Bayesian estimation of prevalence of paratuberculosis in da…

97

C.G. McAloon

et al.

/ Preventive Veterinary Medicine 128

(2016) 95–100

Table 1 Point

estimates

and

confidence

intervals

extracted

from

studies

evaluating

the

sensitivity

and

specificity

of

3

commercial

ELISA

kits

used

in

Ireland

for

the

serological

“infected” animals.

detection of paratuberculosis

Source

Kit

Se

Confidence

Intervals

Sp

Confidence

Intervals

0.08, 0.70 a

0.849, 0.996 a

Aly et al.

(2014)

Kit B Kit C Kit A Kit A Kit A Kit A

0.34

0.958

0.9859, 0.9874 b

Nielsen et al. Norton et al. Alinovi et al. McKenna et al.

(2013) (2010) (2009)

0.27–0.79

0.9866

25.5, 65.0 a

0.989, 0.999 a

0.41 0.26 0.07 0.22

0.997

1.00

– – –

0.03, 0.11 a

(2005)

– –

Jubb et al.

(2004)

a 95% b 99%

confidence confidence

interval. interval.

The

first

study

was

limited

to

a

population

of

cull

cows

2.2.4.

Sensitivity analysis

(McKenna 2010) was carried out on herds with a history of clinical disease and with relatively highATP. A third study (Nielsen et al., 2013), was removed because the target condition “infected”, was in this case, defined based on the longitudinal interpretation of the evaluated serolog- ical test. A final study (Aly et al., 2014) was removed which was based on the evaluation of the test on a single herd. After removing these estimates, 2 evaluation studies were avail- able for kit Awith no appropriate published values available for kits B and C. When test characteristics were presented by age group, a weighted mean of the test Se was calculated relative to the age dis- tribution of the present study. A sample size weighted mean was next calculated for the Se of kit A (0.224) using the two estimates extracted from the study. A previously constructed estimate for the Se and Sp of kit B was available (Nielsen and Toft, 2009) which has been used in subsequent prevalence estimates (Pozzato et al., 2011), kits B and C are known to have similar ancestry, therefore the same values were adopted for kit C. The parameters for the beta-distribution were found using “betabuster” software (Chun- Lung 2010) based on a given mode and either upper or lower 95th bound. The Se of individual milk ELISA relative to serum ELISA has been shown to be approximately 0.87 (van Weering et al., 2007), therefore in the absence of a Se estimate for milk, the Se of the serum ELISA was multiplied by a factor of 0.87. Final values and associated beta distribution parameters are shown in Table 2. (secondary dataset) froma previously published prevalence survey (Good et al., 2009) were used as follows. Data were removed from animals less than 24 months of age, from animals without a recorded date of birth and from non-dairy enterprises. This dataset included a much higher proportion of small herds relative to the primary dataset, therefore, farms containing less than 20 animals were removed to prevent possible overestimation of CWHP priors due to small herd sizes. The CWHP was estimated for each positive herd using the Rogan-Gladen estimator (Rogan and Gladen, 1978), i.e., CWHP = (AP + Sp − 1)/(Se + Sp − 1), where, AP = Apparent Preva- lence. All serum samples in this survey were tested using the Pourquier ELISA, this kit is now sold as Kit B, and therefore, the test characteristics given for Kit B (Table 2) were used to calculate the prior distribution of within-herd prevalences. The distribution of CWHPs in this dataset were plotted and themean andmode used to fit a beta distribution using the betabuster programme. A number of priors were trialled for HTP including the herd- level apparent prevalence based on a varying number cut point reactors. However, after it was observed that the primary model was extremely insensitive to the prior for HTP, it was decided to use a flat distribution from 0 to 1 as the prior for this variable. et al., 2005) and the second study (Norton et al., 2.2.3. Model priors—HTP and CWHP Prior distributions for HTP and CWHP in Irish dairy herds were required. In order to construct these priors, data

Sensitivity

analysis

of

the

final

estimate

to

the

priors

used

in

assessed

by

varying

the

point

estimate

and

con-

the model was

fidence

intervals

of

the

each

prior

by

10%,

25%

and

50%

in

either

direction

and

repeating

the

analysis.

In

addition,

the prior

for HTP

as

a

uniform

distribution

from

0

to

1

and

the

anal-

was modelled

repeated. The posterior HTP was

ysis

compared with

the

estimate

from

the default priors and

the percentage deviation calculated as;

(HTP S − analysis Version

HTP D )/HTP D , where HTP S andHTP D represent the posterior

estimates of HTP

from

the sensitivity analysis and

the default prior

respectively.

The model was

implemented

in WinBUGS

1.4.1 with

the

first

10,000

iterations

discarded

as

burn-

in and 50,000

iterations used

for posterior

inference. Convergence

assessed

by

visual

inspection

of

the

time

series

trace

plots

was and

autocorrelation

plots

and

by

running multiple

(n = 3)

chains

from different

starting

values.

Figures were

constructed using

the

“ggplots2” package

in R.

3.

Results

3.1.

Descriptive

statistics

3.1.1.

Secondary dataset

(2005);

formulation of priors

In the 2005 dataset. After removing non-relevant results, 5822 test results from 119 herds were available in the final dataset. The modal value for the prior for HTP was 0.32. The 95% confidence intervals were 0–0.92. The beta distribution was fitted with a mode of 0.32 and a 95th percentile of 0.92. The resulting distribution had alpha and beta parameters of 1.18 and 1.25 and 10th, 50th and 90th per- centiles of 0.12, 0.48 and 0.86 respectively. Within infected herds, the CWHP was 0.151 with a mode at 0.1, the resulting beta distri- bution used for the prior had alpha and beta parameters of 2.37 and 13.31 and 10th, 50th and 90th percentiles of 0.051, 0.136 and 0.272 respectively. total, there were 20,323 test results available from

Primary dataset (2013–14) Descriptive statistics are shown

3.1.2.

in Table 3. After

removing error

records, data were available

for 99,101 animals

in 1039 dairy herds.

Average herd size was 95.4 animals,

the majority of

the herds were

in

Leinster

(n = 249)

and Munster

(n = 719)

provinces

and and

located

these

herds

also

had

the

greatest

average

herd

sizes

(108.5

102.1 respectively). Four hundred and an apparent prevalence of 0, tribution of apparent prevalence

forty eight herds (43.1%) had

i.e. no animals testing positive. The dis- for herds with 1 or more animals

testing positive

is

shown

in Fig. 1.

3.2.

Model outcomes

The median

posterior

estimate

for HTP

(95%

posterior

proba-

interval) was

0.28

(0.23,

0.32). Across

all

herds,

the median

bility

ATP was

found

to

be

0.032

(0.009,

0.145), whilst within

infected

the median CWHP was 0.137

(0.033, 0.348). Fig. 2 shows

the

herds,

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