003) in which the testing veterinarian was included as
a random effect. Such a model allowed us to distinguish between sources of
overdispersion due to residual variation and clustered random effects.(Tempelman and
Gianola, 1996) The dependent variable of interest was the proportion of PP results (PFP)
on the CFT for any given ‘whole herd test’ meeting the above stated selection criteria.
The outcome variable for the negative binomial regression was the number of FF results
on the CFT at a given ‘whole herd’ test, where the natural log (In) of number of animals
tested used as offsets.(Stokes et al., 2000) Thus we were fitting a loglinear mixed mode]

to the proportion of CFT suspects to the independent variables.

113

Figure 6-2. Nine agricultural regions in Michigan.

 

The PFP was calculated as the number of animals suspect on the CFT/total
number of animals tested, assuming that all the CFT suspect results were false positive.
Explanatory variables, including herd type, agricultural region (figure 6-2), and the
season of testing were each independently compared with PFP using a univariate negative
binomial regression model. Explanatory variables with a likelihood ratio chi-squared test
less than p<0.25 in the univariate analysis were evaluated by the multivariable negative
binomial regression model. Backward stepwise elimination procedure was used to obtain
the final multivariable model. Inclusion of explanatory variables in the final model were

based on the likelihood ratio chi-squared test with p<0.05. In the multivariable negative

114

binomial regression, the identity of the testing veterinarians (VET) was included as a
random variable. The goodness of fit measure, pseudo R2, was calculated as follows:
(log-likelihood null model — log-likelihood full model)/log-likelihood full model), where
the null model only includes the intercept.(Anonymous, 1997) Using a generalized
estimating equations (GEE) method (Liang and Seger, 1986), the log-link mixed model

used was as follows:
Number of CFT suspects in a herd,- = a + ln(herd size),- + ,ijarj + uk + eijk.
or = intercept,
ln(herd size),- = natural logarithm of the number of cattle tested in a herd (offset
variable).

,6,- = regression coefficients for var},
varj = factor j for herd i.

uk = random effects term,

eijk = residual random error.

Association between PFP and the number of herds tested by a veterinarian was

estimated using Pearson product moment correlation (Ho: rho=0).

Spatial analysis

The exact spatial coordinates (latitude and longitude) of the tested herds were not
available, so the geographic location of herds was obtained by mapping (geocoding) the
address of the herd to spatial data on roads in Michigan using ArcINfO (ESRI, Redlands,

CA). The spatial reference data on roads in Michigan were obtained from the 2000

115

Census (http://wwwmichigan.gov/cgiz). Herds that had an address match 2 80% to the

reference address were considered an acceptable match.

Spatial clustering of high PFP was assessed using the spatial scan
statistic,(Kulldorff and Nargawalla, 1995), because this method can assess the location of
clusters. Ward and Carpenter (2000) reviewed the theoretical basis and general
characteristics of this statistical method of detecting disease clusters and its use in
veterinary epidemiology. In short, the spatial scan statistic creates multiple geographic
circles (windows) centered around possible clusters in the study region. The radius of the
window is determined by the investigator and may vary between 0 and an upper limit,
which is recommended not to exceed 50% of the study area.(Kulldorff et al., 2003) Each
geographic window is assessed by testing whether the probability of being a case within
the circle is equal to the probability of being a case outside the circle. The null
hypothesis is that these two probabilities are equal, which corresponds to complete spatial
randomness.(Kulldorff and Nargawalla, 1995) The maximum likelihood test is used as
the test statistic. The p-value for the maximum likelihood test is obtained through Monte
Carlo simulation. The Poisson model was used to model our data and allowed control for
the effects of herd type on spatial clusters of herds with a high proportion of CFT
suspects. In this study, the scan statistic was used to detect geographical areas with
unusually high proportions of FP results on the CFT. All spatial analyses were
performed in SaTScan Ver. 3.1.2, a shareware program (http://wwwsatscanorgl), using a

scan window of 2%.

116

Ecological associations

Spatial information on topography and wetland location in Michigan was obtained
from http://wwwmichigan.gov/cgi/, and association with PFP was assessed through
univariate negative binomial regression as described above for herd factors. A
multivariable analysis was performed controlling for herd factors that were significant in

the previous multivariable analysis. The testing veterinarian was again included as a

random effect.

RESULTS

Descriptive statistics

Table 6-1 shows the number of observations, mean, standard deviation (Std), 0th
(minimum), 25‘“, 50th (median), 75th and 100th (maximum) percentiles of the proportion
of CFT false positive (PFP) in all herds, beef and dairy herds, and each of 9 agricultural
regions. Table 6-2 shows the similar statistics for herd size stratified by herd type and
agricultural region. The PFP clearly differs between beef and dairy herds and among
agricultural regions. For example, the mean PFP in beef dairy herds was 0.0341 and
0.0558 in dairy herds. The distribution of PFP by herd is shown in figure 6-3 (72 = 4,989),
and it is obvious that the variability of PFP is larger among small herds as compared to
larger herds.

The mean, std, 0th, 25th 50‘”, 75‘", and 100th percentiles of the number of herds
tested by individual veterinarians were 56.0, 39.6, 4, 31, 47, 71, and 217, respectively.

The distribution of the mean PFP by the number of herds tested by individual

117

veterinarians are shown in figure 6-4. No obvious pattern was observed between PFP and
the number of herds a veterinarian had tested (p=0. 1060). The number of herds tested in

1996, 1997, 1998, 1999, 2000, and 2001 were 7, 4, 44, 31, 1689, and 3214, respectively.

118

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Figure 6-3. Distribution of proportion of CFI‘ false positive (PFP) by herd size.

 

 

 

 

 

.
.
. O
.
o 0 °
0 O
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. . ..
1- . 1 . . . 1 1
700 900 900 1000

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Figure 6-4. Distribution of the mean proportion of CFT false positive test
results (PFP) by veterinarian.

 

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dispersion at lower number of herds tested.
Negative binomial regression model

Then mean and variance of the number of CFT suspects for all herds were 4.97
and 84.64, respectively, indicating that the data were overdispersed, and negative
binomial regression model was appropriate to model the data.

By univariate analyses (PFP vs one factor at a time), PFP was significantly lower

in beef herds as compared to dairy herds (3.36 versus 5.51 cases per hundred tested

animals, p < 0.0001) (Table 6-4). Cattle herds in agricultural region 2, 3, and 5, had

122

significantly higher PFP than what was found in agricultural region 9 (8.27, 6.83, and
6.24 versus 4.02 cases per hundred tested animals, respectively, p < 0.0001) (Table 6-3).
Furthermore, the PFP was slightly higher in herds tested in the summer as compared to
herds tested in the winter (Season) (5.15 versus 4.66, p = 0.09) (Table 6-3). Several other
variables expressing the location of the herds and the time of year that herds were also

tested, but they were not included in the final model to avoid multicolliniarity.

In the final model, herd type and agricultural region were associated with the
proportion of false positive results on the CFT (Table 6-4). The regression coefficients

are adjusted for the effect of the random effect and offset variable.(Stokes et al., 2000)

The regression function was hence:

PFP = exp(-3.1275 + ,6] (herd type) + fl2(agricultural region))

Three biologically plausible two-way interaction terms between herd type,
agricultural region, and season of testing were tested with the final model, but none were
found to be statistically significant. The adjusted OR for beef cattle was 0.41 as
compared to dairy herds. Herds in agricultural regions 1, 2, 3, 5, and 6 had higher odds

of PFP as compared to herds in region 9. The pseudo R2 was 0.009.

123

Table 6—3. Univariate analysis of factors associated with the proportion of false
positive (PFP) on caudal fold tuberculin test (CFT) in Michigan.

 

 

Parameter cObs. 3Cases ”on f95% c1 gLR "df p-value
Herdtype

Beef 1735 3.36 0.61 0.57, 0.66

Dairy 3254 5.51 1.00 170.28 1 <0.0001
a'Agl'ic. region

1 438 4.07 1.01 0.86, 1.19

2 299 8.27 2.06 1.74, 2.43

3 596 6.83 1.70 1.47, 1.97

4 292 4.36 1.08 0.91, 1.29

5 798 6.24 1.55 1.35, 1.79

6 624 3.65 0.91 0.78, 1.05

7 549 3.94 0.98 0.84, 1.14

8 1036 3.98 0.99 0.86, 1.13

9 357 4.02 1.00 291.77 8 <0.0001
bQuarter

1‘t 1337 4.97 1.06 0.97, 1.17 3

2nd 1097 5.15 1.10 1.00, 1.22 3

3rd 975 4.66 1.00 0.90, 1.1 1 3

4‘h 1580 4.66 1.00 6.4 3 0.0937

 

aAgricultural region. bCalendar quarters. cNumber of observations. dNumber of CFT
suspects per 100 animals tested. 6Odds Ratio. f95% confidence interval of the OR.
gLikelihood ratio statistic. hDegrees of freedom.

124

Table 6-4. Multivariable analysis of factors associated with number of CFT
suspect results.

Parameter bEstimate cCases dOR c95% CI f

LR gc118 p-value

Intercept -3. 1275
Herd type
Beef -0.6656 2.25 0.41 0.44, 0.51
Dairy 0 4.38 1.00 49.79 1 <0.0001

aAgric. region

1 0.3225 6.05 1.18 1.01, 1.38
2 0.4419 6.82 2.27 1.92, 2.67
3 0.3240 6.06 2.01 1.74, 2.33
4 0.3356 6.13 1.05 0.89, 1.25
5 0.3922 6.49 1.66 1.45, 1.91
6 -0.0421 4.20 1.19 1.03, 1.38
7 0.2566 5.66 1.00 0.87, 1.16
8 0.1501 5.09 1.02 0.89, 1.17
9 0 4.38 1.00 20.27 8 0.0094

 

aAgricultural region. I)Parameter estimate 0Number of CFT suspects per 100 animals
tested. dOdds Ratio. 695% confidence interval of the OR. fLikelihood ratio statistic.
gDegrees of freedom.
Spatial analysis

Spatial coordinates (x,y coordinates, Michigan GeoRet) were obtained for 1039

beef and 2,262 dairy herds, respectively. These herds (n = 3,301) were used in the spatial

analysis. A spatial distribution of these herds in Michigan is shown in figure 6-5.

