Bayesian estimation of true prevalence, sensitivity and specificity of indirect ELISA, Rose Bengal Test and Slow Agglutination Test for the diagnosis of brucellosis in sheep and goats in Bangladesh

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Preventive

Veterinary

Medicine

jo u r n al h om ep a ge :w ww . e l s e v i e r . c o m / l o c a t e / p r e v e t m e d

Bayesian

estimation

of

true

prevalence,

sensitivity

and

speciﬁcity

of

indirect

ELISA,

Rose

Bengal

Test

and

Slow

Agglutination

Test

for

the

diagnosis

of

brucellosis

in

sheep

and

goats

in

Bangladesh

A.K.M.

Anisur

Rahman

a,b,c,∗

,

Claude

Saegerman

b

,

Dirk

Berkvens

c

,

David

Fretin

d

,

Md.

Osman

Gani

e

_,

_Md.

_{Ershaduzzaman}

e

_,

_Muzahed

_Uddin

_Ahmed

a

_,

_Abatih

_Emmanuel

c

a_Department_of_Medicine,_Bangladesh_Agricultural_University,_Mymensingh_2202,_Bangladesh

b_Research_Unit_of_Epidemiology_and_Risk_Analysis_Applied_to_the_Veterinary_Sciences_(UREAR),_Department_of_Infectious_and_Parasitic_Diseases,

FacultyofVeterinaryMedicine,UniversityofLiège,Liège,Belgium

c_Unit_of_{Epidemiology,}_Department_of_Biomedical_Sciences,_Institute_of_Tropical_Medicine,_Antwerpen,_Belgium d_Department_of_Bacteriology_and_Immunology,_Veterinary_and_Agrochemical_Research_Centre,_Brussels,_Belgium e_Goat_and_Sheep_Production_Research_Division,_Bangladesh_Livestock_Research_Institute,_Savar,_Dhaka_1341,_Bangladesh

a r t i c l e i n f o

Articlehistory: Received14May2012 Receivedinrevisedform 29November2012 Accepted30November2012 Keywords: Bayesianmodel Smallruminants Brucellosis Diagnostictests Sensitivity Speciﬁcity a b s t r a c t

Thetrueprevalenceofbrucellosisanddiagnostictestcharacteristicsofthree condition-allydependentserologicaltestswereestimatedusingtheBayesianapproachingoatsand sheeppopulationsofBangladesh.Serumsamplesfromarandomselectionof636goatsand 1044sheepweretestedinparallelbyindirectELISA(iELISA),RoseBengalTest(RBT)and SlowAgglutinationTest(SAT).Thetrueprevalenceofbrucellosisingoatsandsheepwere estimatedas1%(95%credibilityinterval(CrI):0.7–1.8)and1.2%(95%CrI:0.6–2.2) respec-tively.ThesensitivityofiELISAwas92.9%ingoatsand92.0%insheepwithcorresponding specificitiesof96.5%and99.5%respectively.ThesensitivityandspecificityestimatesofRBT were80.2%and99.6%ingoatsand82.8%and98.3%insheep.Thesensitivityandspecificity ofSATwere57.1%and99.3%ingoatsand72.0%and98.6%insheep.Inthisstudy,three conditionallydependentserologicaltestsforthediagnosisofsmallruminantbrucellosis inBangladeshwerevalidated.ConsiderableconditionaldependencebetweenIELISAand RBTandbetweenRBTandSATwasobservedamongsheep.Theinfluenceofthepriorson themodelfitandestimatedparametervalueswascheckedusingsensitivityanalysis.In multipletestvalidation,conditionaldependenceshouldnotbeignoredwhenthetestsare infactconditionallydependent.

1. Introduction

Brucellamelitensis,primarilyresponsibleforbrucellosis insheepandgoatsisbyfar,themostimportantzoonotic agent among Brucella spp. (Anonymous, 1986; Solorio-Riveraetal.,2007).Brucellosisinsheepandgoatsisrarely

∗ Correspondingauthorat:BangladeshAgriculturalUniversity, Depart-mentofMedicine,BAUCampus,Mymensingh2202,Bangladesh. Tel.:+8801713409196;fax:+8809161510.

E-mailaddress:ranisur@itg.be(A.K.M.A.Rahman).

causedbyBrucellaabortusandBrucellasuis(EC,2001). Bru-cella ovis causes epididymitis in rams but rarely causes abortion inewes (VanTonder etal., 1994)and doesnot cause disease in humans. In the majority of industrial-izedcountries,bovinebrucellosis hasbeeneradicatedor controlled.However,smallruminantbrucellosisremainsa probleminsomeofthesecountriesaswellasinall devel-oping countries. Basically, brucellosis is almost always present wheresmallruminantsarekept(Godfroid etal., 2005;Francoetal.,2007).

