Bayesian estimation of prevalence of paratuberculosis in da…

96

C.G. McAloon

et al.

/ Preventive Veterinary Medicine 128

(2016) 95–100

berculosis number of

across

countries (Nielsen

in

Europe

identified

critical

issues

in

a

test

strategy. The

“herd”

in

this

study was

therefore defined as

the

number month

studies

and Toft, 2009), primarily

these

issues

of unique

and

eligible

animals

on

the

farm within

the

14

related to the

incorrect values for test sensitivity (Se) and specificity

sampling

frame.

in

the analysis.

(Sp)

Estimates

of

Se

and

Sp

of

diagnostic

tests

for

paratuberculosis

2.2.

Statistical analysis

vary tion and tion

considerably

(Nielsen

and

Toft,

2008). Much

of

this

varia-

can be

attributed

to differences

among

reference populations

2.2.1.

Analytical model

sampling procedure

strategies (Greiner

that and

have

been

used

for

the

test

valida-

Prevalence

was

estimated

with

a

Bayesian

model

extended

Gardner,

2000).

However

estimates

from

that

proposed

by

Branscum

et

al.

(2004), which was

based num-

of

Se

and

Sp may

also

vary

according

to

prevalence

(Brenner

and

on methodology

introduced

by

Hanson

et

al.

(2003).

The

Gefeller, 1997) and (Greiner and Gardner, 2000). Consequently, the relationship between true prevalence (TP) and apparent prevalence (AP) can be expected to vary between populations. It may therefore be unreasonable to assume a fixed, constant, Se and Sp over different populations (Berkvens et al., 2006). In Bayesian analyses, all parameters are considered ran- dom variables and can be modelled using probability distributions. Uncertainty and variability associated with estimates of test Se and Spmay therefore be incorporated in the analysis. In addition, in this instance, a Bayesian posterior probability will provide inference on a prevalence estimate, conditional on both currently observed data and previous information about the disease. This methodology has not yet been applied to the estimation of the prevalence of paratu- berculosis in Irish dairy herds, but has been used extensively to estimate the prevalence in other countries (Pozzato et al., 2011; Lombard et al., 2013; Verdugo et al., 2015). The aim of this study, therefore was to estimate the HTP and overall animal-level true prevalence (ATP) of paratuberculosis among herds enrolled in a national voluntary control programme. therefore between herds

of

animals

testing

positive

in

each

herd was

considered

to

be

ber

binomially

distributed.

A

binomial

rather

than

a hypergeometric in each herd were

distribution was used because all

adult

animals

sampled. The model was

constructed as;

npos ijk ∼

Binomial (  i ,

nherd i

)

(1)

Se jk ×

ATP i +

(1

ATP i

)

(1

Sp jk

)

(2)

 i =

×

ATP i = HTP i ∼

HTP i ×

CWHP i

(3)

Bernoulli (  )

(4)

CWHP i ∼

Beta (a CWHP ,

b CWHP )

(5)

Se jk ∼ Sp jk ∼

(6)

Beta (a Se ,

b Se )

Beta (a Sp ,

b Sp )

(7)

Beta (a  ,

b  )

(8)



where npos ijk

equals

the number of animals

testing positive

in

the

i-th herd

(herd i

) using

the

j-th ELISA kit and

the k-th

test medium,

a

probability

of

each

animal

testing

positive

(  i

)

and

num-

given

2.

Materials and methods

ber

of

animals

in

the herd

(nherd i

).

The probability of a

randomly

chosen

animal

from

a

herd

testing

positive was

a

function

of

the

Two datasets were analysed in

this

study. The primary analysis

true prevalence

(ATP) within herd i , and Sp, which varied

and

the diagnos-

animal-level

test

data

collected

from

the

national

control

programme

utilised between

tic

test

characteristics; Se

according

to kit

(j) as

2013

and

2014. Model

priors

for

this

analysis were

con-

and

test medium

(k).

The

ATP

for

a

given

herd was modelled

structed by analysing a

secondary

(2005) dataset.

a mixture prevalence

distribution:

the

product

of HTP

and

conditional-herd

(CWHP). The HTP was modelled as a Bernoulli distribu-

is used

to model

random variables

tion. The Bernoulli distribution

Study population

2.1.

with to be

two

possible

outcomes,

in

this

case

a

herd was

considered

“infected” with probability  to

indicate

the probability of

a

The

primary

(2013–2014)

dataset

for

the

current

study

was

randomly

chosen herd

containing

one

or more

truly

infected

ani-

obtained

from

herds

voluntarily

enrolled

in

the

national enrolled

volun-

and

“uninfected” with

a

probability

1-  .

Then,

conditional

mals

Johne’s

Disease

control

programme.

Herds

in

the

tary

on

the herd being

infected,

the conditional within-herd prevalence

voluntary programme

are

required

to have

all

animals

that

are 24 serum

as

beta

distribution.

Beta

distributions real number

are line

(CWHP) was modelled a relatively flexible

months or milk

of

age

and

older

serologically

tested

using

either

family of distributions on

the

samples. Diagnostic

testing

is

conducted

in

both

govern-

from 0

to 1 and are a

common method of modelling prevalence.

laboratories using one of 3 commercial ELISA

ment and commercial

The effect of ELISA kit and

test medium used was assessed using

kits ics,

approved

for

use

in

the

AHI

programme;

Parachek,

Prion-

and fixed

effects, however

the

change

in

the

animal-level

random

Switzerland

(kit A),

Paratuberculosis Antibody

Screening

Test,

apparent prevalence due

to

the effect of

these variables was

found

USA

(kit

B)

and

ID

Screen,

IDVet, Montpellier,

France sample

(kit are

Idexx,

to be

low

(<0.005) and

they were

removed again

from

the model.

C).

Producers

that

elect

to

test

using

blood

or milk

required

to

test

all

eligible

animals once or

twice per year

respec- centrally

Test Irish

data,

including

follow

up

testing,

are

stored

tively.

2.2.2. characteristics Nielsen and Toft (2008) proposed the case definitions “infected”, “infectious” and “affected” in an attempt to reduce variability between reported estimates of test Se. The subgroup “infected” also includes animals that are “infectious” and “affected”, and is the population of interest in this prevalence study. To estimate the Se and Sp of each commercial kit, a published review of the literature (Nielsen and Toft, 2008) was examined and supplemented with searches in PubMed and CABdirect of all literature published between 2007 and 2015 on paratuberculosis diagnostic test evaluation. Test characteristics for each test kit used in Ireland evaluating the “infected” sub group, were extracted from each peer-reviewed article from this search and from the 2008 review publication (Table 1). Model priors—test

in

the

Cattle

Breeding

Federation

computer

database.

Data

were

extracted

for

the

period

beginning

1st November

2013

and and

ending

30th

December

2014

and

included

anonymised

cow

herd

identifiers,

test-date,

sample-to-positive

(S/P)

ratio,

labora-

tory interpretation (negative, suspect, positive), sample type (blood or milk), testing laboratory (test kit) and county. Test data also included follow up testing data on subsamples of animals within herds. Herd test data were available for 1040 herds, 436 of these had conducted 2 or more additional rounds of testing. In order to avoid bias that may have been introduced by some herds conducting greater than 1 herd screen, only one test per animal was used. The first recorded test result for each animal was used for the purpose of this analysis and Se and Sp values were based on a single

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