125

Significant (p <0.05) clustering of false positive animals on the CFT was detected using
the spatial scan statistic. The most likely cluster was found in the center of Alpena
county and had a radius of 19.5 km. A total of 759 CFT FP cattle were observed in this
area, and the expected number was 331.1. An additional 32 secondary clusters (p < 0.05)

were located throughout Michigan (figure 6-5).

Figure 6-5. Spatial distribution of herds tested for bovine tuberculosis with the
caudal fold tuberculin test in Michigan, including spatial clusters of herds with a high
proportion of CFT false positive test results.

 

 

 

 

 

 

 

 

 

 

 

 

I .0 .
a. A - ,
r." I v n S
. 3. 0’ ‘ .
. ~ 0' .1“,
35~ 2
. 3'
O O
‘2 -.E ‘ 9
0’ °.’ . e . '2
.:: . "I
-- o s '0
"s
‘0: ’.$
. O
0’ u ' 0 5'9.
«0 I“ ' ~
3’. be .0 's .
.4 “5:: .°

 

0 Individual herds.
0 Spatial clusters.

126

Ecological associations

The same herds as used for the spatial analysis was used to investigate
associations between PFP and the elevation (in meters) of respective herds, and of herds
that were located within 0.25 and 0.50 miles of defined wetlands. Results of the
univariate analysis are shown in Table 6-5. Furthermore, the elevation of the farm was
significantly positively associated with PFP (p < 0.0001). Neither of the variables of
distance to wetland or elevation were significantly associated with PFP when the testing

veterinarian was added as a random effect together with herd type and agricultural region.

Table 6-5. Univariate analysis of ecological factors associated with the
proportion of false positive (PFP) on caudal fold tuberculin test (CFT) in Michigan.

 

 

Parameter cObs. dCases cOR f95% CI gLR hdf p-value
aWetland within
0.25 miles

1 129 4.98 1.24 1.01, 1.51

2 3172 4.02 1.00 4.54 1 0.0332
aWetland within
0.50 miles

1 317 4.66 1.16 1.02, 1.32

2 2984 4.02 1 .0 5.07 1 0.0243

 

aHerds were located within 0.25 miles of designated wetland area. bHerds were located
within 0.50 miles of designated wetland. dNumber of CFT suspects per 100 animals
tested. eOdds Ratio. f95% confidence interval of the OR. gLikelihood ratio statistic.
hDegrees of freedom.

127

DISCUSSION

In populations with a very low disease prevalence (< l %), the specificity of a test
maybe be estimated by the proportion of false positive animals. The overall individual
animal bTb prevalence in Michigan is well below 1 %. The overall PFP for both dairy
and beef herds together was 0.0482, which means that the specificity of the CFT is
approximately 0.952. This is slightly higher than the specificity of the CFT (0.939)
estimated in cattle located in the bTb-infected area in northern Michigan(Norby et al.,
2003b) Although small, this difference may be due to the specificity being overestimated
when evaluated in a population of disease free animals.(Greiner and Gardner, 2000) For
example, the quantity of cross-reacting mycobacteria may vary between geographical
areas.

In this study, it was assumed that none of the herds we studied had any cattle truly
infected with bTb. All CFT suspect cattle had either been found negative on CCT, or
were found positive on CCT and then subsequently negative on necropsy, histopathology,
culture and PCR.(Norby et al., 2003a) The herd-level predictive value negative (HPVN)
is high when applied to a population of cattle consistent with low prevalence of bTb
positive herds as seen in Michigan(Norby et al., 2003c) Nonetheless, it is possible that a
few herds that were truly infected with bTb were included in this study. However, as bTb
is only present in the northern lower peninsula and the prevalence is very low among
herds, the number of bTb positive herds potentially included in this study would not be

more than 1 or 2, and thus our results would not be greatly affected.

128

The study was limited to herds where the testing veterinarian had tested at least 3
herds for bTb, and beef and dairy herds with at least 13 and 23 animals, respectively.
This was done to reduce the amount of variation that inexperienced veterinarians might
introduce in the PFP. Small herd sizes were eliminated because a single FP animal in a
small herd would have an unjustifiably high influence on the mean PFP.

There was a large variation in the PFP among herds and overdispersion was
clearly present (Table 6-1), indicating that a negative binomial regression was preferred
over a Poisson regression. Studies on incidence density rate of foot rot in sheep showing
similar data distributions have shown that such data were best fit by a negative binomial
distribution.(Wassink et al., 2003) Because a large number of herds had 0% FP results a
zero-inflated negative binomial model(Anonymous, 1997) could be warranted for this
analysis. However, such a model did not improve the fit of the model.

Univariate analyses showed that PFP was associated with herd type, agricultural
region, and the time of year the herd was tested, however, the season of testing was not
significant in the final model. Hence, the final model included herd type, agricultural
region, and the testing veterinarian as a random effect. Beef herd had a significantly
lower PFP than dairy herds. This was somewhat surprising, because beef herds in
general are more likely to be on pasture where they may ingest mycobacteria that cross-
react with the CFT. However, because dairy cattle are more used to being handled and
hence calmer when tested, it may be easier to read the CFT results, and more subtle
inflammatory reaction in the skin were easier to detect. Test results may be correlated

between herds when performed by the same veterinarian, and it cannot be assumed that

129

such measurements are independent. Hence, the veterinarian performing the herd test
was included as a random effect in the final generalized estimating equation model.

The PFP was higher in the northern agricultural regions of the lower peninsula in
Michigan as compared to the southern areas, and the primary cluster of FF animals were
also detected in this area by the spatial analysis (see below). Bovine tuberculosis has
only been detected in the northern part of the lower peninsula, and it is probable that
veterinarians in this area may be more likely to judge a small reaction in the skin as a
CFT suspect, because an animal is more likely to be infected in this area. It is human
nature that people tend to see what they expect to see, and may also be more careful or
willing to report a “suspect” CFT in an area where bTb is known to occur. It could also
be explained by the fact that regulatory veterinarians perform more of the testing in this
area, and that they were more rigorous in their interpretation of the CFT.

Our results may be useful for the bTb control effort by adjusting the observed
proportion of FP on the CFT by herd type and geographical location, and hence improve
the interpretation of a CFT, i.e. determine if the herd needs further testing. Also, our
results could help determine if veterinarians with an unusually low (or high) PFP test
record need to be contacted for retraining in the use of the CFT. In the current bTb
testing scheme in Michigan, all animals with a suspect CFT have to be retested with the
CCT within 7 days of reading the CFT(USDA and APHIS, 1999) and animals positive on
the CCT will be culled and submitted for mycobacterial culture and/or PCR. The results
of this study make it possible to statistically test whether the observed numbers of CFT
suspects are significantly different from what would be expected according to herd type

and geographical location of the herd. Such an analysis may be performed using standard

130

statistical tests for comparison of binomial proportion.(Rosner, 2000) However, this
approach should be validated on available test data from Michigan. Similarly,
veterinarians with unusually low (or high) PFP on the CFT can be identified and called in
for retraining.

We used the spatial scan statistic(Kulldorff and Nargawalla, 1995) to investigate
if there were spatial clusters of PFP on the CFT, because it permits identification of the
location of high (or low) clusters of PFP. An advantage of the scan statistic and SaTScan
in particular is that the ID’s of herds in each cluster are produced. This makes it easy for
regulatory veterinarians to investigate herds with particularly high PFP. The primary
cluster was located in the bTb-infected region in Michigan, but secondary clusters were
also detected outside this area (figure 6-5). This suggests that there might be other
factors than being a herd in the bTb area that affect the PFP. Such factors may include:
differences in mycobacteria found in the environment that cause cross-reaction on the
CFT or veterinarians that consistently have high PFP on the CFT or the testing
veterinarian. A spatial analysis may also be used to detect areas with unusually low PFP.
A scanning window of 2% was used in this analysis, which resulted in some of the
secondary cluster representing only one herd. We chose a 2% scanning window to be
able to detect fairly small clusters (specific areas) with unusually high PFP. However,
this procedure may also be used to detect areas with unusually low PFP.

We were not able to investigate the effect of age and other individual animal
factors that may affect the PFP of the tested herds because these data were unavailable.
Further studies must be conducted for this purpose. However, the associations between

PFP and two ecological factors, elevation and the presence of wetland close to the farm

131

were investigated. On univariate analysis, there were significant positive associations
between PFP and the elevation of the farm and whether a farm was located in the
proximity of wetland (Table 6-5). In both instances an increase in elevation and the
presence of wetland close to the farm, increase the expected PFP for cattle herds. This
may be explained by a quantitative and/or qualitative difference in non—typical
mycobacterial flora in the environment, because exposure to certain non-typical
mycobacteria may cause non-specific reactions on the tuberculin skin tests.(Cooney et al.,
1997; Comer and Pearson, 1978a, 1978b) Johnson-Ifearulundu and Kaneene (1999)
showed that the prevalence of Johne’s disease among and within herds was positively
associated with acidic soil, increased soil iron content, and soil type. This suggests that
there may be an association between certain environmental factors and the presence of
mycobacteria in the environment. In this study it was not possible to investigate the
effect of soil type, iron content and pH, because these data were only available for less
than 1/4 of the counties in Michigan.