There are about 36.5 million goats and 1.69 million sheeprepresenting morethan57% ofthe total livestock

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of Bangladesh. About85% of rural householdsown ani-malsand75%ofthepopulationrelyonlivestocktosome extentfortheirlivelihood(Anonymous,2005;BBS,2004). Morethan98%ofgoatsareownedbythesmall,marginal andlandlessfarmersinthevillages.Theirsmallbodysize andeasymanagementespeciallybyfeedingonroadside grasses,treeleavesandkitchenvegetablewastesi.e. invest-ingpracticallynothing,attractspoorwomenandchildren tosmallruminantrearing (Amin,2006).Agood propor-tion of humans in Bangladesh have very close contacts withsmallruminantsand directcontactwith animalsis the principal route of brucellosis transmission. The epi-demiologicalunderstandingofsmallruminantbrucellosis isinaverypreliminarystageinBangladesh.Theestimated seroprevalenceofbrucellosisinBangladeshbasedon pre-viousstudiesrangesfrom0.7%to14.6%ingoats(Mustafa, 1984;Rahmanetal.,1988,2011a,b)and0to4.8%insheep (Mustafa,1984;Amin,2003;Uddin,2006;Rahmanetal., 2011a,b).

The serological tests used in previous studies were theRose BengalTest(RBT),Standard TubeAgglutination Test,ELISAorPlateAgglutinationTest.Noneofthe afore-mentioned testsareperfect. So,the prevalencereported usingthesetestsarenottrueprevalencedueto misclas-siﬁcation of some of the tested animals. Moreover, the performanceofthesetestshasnotbeenvalidatedin nat-urally infectedsmallruminants of Bangladesh.Testsare normallyvalidatedbycomparing withthe goldstandard orperfecttest.However,the goldstandardforthe diag-nosis of brucellosis is isolation and identiﬁcationof the organism(Altonetal.,1988;OIE,2008)whichisnoteasy toperformin adeveloping andresource-limitedcountry likeBangladesh.Intheabsenceofagoldstandard, simul-taneousestimationoftrueprevalenceanddiagnostictest characteristicscanbeperformedsuccessfullywhen apply-ingmultiple diagnostictests toeveryindividual subject, using a Bayesian approach which combines test results andexternalinformation(Berkvensetal.,2006;Adeletal., 2010;Praudetal.,2012).

Animportantconsiderationin theevaluationof mul-tiplediagnostic tests is whether or notthe tests can be assumed conditionally independentof each other given the true disease status. It has been demonstrated that the assumption of conditional independence may lead to biased estimates for test characteristics ifin fact the testsareconditionally dependent (Vacek,1985; Gardner etal., 2000).SinceiELISA,RBT andSATarebased onthe same biologicalprocess (Nielsen, 2002) i.e. detection of anti-Brucella-smooth-lipopolysaccharide (SLPS) antibod-ies,theycanbeconsideredtobeconditionallydependent (Gardneretal.,2000).Therefore,theestimationprocedures shouldbeadjustedforthedependenciesamongthetests (DendukuriandJoseph,2001;Branscumetal.,2005).Few reports have been noted where authors considered test dependenceinamultipletestingstrategyforthe diagno-sisof porcine andbovine brucellosis (Ferriset al., 1995; Mainar-Jaimeetal.,2005;Praudetal.,2012)butnonewas notedforthediagnosisofsmallruminantsbrucellosis.

Theaimofthisstudywastoestimatethetrue preva-lence of brucellosis in small ruminants of Bangladesh and to evaluate the performance of three conditionally

dependent serological tests namely indirect ELISA, RBT andSATusingaBayesianmodelingapproach.