In this study we showed that the PFP varies between beef and dairy herds and by
geographical region when adjusting for the veterinarian performing the CFT. These
results can be used by regulatory veterinarians to adjust the observed PFP by herd type
and geographical region and to detect geographical locations in Michigan where
particularly high or low PFP are present.

We recommend that geographical locations are obtained for all tested farms to facilitate

future spatial analyses.

132

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135

SUMMARY

While likely not the last word on bovine tuberculosis testing in Michigan, this
study offer some insight to the performance of the tuberculin skin tests in individual
animals and the herd-level performance of these tests, as well as factors that may affect
these tests. Estimates of sensitivities and specificities of the caudal fold test were in
general close to estimates reported in other studies in the United States. Only very little
information is available on the performance of the caudal fold and comparative cervical
tests when used in serial interpretation. However, our results seem to agree with limited
results from the United States.

Besides estimating the sensitivity of the two tuberculin skin tests, we were also
able to estimate the sensitivity of gross necropsy. Gross necropsy is often used alone or
in combination with other tests as the ‘gold standard’ for estimation of sensitivity (and
specificity) of the skin tests, hence the sensitivity of gross necropsy cannot be estimated.
However, in this study, we were able to estimate the sensitivity of the gross post-mortem
necropsy exam, which perhaps can be viewed as the “upper detection limit” of any
practical slaughter-based system for bTb.

Four different ‘two-population-two-tests’ latent-class models were used to
estimate the sensitivity and specificity of the tuberculin skin tests. The models allowed
us to account for possible dependence between the tests conditional on true disease status.
All the models performed well, especially taking into account the relatively small sample

of animals and low disease prevalence. Both the sensitivities and specificities in

136

particular are high. So the potential forthese tests to perform well in an eradication
program is high.

The next logical step in evaluation of the tuberculin skin tests, was to investigate
how well they work in a population of cattle herds infected with bovine tuberculosis.
Historically, eradication of bovine tuberculosis from many countries around the world
demonstrates that the skin tests perform very well on the herd-level. Because many
factors affect the herd-level sensitivity, specificity, and predictive values, it is not
straightforward to predict how individual animal sensitivity, specificity and prevalence in
particular, affect the herd-level parameters. Assuming that only one tuberculosis positive
animal is enough to declare the herd tuberculosis positive and the array of tests used to
classify a single animal as positive for bovine tuberculosis has a specificity of 1.0, then
the herd-level performance of the tuberculin skin tests in Michigan is very good. When
the prevalence is low, individual animal sensitivity has little effect on herd-level
sensitivity, which seems to be more correlated with the disease prevalence and the size of
the tested herd. More importantly, the predictive value negative of a tested herd is very
high, only decreasing slightly when the herd size decreases. These results show that to
fulfill the goal of eradication of bovine tuberculosis particular attention should be paid to
smaller herds.

It has long been known that some cattle that are not infected with Mycobacterium
bovis still react to the tuberculin injected intradermally when tested, i.e. they have false
positive test results. This adds to the cost of the eradication program because
tuberculosis negative animals that test positive on the caudal fold test must be retested

with the comparative cervical test. Furthermore, animals with false positive results on

137

the comparative cervical test are euthanized, necropsied, and selected samples are
submitted for tissue culture, histologic exam and possibly PCR. If factors that predispose
animals to a false negative result could be identified the cost of the eradication program
could be lowered. Furthermore, they could be used to adjust the proportion of false
positive animals, and a decision made whether to retest the herd or not. Furthermore,

veterinarians that consistently have high (or low) proportion of caudal fold positive

animals could be called in for retraining.

138

CONCLUSIONS

In this study I sought to answer five research objectives regarding the
performance of tests used to diagnose bovine tuberculosis (bTb). The first objective of
this study was to determine the sensitivity of the caudal fold tuberculin test (CFT) and the
CFT and the comparative cervical tuberculin tests used in serial interpretation as well as
gross necropsy using a gold standard approach. The sensitivity (Se) of the caudal fold
tuberculin tests (CFT) was as expected to be higher than when the CFT and the

comparative cervical test (CCT) were used in serial interpretation (CFI‘CCI‘ 313R). Our Se

estimate of the CFT is slightly higher than that reported by other studies in the United
States(Gaboric et al., 1996; Whipple etal., 1995) This might be explained by

differences in disease prevalence or status in our and their cattle populations. Our

estimates of Se for the CFI’CCTSER are very close to similar estimates reported by

Roswurm and Konyha. (1973). It is well accepted that the CFT and CFTCCTSER are
more suited to the detection of infected herds rather than the detection of infected cattle,
i.e. some bTb-infected animals will escape detection when the skin tests are used to
assess the infection status of individual animals. This finding supports a disease control
policy of total herd depopulation over a test and slaughter approach, because findings in
this study suggest that the test and slaughter approach would fail to detect all infected

animals in approximately 29% of the herds. The sensitivity of necropsy was almost as

high as CFTCCI‘SER. Furthermore, the sensitivity of gross necropsy increased to 100%

when 2 or more lesions were present. Such animals with multiple lesion sites would

expectedly shed greater numbers of infective Mycobacterium bovis and thus would be a

139

more important source of disease transmission. The gross post-mortem necropsy exam
can perhaps be viewed as the “upper detection limit” of any practical slaughter-based
system for bTb.

The second objective was to determine the sensitivity and specificity of the caudal
fold tuberculin test (CFT) and the CFT and comparative cervical tuberculin tests used in
serial interpretation using a method that does not require the assumption of a gold
standard and which can account for correlation between tests. Sensitivity and Sp of the
two tuberculin skin tests were estimated using a two-test-two-population approach using
four different simulation-based Bayesian models allowing for correction for possible

correlation between the two tests. There was a small significant negative correlation
between the CFTCCI‘SER and bacteriologic culture. This means that animals that are

negative on one tests are less likely to be negative on the other test than would be
expected if the tests were independent conditional on disease status. A negative
correlation is difficult to explain, but the lack of some biologic phenomenon may affect
both tests. Our estimates of the Sc of the CFT were very similar to other US. estimates.
(range:0.804-0.849).(Anonymous, 1992; Gaboric et al., 1996; Whipple et al., 1995) The
estimates of Sp of the CPI are similar to estimates reported by the USDA(Anonymous,

1992), but slightly higher than estimated by Gaboric et al. (1996). Our results for the
CFTCCTSER were close to other reported estimates.(Anonymous, 1992; Roswurm and

Konyha, 1973) Results obtained completing this objective will be a good estimate of
how the tuberculin skin tests perform in Michigan. However, it is important to keep in
mind that as the eradication program progresses, the bTb prevalence within herds is likely

to change and hence sensitivity and specificity estimates may do the same.

140

Completing the third objective presents herd-level sensitivity (HSe) and
specificity (HSp) estimates of the of the caudal fold tuberculin test (CFT) and the CFT
and comparative cervical tuberculin test when used in the bovine tuberculosis infected
area in Michigan. From a review of the literature, this seems to be the first attempt to
address herd-level performance of the tuberculin skin tests, so it is not possible to
compare our results to other work. However, our results reflect the behavior of changes
in Se and Sp and herd size as has been reviewed by Christensen and Gardner (2000). The
Sp is most likely equal to 100%, because all the tests are used in series in the eradication
program as reflected in scenarios 3 and 4. This will automatically result in a HSp of
100%. Equally the herd-level predictive value positive (HPVP) will also be 100%.
However, from a regulatory/eradication standpoint, the most interesting parameter is
probably herd-level predictive value negative (HPVN), because some herds may have a
negative herd-level test and still be infected with bTb. The HSe is very sensitive to the
herd size (sample size), and the smaller a herd is, the lower the HSe is. Decreasing herd
sizes also means a decrease in HPVN. Hence it may be beneficial to the eradication
effort to retest smaller herds more frequently than larger herds. It is worth to note, that if
Se and Sp changes over the course of the eradication program, then HSe, HSp, HPVP,
and HPVN may change also.

The fourth objective was to determine herd, geographic, and ecologic factors that
may affect the outcome of the CFT. Not unexpectedly, there was a large variation in the
proportion of false positive results (PFP) on the CFT among herds and overdispersion

was clearly present, indicating that a negative binomial regression was preferred over a

141

Poisson regression. Studies on incidence density rate of foot rot in sheep showing similar
data distributions have shown that such data were best fit by a negative binomial
distribution.(Wassink et al., 2003) The study showed that there was a much larger
variation in the predicted proportion of false positive results on the CFT (PFP) among
smaller herds than among large herds. This is to be expected because the result of just
one or a few false positive results will give a proportionately higher PFP than in a large
herd. The multiple negative binomial regression showed that the predicted proportion of
false positive results on the CFT is approximately half as large in beef cattle as compared
to dairy herds. This was somewhat surprising, because beef herds in general are more
likely to be on pasture where they may ingest mycobacteria that cross react with the CFT.
However, because dairy cattle are more used to be handled and hence calmer when
tested, it may be easier to read the CFT results, and more subtle inflammatory reaction in
the skin were easier to detect. The PFP was higher in the northern agricultural regions of
the lower peninsula in Michigan as compared to the southern areas, and the primary
cluster of FP animals were also detected in this area by the spatial analysis. Bovine
tuberculosis has only been detected in the northern part of the lower peninsula, and it is
probable that veterinarians in this area may be more likely to judge a small reaction in the
skin as a CFT suspect, because an animal is more likely to be infected in this area. It is
human nature that people tend to see what they expect to see, and may also be more
careful or willing to report a “suspect” CFT in an area where bTb is known to occur. It
could also be explained by the fact that regulatory veterinarians perform more of the

testing in this area, and that they were more rigorous in their interpretation of the CFT.

142

Finally, completing the fifth objective stressed that there maybe ‘unidentified’
factors that cause PFP to cluster. This may be explained by a quantitative and/or
qualitative difference in non-typical mycobacterial flora in the environment, because
exposure to certain non—typical mycobacteria may cause non-specific reaction on the
tuberculin skin tests.(Cooney et al., 1997; Corner and Pearson, 1978a, 1978b; Wassink et
al., 2003) J ohnson-Ifearulundu and Kaneene (1999) showed that the prevalence of
Johne’s disease among and within herds was positively associated with acidic soil,
increased soil iron content, and soil type. This suggests that there may be an association
between certain environmental factors and the presence of mycobacteria in the
environment. In this study it was not possible to investigate the effect of soil type, iron
content and pH, because these data were only available for less than Mr of the counties in
Michigan. Further studies will have to shed light on this subject.

Overall, this study presents regulatory veterinarians with some tools that may be
of help in evaluating the current bTb eradication program in Michigan or if adjustments

need to be made to the current program.

143

REFERENCES

Anonymous 1992. Assessment of risk factors for Mycobacterium bovis in the United
States (Fort Collins, Colorado USA, USDA, APHIS, VS).

Christensen, J ., Gardner, I.A., 2000, Herd-level interpretation of test results for
epidemiologic studies of animal diseases. Prev. Vet. Med. 45, 83-106.

Cooney, R., Kazda, J ., Quinn, J ., Cook, B., Muller, K., Monaghan, M., 1997,
Environmental mycobacteria in Ireland as a source of non-specific sensitization to
tuberculins. Irish Vet. J. 50, 370-373.

Corner, L.A., Pearson, C.W., 19788, Pathogenicity in cattle of atypical mycobacteria
isolated from feral pigs and cattle and the correlation of lesions with tuberculin
sensitivity. Austr. Vet. J. 54, 280-286.

Corner, L.A., Pearson, C.W., 1978b, Response of cattle to inoculation with atypical
mycobacteria of bovine origin. Austr. Vet. J. 54, 379-382.

Gaboric, C.M., Salman, M.D., Ellis, R.P., Triantis, J., 1996, Evaluation of five-antigen
ELISA for diagnosis of tuberculosis in cattle and Cervidae. J AVMA 209, 962-966.

Johnson-Ifearulundu, Y., Kaneene, J .B., 1999, Distribution and environmental risk
factors for paratuberculosis in dairy cattle herds in Michigan. AJVR 60, 589-596.

Roswurm, J .D., Konyha, 1973, The comparative cervical tuberculin test as an aid to

diagnosing bovine tuberculosis. Proc. Annu. Meet. U.S. Anim. Health Assoc. 77, 368-
389.

Wassink, G.J., Grogono-Thomas, R., Moore, L.J., Green, LE, 2003, Risk factors
associated with the prevalence of foot rot in sheep from 1999 to 2000. Vet. Rec. 152,
351-358.

Whipple, D.L., Bolin, C.A., Davis, A.J., Jamagin, J .L., Johnson, D.C., Payer, J .B., Saari,
D.A., Wilson, A.J., Wolf, M.M., 1995, Comparison of the sensitivity of the caudal fold

skin test and a commercial gamma-interferon assay for diagnosis of bovine tuberculosis.
Am J Vet Res 56, 415-419.

144

APPENDIX B.

The author takes no responsibility for errors and incorrect results obtained with this code.

Conditional independence model:

*********************it********************************

This code is based on a paper by W0 Johnson.
Wesley O. johnson et al., Am J of Epidemiology
2001, 153: 921-924, ”Screening without a gold
standard: The Hui-Walter paradigm revisited.

x-ijk refers to the observed number of in the cell
of the i-th and j-th tests (i=j=1,2) and the k—th
population (here k=1,2) (2 populations)

****************************************************

I’lrtl-l'fil-tlri

*
'k
*
*
*
*
*
*
'k
*

proc inl ;
/* Seed values for the binomial distributions */
seedl=1;

/* Number of burn-in samples */
burnin = 2000;

/* Total number of samples (cycles) */
ncycle = 12000;

/* Population 1 */

x111=23; x121=7; x21l=d; x221=162;
/* Population 2*/

x112=10; X122=5; x212=1; x222=282;

/* Starting values for prevalence, sensitivity, and specificity */
P1=0.1; P2=0.5; Se1=0.9; Se2=0.5; Spl=0.9; Sp2=0.5;

/* Prior beta-distributions {beta(a,b)} for prevalence, sensitivity,
and specificity */

/* Population 1 and 2 */

/* P1 ~ beta(1.27,9.65) and P2 ~ beta(l.73,2.71) */

/* Sensitivity for tests 1 and 2 */

/* Sel ~ beta(2.82,2.49) and Se2 ~ beta(8.29,1.81) */

/* Specificity for tests 1 and 2*/

/* Spl ~ beta(15.7,2.49) and Sp2 ~ beta(10.69,2.7l) */

/* Coding of the alpha and beta parameters for the prior distributions
*/

/* a=alpha and b=beta parameters for the beta distributions */

/* Alpha and beta parameters for prior distributions of prevalence */

145

aP1=13.63;
bP1=57.94;
aP2=1;
bP2=1;
/* Alpha and beta parameters for prior distributions of sensitivity */
aSel=1;
bSel=1;
aSe2=1;
bSe2=1;
/* Alpha and beta parameters for prior distributions of Specificity */
aSp1=1;
bSp1=1;
aSp2=1;
bSp2=1;

/* Creating subroutine named gibbs*/
Start gibbs;

/* Marginal frequences for observed counts */
/* Sample sizes for the two populations 3/

n1 = (x111 + x121 + x211 + x221);

n2 = (x112 + x122 + x212 + x222);

/* Observed marginal counts, d indicates summation over a row or
column */

xldd = (x111 + x121 + x112 + x122);
x2dd = (x211 + x221 + x212 + x222);
xdld = (x111 + x112 + x211 + x212);
ded = (x121 + x122 + x221 + x222);

*Start Gibbs;
/* Imputation step */
/* Sampling of z-ijk's., which are bin(x-ijk, p-ijk) */
if x1119=0 then
do;
p111 = (p1*Se1*Se2/(p1*Se1*Se2+(1-p1)*(l-Spl)*(1-Sp2)));
2111 = ranbin(seed1, x111, p111);
end;
else 2111 = 0;

if x121“=0 then
do;
p121 (p1*se1*(1-Se2)/(p1*Se1*(1—Se2)+(1—pl)*(1-Spl)*Sp2));
2121 = ranbin(seed1, x121, p121);

end;

else 2121 = 0;

if x2110=0 then

do;

p211 = (p1*(1—Se1)*Se2/(p1*(1-Se1)*Se2+(1-p1)*Sp1*(1—Sp2)));
2211 = ranbin(seed1, x211, p211);

end;

else 2211 = 0;

if x221‘=0 then

146

do;
p221 = (p1*(1-Se1)*(1-Se2)/(pl*(1-Sel)*(1—Se2)+(1-
p1)*Spl*Sp2)):
2221 = ranbin(seed1, x221, p221);
end;
else 2221 = 0;

if x112 then
do;
p112 = (p2*Se1*Se2/(p2*Se1*Se2+(1-p2)*(l-Spl)*(1-Sp2)));
2112 = ranbin(seed1, x112, p112);
end;
else 2112 = 0;

if x122‘=0 then
do;
p122 = (p2*se1*(1-Se2)/(p2*Se1*(1—Se2)+(1-p2)*(1—Sp1)*Sp2));
2122 = ranbin(seed1, x122, p122);
end;
else 2122 = 0;

if x212‘=0 then
do;
p212 = (p2*(1—Se1)*Se2/(p2*(1-Se1)*Se2+(1-p2)*Sp1*(1-Sp2)));
2212 = ranbin(seed1, x212, p212);
end;
else 2212 = 0;

if x222“=0 then
do;
p222 = (p2*(1-Se1)*(1-Se2)/(p2*(1-Se1)*(1-Se2)+(1-
p2)*Sp1*Sp2));
2222 = ranbin(seed1, x222, p222);
end;
else 2222 = 0;

/* Latent marginal counts */
zddl = (2111 + 2121 + 2211 + 2221);
zdd2 = (2112 + 2122 + 2212 + 2222);

zldd = (2111 + 2121 + 2112 + 2122);

22dd = (2211 + 2221 + 2212 + 2222);

zdld = (2111 + 2211 + 2112 + 2212);

zd2d = (2121 + 2221 + 2122 + 2222);
/* Posterior step */
/* Sampling marginal probability estimates */
/* Posterior beta for prevalence 1 (P1) */

Pla = rangam(seed1, (aP1+2dd1));
Plb = rangam(seed1, (bP1+n1-2dd1));
P1 = P1a/(P1a+P1b);

/* Posterior beta for prevalence 2 (P2) */
P2a = rangam(seed1, (aP2+zdd2));
P2b = rangam(seed1, (bP2+n2-2dd2));
P2 = P2a/(P2a+P2b);

147

/* Posterior beta for Sensitivity 1 (Sel) */
Sela = rangam(seed1, (aSe1+21dd));
Selb = rangam(seed1, (bSe1+22dd));
Sel = Sela/(Se1a+Se1b);

/* Posterior beta for Sensitivity 2 (Se2) */
Se2a = rangam(seed1, (aSe2+2d1d));
Se2b = rangam(seed1, (bSe2+2d2d));
Se2 = Se2a/(Se2a+Se2b);

/* Posterior beta for Specificity 1 (Spl) */
Spla = rangam(seed1, (aSpl+x2dd-22dd));
Splb = rangam(seed1, (bSp1+x1dd—21dd));
Spl = Spla/(Sp1a+Sp1b);

/* Posterior beta for Specificity 1 (Sp2) */
Sp2a = rangam(seed1, (aSp2+xd2d-zd2d));
Sp2b = rangam(seed1, (bSp2+xd1d-zd1d));
Sp2 = Sp2a/(Sp2a+Sp2b); *print Sp2beta;
finish gibbs;