2. Materialsandmethods 2.1. Studyandsamplingdesign

LivestockherdsinBangladesharenotidentiﬁed region-ally or centrally in the form of a data bank. To obtain random samples in this context a map digitization and herdselectionprocedurewasfollowedintheMymensingh district of Bangladesh. Out of a total of the 146 unions (subUpa-Zilla)ofMymensinghdistrict(consistingof sev-eralUpa-Zillas),28wererandomlyselected.Usuallyone geographicalcoordinatewasrandomlyselectedfromeach selectedunionandlocatedbyahandheldGPSreader. Live-stockfarmerswithin 0.5km radiusof theselected point wereinformedaboutthesurvey.Allanimalsoftheselected herdsweresampled.Sincetherewereveryfewsheepin Mymensingh district,blood samples werealso collected from all other divisionsof Bangladeshexcept in Khulna throughthenationwidenetworkoftheBangladesh Live-stock ResearchInstitute (BLRI)usingthe same sampling design scheme. The study area is shown in Fig. 1. The study was conductedinitially between September 2007 andAugust2008andthenbetweenJanuary2010andMay 2010additionalsheepsampleswerecollected.Inaddition, apretestedquestionnairedesignedtocollectanimaland herdleveldataduringbloodsamplingwasadministered. 2.2. Processingofbloodsamples

About4mlofbloodwascollectedfromeachanimalby jugularvenipuncturewith disposableneedlesand veno-ject tubes,labeled and transported tothe laboratory on ice (after clotting) within 12h of collection. Blood sam-pleswerekeptintherefrigerator(2–8◦C)inthelaboratory andonedaylaterserawereseparatedbycentrifugingat 6000×g for10min. Each serumwas labeled to identify theanimalandstoredat−20◦_C._Blood_samples_collected

fromotherdistrictswereprocessedinrespectivedistricts andserastoredat−20◦_C_in_regional_BLRI_ﬁeld_stations_and

convenientlytransferredtothemedicinedepartment lab-oratoryofBangladeshAgriculturalUniversity(BAU).Each serumwasdividedintotwotubeseachcontainingabout 1mlof serum.Onealiquot wasusedfortestingand the otherwaspreservedinaserumbank.

2.3. Serologicaltests

AllbloodsamplesweretestedinparallelbyiELISA,RBT and SATin the medicinedepartment laboratoryof BAU, Mymensingh,Bangladesh.

iELISAwasperformedaccordingtoLimetetal.(1988)

usingB.abortusbiotype1(Weybridge99)asantigen.The detail procedure was described in a previous paper by

Rahmanetal.(2012).Thecut-offvalueforapositiveresult was deﬁned at2U/ml of test serumfor goats (Godfroid etal.,2002)and6U/mloftestserumforsheep(Pers.Comm. DavidFretin).

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Fig.1. MapofBangladeshshowingthestudyareas.

RBTwasperformedasdescribedbyAltonetal.(1988). Brieﬂy,sufﬁcientantigen,testsera,positiveandnegative controlseraforaday’stestingwereremovedfrom refriger-ationandbroughttoroomtemperature(22±4◦C).Equal volumes(30␮l)ofserumandantigen(concentrated sus-pensionof B.abortusbiotype1(Weybridge 99);Institut Pourquier,France)weremixedandrotatedonaglassplate for4min.Theresultwasconsideredpositivewhen agglu-tinationwasnoticeableafterthisdelay.

SATwas carriedout with ethylenediaminetetraacetic acid(EDTA)asdescribedbyGarinetal.(1985).Theantigen usedwasB.abortusbiotype1(Weybridge99)(Synbiotics Europe,France).One hundredand sixty eight microliter ofSAW bufferin thefirst welland100␮lin thesecond andthethirdwellswereaddedin96-wellmicrotiterplate. Thirtytwomicroliterofserumwasaddedinthefirstwell (dilution1/6.25).Afterpropermixingofdiluentandserum, 100␮lfromthe first wellwastransferredtothe second well(1/12.5).Inthesameway100␮lwastransferredfrom the second to the third well (dilution1/25) and 100␮l discardedfrom the third well. Then in eachwell 100␮l ofstandardizedSAWantigenwasaddedgivingtheserial serumdilutionsof1/12.5,1/25and1/50.Theplateswere agitatedandincubatedat37◦Cfor20–24h.Readingwas doneonthebasisofdegreeofagglutinationandexpressed ininternationalunits(IU).Anyserumwithanantibodytiter

greaterthanorequalto30IU/ml,asprescribedbytheEU (Shey-Njilaetal.,2005),wasconsideredpositive.