/* Burn in*/

/* Running gibbs sampler within burn in*/
lepost = j(ncyc1e,1,0); /* Vector for marginal posterior for P1 */
P2mpost = j(ncyc1e,1,0);
Selmpost j(ncycle,1,0);
Se2mpost j(ncycle,1,0);
Splmpost = j(ncycle,1,0);
Sp2mpost = j(ncyc1e,1,0);
cycle = j(ncyc1e,1,0);
num=0; /* 'Counter' for number of saved samples */

do iter=1 to burnin;
run gibbs;
do;
num=num+1;
P1mpost[num]=P1;
P2mpost[num]=P2;
Selmpost[num]=Sel;
Se2mpost[num]=Se2;
Splmpost[num]=Sp1;
Sp2mpostlnum]=Sp2;
cycle[num]=num;
end;
end;

create burninsmpl var {cycle lepost P2mpost Selmpost
Se2mpost Splmpost Sp2mpost};
append;

/* Running gibbs sampler after burn in*/
lepost j(ncycle,1,0); /* Vector for marginal posterior for P1 */
P2mpost j(ncycle,1,0);

148

Selmpost j(ncyc1e,1,0);

Se2mpost j(ncycle,1,0);

Splmpost = j(ncycle,1,0);

Sp2mpost = j(ncycle,1,0);

cycle = j(ncycle,1,0);

num=0; /* 'Counter' for number of saved samples */

do iter = 1 to ncycle;
run gibbs;
do;
num = num+1;
P1mpost[num]=P1;
P2mpost[num]=P2;
Selmpost[num]=Se1;
Se2mpost[num]=Se2;
Splmpost[num]=Sp1;
Sp2mpost[num]=Sp2;
cycle[numl=num; /* collects the number of cycles (=ncycle)
*/
end;
end;

/* Creating prior distributions */
start prior;
/* Prior beta for prevalence 1 (P1) */
P1apr = rangam(seed1, aPl); /*Creating alpha parameter for beta
dist*/
Plbpr = rangam(seed1, bPl); *print Plb;
Plbetapr = P1apr/(P1apr+P1bpr); *print Plbeta;

/* Prior beta for prevalence 2 (P2) */
P2apr = rangam(seed1, aPZ);
P2bpr = rangam(seedl, bPZ);
P2betapr = P2apr/(P2apr+P2bpr);

/* Prior beta for Sensitivity 1 (Sel) */
Selapr = rangam(seed1, aSel);
Selbpr = rangam(seed1, bSel);
Selbetapr = Selapr/(Selapr+Se1bpr);

/* Prior beta for Sensitivity 2 (Se2) */
Se2apr = rangam(seed1, aSe2);
Se2bpr = rangam(seed1, bSe2);
Se2betapr = Se2apr/(Se2apr+Se2bpr);

/* Prior beta for Specificity 1 (Spl) */
Splapr = rangam(seed1, aSpl);
Splbpr = rangam(seed1, bSpl);
Splbetapr = Splapr/(Splapr+Sp1bpr);

/* Prior beta for Specificity 1 (Spl) */
Sp2apr = rangam(seed1, aSp2);
Sp2bpr = rangam(seed1, bSpZ);
Sp2betapr = Sp2apr/(Sp2apr+Sp2bpr); *print Sp2beta;
finish prior;

149

Plpr = j(ncycle,1,0); /* Vector for marginal posterior for P1 */
P2pr = j(ncycle,1,0);

Selpr = j(ncycle,1,0);

Se2pr = j(ncyc1e,1,0);

Splpr = j(ncycle,1,0);
Sp2pr = j(ncycle,1,0);
cyclepr = j(ncycle,1,0);

numpr=0;
do iter = 1 to ncycle;
run prior;
do;

numpr = numpr+1;
P1pr[numpr]=P1betapr;
P2pr[numpr]=P2betapr;
Selpr[numpr]=Se1betapr;
Se2pr[numpr]=Se2betapr;
Splpr[numpr]=Sp1betapr;
Sp2pr[numpr]=Sp2betapr;
cyclepr[numpr]=numpr; /* collects the number of cycles
(=ncycle) */
end;
end;
create margdist var {cycle Plpr P2pr Selpr Se2pr Splpr Sp2pr
lepost P2mpost Selmpost Se2mpost Splmpost
Sp2mpost};
append;
QUit;
run;

/* Macro for graphing the prior distributions and */
/* printing summary statistics */
titlel 'Prior distribution for ...';
title2 'Cycles: Burn in = 200 and total = 1200‘;
%nncro table(dsp);
proc univariate noprint data=margdist; var &dsp;
histogram / vscale=count beta (noprint theta=0 sigma=1 color=red
percents=1 2.5 5 10 50 90 95 97.5 99);
output out=&dsp mean=mean std=std pctlpre=P_
pctlpts=0, 1, 2.5, 5, 10, 50, 90, 95, 97.5, 99, 100;
data &dsp; set &dsp; var='&dsp';
knead;
%tablc(Plpr) %tablc(P2pr); %tablo(Se1pr);
%tablo(Se2pr); %tab1¢(Sp1pr); %tab10(Sp2pr);
data margdistmacrohp; set Plpr P2pr Selpr Splpr Se2pr Sp2pr;
title 'Summary statistics for prior distributions for P1, P2, Sel, Se2,
Spl, SpZ';
proc print; id var; var P_O P_l P_2_5 P_S P_SO P_95 P_97_5 P_99 P_100;
format P_l P_2_5 P_S P_SO P_95 P_97_S P_99 P_lOO;
run;

titlel 'Trace Plot burnin';
proc gplot data=burninsmpl;

150

plot P1mpost*cycle / overlay;
plot P2mpost*cycle / overlay;

plot Selmpost*cycle / overlay;
plot Se2mpost*cyc1e / overlay;
plot Splmpost*cyc1e / overlay;
plot Sp2mpost*cyc1e / overlay;
symboll
value=circle
cv=black;

run; quit;

titlel 'Trace Plot';

proc gplot data=margdist;
plot P1mpost*cycle / overlay;
plot P2mpost*cycle / overlay;

plot Selmpost*cycle / overlay;
plot Se2mpost*cycle / overlay;
plot Splmpost*cyc1e / overlay;
plot Sp2mpost*cycle / overlay;
symboll
value=circle
cv=black;

run; quit;

data trace;
join burninsmpl margdist;
run;

/* Macro for graphing the posterior distributions and */
/* printing summary statistics */
titlel ";
title2 ";
knacro table(ds);

proc univariate noprint data=margdist; var &ds;

histogram / vscale=count beta (noprint theta=0 sigma=1 color=red
percents=1 2.5 5 10 50 90 95 97.5 99);
output out=&ds mean=mean std=std mode=mode pctlpre=P_
pctlpts=0, 1, 2.5, 5, 10, 50, 90, 95, 97.5, 99, 100;

data &ds; set &ds; var="&ds';
Xmond;
%tabla(P1mpost) %tabla(P2mpost); %tabla(Se1mpost);
%tabla(Se2mpost); %tabla(Sp1mpost); %tablo(Sp2mpost);
data margdistmacroh; set lepost P2mpost Selmpost Splmpost Se2mpost
Sp2mpost;
title 'Summary statistics for posterior distributions for P1, P2, Sel,
Se2, Spl, Sp2';

proc print; id var; var P_O P_1 P_2_5 P_S P_SO mode P_95 P_97_5 P_99
P_lOO;

format P_0 P_l P_2_5 P_S P_SO mode P_9S P_97_5 P_99 P_lOO;
run;

151

Conditional dependence model (M2).

proc 11.1111 ;

/*

/*

/*

/*

/*

/*

/*

/*

/*
*/
/*
/*

/*

Seed values for the binomial distributions */
seed=1;

Number of burn-in samples */

Total number of samples (cycles) */
total = 12000;

Number of burn-in samples */
burnin = 2000; *burnin sample;
skip = 1; *sample every 100 cycles;

Starting values for prevalence, sensitivity, and specificity etc*/
Selpre=.3; Se2pre=.‘; Splpre=0.5; Sp2pre=0.4;
p111pre=.4; p101pre=.4; p011pre=.4; p001pre=.4;
p110pre=.4; p100pre=.4; p010pre=.d; p000pre=.4;
P1=.2; P2=.2; Se1=.6; Se2=.5; Spl=.6; Sp2=.5; p111=.1; p000=.1;

files to save different parameters */

alphaSsav=.;
alphaCsav=.;
Plpar=Pl;
P2par=P2;
Selpar=Se1;
Se2par=Se2;
Splpar=Sp1;
Sp2par=Sp2;
p111par=p111;
p000par=p000;
uSsav=0;
quav=0;
dcpar=dc;
dspar=ds;

Observed cell values, x */

/* Population 1 */

x111=23; x101=7; x011=4; x001=162;
Population 2*/

x112=10; x102=5; x012=1; x002=282;

Coding of the alpha and beta parameters for the prior distributions

a=alpha and b=beta parameters for the beta distributions */
Alpha and beta parameters for prior distributions of prevalence */
aP1=1;
bP1=1;
aP2=1; *5.98;
bP2=1;

Alpha and beta parameters for prior distributions of sensitivity */
aSl=1;
bSl=1;
aSZ=1;
b52=1;

152

/* Alpha and beta parameters for prior distributions of Specificity */
aC1=1;
bC1=1;
aC2=360.d; *1; *21.11; *20.6; *360.4;
bC2=1.36; *1; *2.06; *1.2; *1.36;
/* prior parameters for Dirichlet distribution */
aDRL=1;
bDRL=1;
CDRL=1;
dDRL=1;

/* Gibbs and MH algorithm */
do ncycle = 1 to total; /*Start MH and Gibbs mixing */

/* Sampling full conditional distributions */
if x111“=0 then
do;
palll = (pl*p111/(p1*p111+(1-p1)*(1-Sp1-Sp2+p000)));
a111 = ranbin(seed, x111, palll);
end;
else a111 = 0;

if x101‘=0 then
do;
pa101 = (p1*(Se1-p111)/(p1*(Sel-p111)+(1-p1)*(Sp2—p000)));
a101 = ranbin(seed, x101, pa101);

end;

else a101 = 0;

if x0119=0 then
do;
pa011 = (p1*(Se2-p111)/(p1*(Se2—p111)+(1—p1)*(Spl-pOOO)));
a011 = ranbin(seed, x011, paOll);
end;
else a011 = 0;

if x0010=0 then
do;
pa001 = (p1*(1-Sel-Se2+p111)/(p1*(1-Sel-Se2+p111)+(1-
P1)*P000));
a001 = ranbin(seed, x001, paOOl);
end;
else a001 = 0;

if x1129=0 then
do;
pa112 = (p2*p111/(p2*p111+(1-p2)*(1-Sp1-Sp2+p000)));
a112 = ranbin(seed, x112, pa112);
end;
else a112 = 0;

if x102“=0 then
do;
pa102 = (p2*(Se1-p111)/(p2*(Se1~p111)+(1-p2)*(SpZ-pOOO)));
a102 = ranbin(seed, x102, pa102);

end;

else a102 = 0;

153

if x012‘=0 then
do;
pa012 = (p2*(Se2-p111)/(p2*(Se2-p111)+(1-p2)*(Spl-pOOO)));
a012 = ranbin(seed, x012, pa012);
end;
else a012 = 0;

if x0029=0 then
do;
pa002 = (p2*(1-Sel-Se2+p111)/(pZ*(1—Se1-Se2+p111)+(1-
P2)*p000));
a002 = ranbin(seed, x002, pa002);
end;
else a002 = 0;

/* Calculating latent cell counts */

A1=a111+a101+a011+a001;
blll=X111-a111;

b101=x101-a101;

b011=x011-a011;

b001=x001-a001;
Bl=b001+b011+b101+b111;

N1=A1+Bl;

A2=a112+a102+a012+a002;

b112=x112-a112;

b102=x102-a102;

b012=x012-a012;

b002=x002-a002;

82=b002+b012+b102+b112;
N2=A2+BZ;

a11d=a111+a112;
a10d=a101+a102;
a01d=a011+a012;
a00d=a001+a002;

b11d=b111+b112t
b10d=b101+b102;
b01d=b011+b012i
b00d=b001+b002t

A=A1+A2;
B=Bl+BZ;
N=A+B;

/* Sampling full conditional for prevalence */
Pla = rangam(seed, (aP1+A1));
Plb = rangam(seed, (bP1+Bl));
P1 P1a/(P1a+P1b):

P2a rangam(seed, (aP2+A2));
P2b = rangam(seed, (bP2+B2));
P2 = P2a/(P2a+P2b);

154

do iter=1 to 1; /*Start MH*/
aGAM = rangam(seed,(a11d+aDRL));
bGAM = rangam(seed,(a10d+bDRL));
cGAM rangam(seed,(a01d+cDRL));
dGAM = rangam(seed,(a00d+dDRL));

/* Proposed probabilities for P11, P10, P01, P00 */
p111 = aGAM/(aGAM+bGAM+cGAM+dGAM);
p101 = bGAM/(aGAM+bGAM+cGAM+dGAM);
p011 CGAM/(aGAM+bGAM+cGAM+dGAM);
p001 dGAM/(aGAM+bGAM+cGAM+dGAM):
Sel = p111+p101;
se2 = p111+p011;
/* end;*/

/* Acceptance rate (P-move) for Sensitivity */

logAlphaS = log(min(Se1pre,Se2pre)-Se1pre*se2pre)-
log(min(Se1,Se2)-Se1*Se2)+

(aS1-1)*(log(Se1)-log(Se1pre))+(bSl-1)*(log(1-Se1)-
log(1-Se1pre))+
(aSZ-1)*(log(Se2)-log(Se2pre))+(b82-1)*(log(1-Se2)-

log(1-Se2prel);

AlphaSl=exp(logAlphaS);

Alphas = min(alpha81,1);
if (alphas < 1) then
do;
uS = ranuni(seed);
if (uS < alphaS) then
do;
Selpre=Se1;
Se2pre=Se2;
p111pre=p111;
p101pre=p101;
p011pre=p011;
end;
else
Sel = Selpre;
Se2 = Se2pre;
p111=p111pre;
p101=p101pre;
p011=p011pre;
end;
else
do;

Selpre Sel;
Se2pre = Se2;
p111pre=p111;
p101pre=p101;
p011pre=p011;
end;

/* Acceptance rate (P-move) for Specificity */
eGAM = rangam(seed,(b11d+aDRL));
fGAM rangam(seed,(b10d+bDRL));
gGAM rangam(seed,(b01d+cDRL));

155

hGAM

rangam(seed,(b00d+dDRL));

p110 = eGAM/(eGAM+fGAM+gGAM+hGAM);
p100 = fGAM/(eGAM+fGAM+gGAM+hGAM);
p010 = gGAM/(eGAM+fGAM+gGAM+hGAM);
p000 = hGAM/(eGAM+fGAM+gGAM+hGAM);
Spl = p000 + p010;
Sp2 = p000 + p100;

logAlphaC = log(min(Sp1pre,Sp2pre)-Sp1pre*sp2pre)-
log(min(Sp1,Sp2)-Sp1*Sp2)+
(aC1-1)*(log(Sp1)-log(Sp1pre))+(bC1-1)*(log(1—Spl)-
log(1-Sp1prel)+
(aC2-1)*(log(Sp2)-log(Sp2pre))+(bC2-1)*(log(1-Sp2)—
log(l-Sp2pre11;
AlphaC1=exp(logAlphaC);

alphaC = min(AlphaC1,1);
if (alphaC < 1) then
do;
uC = ranuni(seed);
if (uC < alphaC) then
do;
Splpre=Sp1;
Sp2pre=Sp2;
p100pre=p100;
p010pre=p010;
p000pre=p000;
end;
else
Spl = Splpre;
Sp2 = Sp2pre;
p100=p100pre;
p010=p010pre;
p000=p000pre;

end;
else
do;

Splpre Spl;
Sp2pre = Sp2;
p100pre=p100;
p010pre=p010;
p000pre=p000;
end;

dc=(p000-Sp1*Sp2)/(sqrt(Spl*(1-Sp1)*Sp2*(1-sp2)));
ds=(p111-Se1*Se2)/(sqrt(Se1*(1-Se1)*Se2*(1—Se2)));

end; /*end MH */

if(mod(ncycle,skip)=0 & ncycle > burnin) then /* sampling according to
ncycle */
/* burnin, and skip */
do;
cycle=cycle//ncycle;
alphaSsav=alphaSsav//a1phaS;

156

alphaCsav=a1phaCsav//alphaC;

P1par=P1par//P1;

P2par=P2par//P2;

Selpar=Se1par//Se1;

Splpar=Splpar//Sp1;

Se2par=Se2par//Se2;

Sp2par=Sp2par//Sp2;
p111par=p111par//p111;
p000par=p000par//p000;
dspar=dspar/lds;
dcpar=dcpar//dc;

uSsav=uSsav//uS;

quav=quav//uC;

end;
end; /*End MH gibs mixing */

create outputl var {cycle alphaSsav alphaCsav usav Plpar P2par
Selpar Se2par Splpar Sp2par plllpar pOOOpar dspar dcpar};
append;

quit;
run;

/* Macro used to calculate median and 95% CI's for parameter estimates
*/
titlel ";
title2 ";
%nacro table(ds);
proc univariate noprint data=output1; var &ds;
histogram / vscale=count beta (noprint theta=0 sigma=1 color=red
percents=1 2.5 5 10 50 90 95 97.5 99);
output out=&ds mean=mean std=std mode=mode pctlpre=P_
pctlpts=0, 1, 2.5, 5, 10, 50, 90, 95, 97.5, 99, 100;
data &ds; set &ds; var='&ds';
%nnnd;
%tabla(P1par); %tabla(P2par); %tabla(Se1par); %tabla(Se2par);
%tabla(Sp1par); %tabla(Sp2par);
%tab1a(p111par); %tabla(p000par); %tabla(dspar); %tab10(dcpar);
data margdistmacroh; set Plpar P2par Selpar Splpar Se2par Sp2par
plllpar pOOOpar dspar dcpar;
title 'Summary statistics for posterior distributions for P1, Sel, Se2,
Spl, Sp2, p111 p000 dspar dcpar';
proc print; id var; var P_l P_2_5 P_S P_SO /*mean*/ P_9S P_97_S P_99;
format P_1 P_2_5 P_S P_SO /*mean*/ P_95 P_97_5 P_99;
run;

/*Creating trace plot to assure sufficient burnin */
titlel 'Trace Plot ...';
proc gplot data=output1;

plot P1par*cyc1e / overlay;

plot P2par*cyc1e / overlay;

plot Selpar*cyc1e / overlay;
plot Se2par*cycle / overlay;
plot Splpar*cyc1e / overlay;
plot Sp2par*cycle / overlay;

symboll

157

value=circle
cv=black;
run; quit;

158

Conditional dependence model (M3):

proc inl;
/* Seed values for the binomial distributions */
seed=1;

/* Total number of samples (cycles) */
total = 12000;

/* Number of burn—in samples */
burnin = 2000; *burnin sample;
skip = 1; *sample every 100 cycles;

/* Starting values for prevalence, sensitivity, and specificity etc*/
Selpre=.3; Se2pre=.d; Splpre=0.5; Sp2pre=0.4;
p111pre=.4; p101pre=.4; p011pre=.4; p001pre=.4;
p110pre=.d; p100pre=.4; p010pre=.4; p000pre=.4;
P1=.2; P2=.2; Se1=.6; Se2=.5; Sp1=.6; Sp2=.5; p111=.1; p000=.1;
p001=.1; p101=.1; p100=.1;
ds=1;

/* files to save different parameters */
alphaSsav=.;
alphaCsav=.;
P1par=P1;
P2par=P2;
Selpar=Se1;
Se2par=Se2;
Splpar=Sp1;
plllpar=p111;
uSsav=0;
quav=0;
dspar=ds;

/* Observed cell values, x */
/* Population 1 */

x111=23; x101=7; x011=4; x001=162;
/* Population 2*/

x112=10; x102=5; x012=1; x002=282;

/* Coding of the alpha and beta parameters for the prior distributions
*/
/* a=alpha and b=beta parameters for the beta distributions */
/* Alpha and beta parameters for prior distributions of prevalence */
aP1=13.63;
bP1=57.94;
aP2=5.98;
bP2=66.68;

/* Alpha and beta parameters for prior distributions of sensitivity */
aSl=1; ‘
bSl=1;
aSZ=1;
b82=1;

/* Alpha and beta parameters for prior distributions of Specificity */
aCl=1;
bC1=1;

159

/* prior parameters for Dirichlet distribution */
aDRL=1;
bDRL=1;
CDRL=1;
dDRL=1;

/* Gibbs and MH algorithm */
do ncycle = 1 to total; /*Start MH and Gibbs mixing */

a111=x111;

if x101“=0 then
do;
pa101 = (p1*p101/(pl*p101+(1—p1)*(1-Sp1)));
a101 = ranbin(seed, x101, pa101);

end;

else a101 = 0;

a011=x011;
if x001‘=0 then
do;
pa001 = (p1*p001/(p1*p001+(1-p1)*Spl));
a001 = ranbin(seed, x001, pa001);
end;
else a001 = 0;

a112=x112;

if x102‘=0 then
do;
pa102 = (p2*p101/(p2*p101+(1-p2)*(1-Sp1)));
a102 = ranbin(seed, x102, pa102);

end;

else a102 = 0;

a012=x012;
if x0029=0 then
do;
pa002 = (p2*p001/(p2*p001+(1-p2)*Sp1));
a002 = ranbin(seed, x002, pa002);
end;
else a002 = 0;

/* Calculating latent cell counts */
A1=a111+a101+a011+a001;
b111=0;
b101=x101-a101;
b011=0;
b001=x001-a001;
Bl=b001+b101;
N1=A1+B1;

A2=a112+a102+a012+a002;
b112=0;
b102=x102-a102;
b012=0;
b002=x002-a002;
BZ=b002+b102;

160

N2=A2+B2;

a11d=a111+a112;
a10d=a101+a102;
a01d=a011+a012;
a00d=a001+a002;

/* b11d=0;*/
b10d=b101+b1027

/* b01d=0;*/
b00d=b001+b002;

A=A1+A2;
B=Bl+BZ;
N=A+B;

/* Sampling full conditional for prevalence */
Pla = rangam(seed, (aP1+A1));
Plb = rangam(seed, (bP1+B1));
P1 = P1a/(Pla+P1b);

P2a rangam(seed, (aP2+A2));
P2b rangam(seed, (bP2+82));
P2 = P2a/(P2a+P2b);

Spla = rangam(seed, (aC1+b00d));
Splb = rangam(seed, (bC1+b10d));
Spl = Spla/(Sp1a+Sp1b); *print spl;

do iter=1 to 1; /*Start MH*/

/* do until (p111>Se1*Se2);*/
aGAM = rangam(seed,(a11d+aDRL));
bGAM = rangam(seed,(a10d+bDRL));
cGAM rangam(seed,(a01d+cDRL));
dGAM = rangam(seed,(a00d+dDRL));

/* Proposed probabilities for P11, P10, P01, P00 */
p111 = aGAM/(aGAM+bGAM+cGAM+dGAM);

p101 = bGAM/(aGAM+bGAM+cGAM+dGAM);
p011 = cGAM/(aGAM+bGAM+cGAM+dGAM);
p001 = dGAM/(aGAM+bGAM+cGAM+dGAM);

Sel = p111+p101;
se2 = p111+p011;
se12 = Se1*Se2; *not needed!;
/* end;*/

/* Acceptance rate (P—move) for Sensitivity */
logAlphaS = log(min(Se1pre,Se2pre)-Se1pre*se2pre)-
log(min(Se1,Se2)-Se1*Se2)+
(aSl-1)*(1og(Se1)-log(Se1pre))+(bSl-1)*(log(1-Se1)-
log(1-Se1pre))+
(aSZ-l)*(log(Se2)-log(Se2pre))+(bSZ-1)*(log(1-Se2)-
log(1—Se2pre));
AlphaSl=exp(logAlphaS);
Alphas = min(alphaSl,1);
if (alphas < 1) then

161

do;
uS = ranuni(seed);
if (uS < alphaS) then
do;
Selpre=Se1;
Se2pre=Se2;
p111pre=p111;
p101pre=p101;
p011pre=p011;
end;
else
Sel = Selpre;
Se2 = Se2pre;
p111=p111pre;
p101=p101pre;
p011=p011pre;
end;
else
do;

Selpre = Sel;

Se2pre = Se2;
p111pre=p111;
p101pre=p101;
p011pre=p011;

end;

ds=(plll-Se1*Se2)/(sqrt(Se1*(1—Se1)*Se2*(1-Se2)));
end; /*end MH */

if(mod(ncycle,skip)=0 & ncycle > burnin) then /* sampling according to
ncycle */
/* burnin, and skip */
do;
cycle=cycle//ncycle;
alphaSsav=alphaSsav//alphaS;
alphaCsav=a1phaCsav//alphaC;
P1par=P1par//P1;
P2par=P2par//P2;
Selpar=Se1par//Se1;
Splpar=Sp1par//Sp1;
Se2par=Se2par//Se2;
Sp2par=Sp2par//Sp2;
p111par=p111par//p111;
p000par=p000par//p000;
dspar=dspar//ds;
uSsav=uSsav//uS;
quav=quav//uC;
end;
end; /*End MH gibs mixing */

create outputl var {cycle alphaSsav alphaCsav usav Plpar P2par
Selpar Se2par Splpar plllpar pOOOpar dspar};
append;

quit;

162

run;

/* Macro used to calculate median and 95% CI’s for parameter estimates
*/
titlel ";
title2 ";
%nacro table(ds);
proc univariate noprint data=output1; var &ds;
histogram / vscale=count beta (noprint theta=0 sigma=1 color=red
percents=1 2.5 5 10 50 90 95 97.5 99);
output out=&ds mean=mean std=std mode=mode pctlpre=P_
pctlpts=0, 1, 2.5, 5, 10, 50, 90, 95, 97.5, 99, 100;
data &ds; set &ds; var='&ds';
%nand;
%tab10(P1par); %tablo(P2par); %tabla(Se1par); %tabla(Se2par);
%tabla(Sp1par); *%table(Sp2par);
%tabla(p111par); %tablo(p000par); %tabla(dspar); *%table(dcpar);
data margdistmacroh; set Plpar P2par Selpar Splpar Se2par plllpar
pOOOpar dspar;* dcpar;
title 'Summary statistics for posterior distributions for P1, Sel, Se2,
Spl, Sp2, p111 p000 dspar dcpar';
proc print; id var; var P_1 P_2_5 P_S P_50 /*mean*/ P_9S P_97_S P_99;
format P_1 P_2_S P_S P_SO /*mean*/ P_95 P_97_5 P_99;
run;

/*Creating trace plot to assure sufficient burnin */
titlel 'Trace Plot ...';
proc gplot data=output1;
plot P1par*cycle / overlay;
plot P2par*cycle / overlay;
plot Selpar*cyc1e / overlay;
plot Se2par*cyc1e / overlay;
plot Splpar*cycle / overlay;
/* plot Sp2par*cyc1e / overlay;*/
symboll
value=circle
cv=black;
run; quit;

163

Conditional dependence model (M4)[Georgiadis et al., 2003]:

*

this program is based on a paper by MP Georgiadis, WO Johnson
IA Gardner and R Singh. Appl. Statist. (2003) 52, pp. 1—14

Test 1: MAT (Prior info is selected for this parameter)
Test 2: ELISA (No prior info [Paramters to be 'estimated']);

Notation

P1: prevalence in population 1

P2: prevalence in population 2

Sell, 8e12, Se21, Se22 conditional probabilities (eta in paper)
Spll, Sp12, Sp21, Sp22 Conditional probabilities (theta in paper)
Sel=Se11+Se12z sensitivity of test 1 (eta in paper)
Spl=Sp21+Sp22: specificity of test 1 (theta in paper)

D: diseased (D in paper)

H: healthy (D with bar over in paper)

1: lambda

g: gamma

w: xxxxx. Vector of parameters: w=(P1, P2, Sel, Spl, 1D, gD, 1H, gH)
lD=Se11/Se1

gD=Sp21/(1-Sel)

lH=Sp22/Spl

gH=Sp12/(1-Sp1)

r: rho

rD: correlation parameter for diseased animals (D)

rH: correlation parameter for healthy animals (H)

See paper p. S for the reparameterizations using lambda and gamma;

proc 1nd;

/*

/*

/*

files to save different parameters */

P1par=P1;
P1par=P2;
Selpar=Sel;
Se2par=Se2;
Sp1par=Sp1;
Sp2par=Sp2;
1Dpar=1D;
alar=lH;
gDpar=gD;
ngar=gH;
erar=rD;
erar=rH;
dspar=ds;
dcpar=dc;

Seed values for the binomial distributions */

seed1=1;

Starting values for prevalence, sensitivity, and specificity */

Pl=0.1; P2=0.5; Se1=0.1; Sp1=0.1;
1D=0.1; 1H=0.1; gD=0.1; gH=0.1;

164

/* Observed cell values, x */
/* Population 1 */

x111=27; x121=2; x211=7; x221=63;
/* Population 2*/

x112=32; x122=5; x212=11; x222=243;

/* Priors for prevalence, Sel, Spl, lambda, and gamma*/
/* Coding of the alpha and beta parameters for the prior distributions
*/
/* a=alpha and b=beta parameters for the beta distributions */
/* Alpha and beta parameters for prior distributions of prevalence */
aP1=19.16; *13.63;
bPl=27.79; *S7.94;
aP2=3.11; *5.98;
bP2=36.56; *66.68;
/* Alpha and beta parameters for prior distributions of sensitivity
*/
aSe1=1;
bSel=1;
/* Alpha and beta parameters for prior distributions of Specificity */
aSp1=360.‘;
bSp1=1.36;
/* Alpha and beta parameters for prior distributions of lambda */
alD=1;
b1D=1;
alH=1;
b1H=1;
/* Alpha and beta parameters for prior distributions of gamma */
agD=1;
bgD=1;
agH=1;
bgH=1;

/* Total number of samples (cycles) */
total = 12000;
burnin = 2000; *burnin sample;
skip = 1; *sample every 100 cycles;
/* Sample every 100 cycles */

/* Starting Gibbs sampler */
do ncycle=1 to total;

/* Marginal frequencies for observed counts*/
/* Observed marginal counts, d indicates summation over a row or
column */
xdd1=(x111+x121+x211+x221);
xdd2=(x112+x122+x212+x222);
x1dd=(x111+x121+x112+x122);
x2dd=(x211+x212+x221+x222);
x21d=(x211+x212);
x22d=(x221+x222);
x11d=(x111+x112);
x12d=(x121+x122);

165

*Start Gibbs;

/* Imputation step */

/* Sampling of z-ijk's., which are bin(x-ijk, p—ijk) */
if x111“=0 then

do;
p111 = (p1*Se1*lD/(pl*Se1*1D+(1—p1)*(1-Spl)*(1-gH)));
2111 = ranbin(seedl, x111, p111);
end;

else 2111 = 0; *print zlllsample;

if x121“=0 then

do;
p121 = (p1*se1*(1-1D)/(p1*Se1*(1-lD)+(1-pl)*(1-Sp1)*gH));
2121 = ranbin(seedl, x121, p121);

end;

else 2121 = 0;

if x211“=0 then

do;

p211 = (p1*(1-Se1)*gD/(p1*(1-Se1)*gD+(1-p1)*Sp1*(1—1H)));
2211 = ranbin(seedl, x211, p211);

end;

else 2211 = 0;

if x2219=0 then

do;

p221 = (p1*(1-Se1)*(1-gD)/(p1*(1-Se1)*(1-gD)+(1-p1)*Sp1*lH));
2221 = ranbin(seedl, x221, p221);

end;

else 2221 = 0;

if x112 then
do;
p112 = (p2*Sel*lD/(p2*Se1*lD+(1-p2)*(1-Sp1)*(1-gH)));
2112 = ranbin(seedl, x112, p112);
end;
else 2112 = 0;

if x1220=0 then
do;
p122 = (p2*se1*(1-1D)/(pZ*Se1*(1-lD)+(1—p2)*(1-Sp1)*gH));
2122 = ranbin(seedl, x122, p122);
end;
else 2122 = 0;

if x212“=0 then
do;
p212 = (p2*(1-Se1)*gD/(p2*(1-Se1)*gD+(1-p2)*Sp1*(1—1H)));
2212 = ranbin(seedl, x212, p212);
end;
else 2212 = 0;

if x222“=0 then

do;
p222 = (p2*(1-Sel)*(1-gD)/(p2*(1-Sel)*(1—gD)+(1-p2)*Sp1*lH));

166

/*

/*
/*
/*

/*

/*

/*

/*

/*

/*

2222 = ranbin(seedl, x222, p222);
end;
else 2222 = 0;

Latent marginal counts */
zddl = (2111 + 2121 + 2211 + 2221);
zdd2 = (2112 + 2122 + 2212 + 2222);

zldd = (2111 + 2121 + 2112 + 2122);
22dd = (2211 + 2221 + 2212 + 2222);

211d = (2111+2112);

212d = (2121+2122);
221d = (2211+2212);
222d = (2221+2222);
211d = (2111+2112);

212d = (2121+2122);

Posterior step */

Sampling marginal probability estimates */

Posterior beta for prevalence 1 (Pl) */
Pla = rangam(seedl, (aP1+zddl));

Plb = rangam(seedl, (bP1+xdd1-zdd1));

P1 = Pla/(P1a+P1b);

Posterior beta for prevalence 2 (P2) */
P2a = rangam(seedl, (aP2+zdd2));

P2b = rangam(seedl, (bP2+xdd2-2dd2));

P2 = P2a/(P2a+P2b);

Posterior beta for Sensitivity l (Sel) */
Sela = rangam(seedl, (aSe1+21dd));

Selb = rangam(seedl, (bSe1+22dd));

Sel = Sela/(Se1a+Selb);

Posterior beta for Specificity 1 (Spl) */

Spla = rangam(seedl, (aSp1+x2dd-22dd));
Splb = rangam(seedl, (bSpl+xldd-zldd));
Spl = Spla/(Spla+Sp1b);

Posterior beta for 1D */
lDa = rangam(seedl, (alD+211d));
lDb = rangam(seedl, (b1D+212d));
ID = lDa/(lDa+lDb);

Posterior beta for lH*/
lHa = rangam(seedl, (alH+x22d-222d));
le = rangam(seedl, (blH+x21d-221d));
1H = 1Ha/(lHa+1Hb);

Posterior beta for 9D */
gDa = rangam(seedl, (agD+221d));
ng = rangam(seedl, (bgD+222d));
gD = gDa/(gDa+ng);

167

/* Posterior beta for 9H */
gHa = rangam(seedl, (agH+x12d-212d));
gHb = rangam(seedl, (bgH+x11d-211d));
gH = gHa/(gHa+gHb);

/* Posterior for Se2 */
Se2 = lD*Se1+gD*(1-Sel);

/* Posterior for Sp2 */
Sp2 = gH*(1-Sp1)+lH*Spl;

/* Posterior for correlation for diseased subjects */
Se11=Se1*lD;
rD = (Sell-Sel*Se2)/sqrt(Se1*(1-Sel)*Se2*(1-Se2));
ds=(Se11-Se1*Se2)/(sqrt(Se1*(1-Se1)*Se2*(1-Se2)));

/* Posterior for correlation for healthy subjects */
Sp22=Spl*lH;
rH = (Sp22-Sp1*Sp2)/sqrt(Sp1*(1—Sp1)*Sp2*(1-Sp2));
dc=(sp22—Spl*Sp2)/(sqrt(Spl*(1-Sp1)*Sp2*(1-sp2)));

if(mod(ncycle,skip)=0 & ncycle > burnin) then

do;
cycle=cycle//ncycle;

P1par=P1par//P1;
P2par=P2par//P2;
Selpar=Selpar//Sel;
Se2par=Se2par//Se2;
SplparzSplpar//Spl;
Sp2par=Sp2par//Sp2;
lear=lear//1D;
alar=alar//1H;
gDpar=gDpar//gD;
ngar=ngar//gH;
erar=erar//rD;
erar=erar//rH;
dspar=dspar//ds;
dcpar=dcpar//dc;

end;

end;
create Marios var {cycle Plpar P2par Selpar Splpar Se2par Sp2par
1Dpar alar gDpar ngar erar erar dspar dcpar};
append;

quit;
run;

/* Macro used to calculate median and 95% CI's for parameter astimates
*/

titlel 'Posterior Marginal Distribution for ...';

title2 'Cycles: Burn in = 5000, total = 1000000, Skip = 100';

168

%nacro table(ds);

proc univariate noprint data=Marios; var &ds;

histogram / vscale=count beta (noprint theta=0 sigma=1 color=red
percents=1 2.5 5 10 50 90 95 97.5 99);
output out=&ds mean=mean std=std mode=mode pctlpre=P_
pctlpts=0, 1, 2.5, 5, 10, 50, 90, 95, 97.5, 99, 100;

data &ds; set &ds; var="&ds';
Md;
%tabla(Plpar); %tabla(P2par); %tabla(Se1par); %tablo(Sp1par);

%tabla(Se2par); %tabla(Sp2par); %tabla(lear); %tabla(alar);
%tab10(gDpar); %tab1¢(ngar); %tabla(erar); %tabla(erar);
%tabla(dspar); %tabla(dcpar);

data mariosmacro; set Plpar P2par Selpar Splpar Se2par Sp2par

lear alar gDpar ngar erar erar dspar

dcpar;
title 'Summary statistics for posterior distributions for P1, Sel, Se2,
Spl, Sp2';

proc print; id var; var P_1 P_2_5 P_S P_SO /*mean*/ P_95 P_97_5 P_99;
format P_l P_2_5 P_S P_SO /*mean*/ P_95 P_97_5 P_99;
run;

/*Creating trace plot to assure sufficient burnin */
titlel 'Trace Plot ...';
proc gplot data=marios;

plot P1par*cycle / overlay;
plot P2par*cycle / overlay;
plot Selpar*cycle / overlay;
plot Sp1par*cycle / overlay;
plot Se2par*cycle / overlay;
plot Sp2par*cyc1e / overlay;
plot lear *cycle / overlay;
plot alar *cycle / overlay;
plot gDpar *cycle / overlay;
plot ngar *cycle / overlay;
plot erar *cycle / overlay;
plot erar *cycle / overlay;
plot dspar *cycle / overlay;
plot dcpar *cycle / overlay;
symboll
value=circle
cv=black;
run; quit;

169

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