2.4. Statisticalanalysis 2.4.1. Modelbuilding

A Bayesian latentclass analysis was implemented in WinBUGS 1.4(Spiegelhalteret al.,2003)andR 2.14.2(R Foundation and Statistical Computing2012) toestimate the prevalence, sensitivity and speciﬁcity of the three tests,usingmodelsdevelopedbyBranscumetal.(2005),

Berkvens et al. (2006), Nérette et al. (2008) and Haley et al. (2011) separately for sheep and goats. In a three test scenario,7parameters needtobeestimated by the multinominalmodelundertheassumptionofconditional independence namely; the prevalence,and the sensitiv-ities and specificities of the threetests. However,under the assumption of conditional dependence, 6 additional parametersneedtobeestimatednamelytheconditional covariancebetweeneachpairoftestsamonginfectedand non-infectedsubjects.Thismodelisinfactnon-identifiable sincethedataonlyallowsforsevenparameterstobe esti-mated. As none of the three tests is considered a gold standard test and the tests are not conditionally inde-pendent, constraints havetobe imposed ona subset of the parametersinorder tomake themodelsidentifiable

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(Branscum et al., 2005). To evaluate the goodness of fit ofthemodels,theposteriorpredictivep-value,Deviance Information Criterion (DIC) (Spiegelhalter et al., 2002) andthenumberofeffectivelyestimatedparameters(pD) (Berkvenset al.,2006) wereusedascalibrating parame-ters.Briefly, the DICensures that aparsimoniousmodel isselected.ItiscalculatedasDIC=pD+DwithDthemean posteriordevianceandpDthenumberofparameters effec-tivelyestimatedbythemodel.ModelswithasmallerDIC shouldbepreferredtomodelswithlargerDIC.The poste-riorpredictivep-valueisaposteriorpredictivecheckthat detectslack-of-fitofthemodeltothedata.Itisbasedonthe differencebetweenthedevianceof theobservationsand thedevianceofobservationsgeneratedrandomlyfromthe currentlyfittedmodeland for modelsthatprovide ade-quatefittothedata, thevalueshouldbearound0.50.A posteriorpredictivep-valueof0.5isthevaluethatwould beobtainedifthedistributionofthedeviancesbasedon theobservedandsimulateddatasetsoverlappedperfectly (KellyandSmith,2011).Theapparentprevalenceforsheep in2007/2008was3.7%[18/482](95%credibilityintervals (CrI):2.2–5.8)andthatin2010was2.5%[14/562](95%CrI: 1.4–4.1).Using the “prtesti”command inStata 12.1, we observedthatthedifferencebetweenthetwoproportions wasnotstatisticallysignificant(p-value=0.3015)therefore dataforthetwophaseswerecombined.

2.4.2. Modelingconditionaldependence

Using the model that assumes conditional indepen-denceamongthethreetestsgiventhetruediseasestatus ofindividualsasthebaselinemodel,conditional depend-ence between each pair of tests was estimated using

different parameterizations of the model that assumed conditional dependence between tests (Branscum et al., 2005; Berkvens et al., 2006; Nérette et al., 2008). Jones et al.(2010)proposedthatin theconstruction of condi-tional dependence models, mainlysimple extensions of theconditionalindependencemodelshouldbeconsidered. Essentially,intheﬁrstsetofsimpleparameterizations,the conditionaldependencebetweeniELISAandRBT,between iELISAandSATandbetweenRBTandSATwereeachadded inturntotheconditionalindependencemodel.Inaddition, threemodelswereconstructedwithconditional depend-ence between the pairs: iELISA–RBT and iELISA–SAT, iELISA–RBT and RBT–SAT and between iELISA–SAT and RBT–SATrespectively(Néretteetal.,2008).Finallyamodel withconditionaldependenceamongallthethreetestswas considered(allpairsinclusive)separatelyamonginfected andnon-infectedindividualsandalsoamonginfectedand non-infectedanimalscombined.Themodelsforbothgoats andsheepalongwiththeircorrespondingparametersare presentedinTable3.

Lettingtobethetrueprevalence,T1,T2andT3to

repre-sentthetestoutcomesforiELISA,RBTandSATrespectively, withpositivetestoutcomesdenotedby1(or+),negative testoutcomesby0(or−),andsensitivitiesandspeciﬁcities bySeandSprespectively,theexpectedcellprobabilities(p) basedonthesethreetestsundertheassumptionof condi-tionaldependencearegivenasfollows:

p(111)=P(T₁+,T₂+,T₃+)=(Se1Se2Se3+Se1a23+Se2a13+Se3a12)+ (1−)((1−Sp₁)(1−Sp₂)(1−Sp₃)+(1−Sp₁)b23+(1−Sp2)b13+(1−Sp3)b12) p(110)=P(T₁+,T₂+,T₃−)=(Se1Se2(1−Se3)−Se1a23−Se2a13+(1−Se3)a12)+ (1−)((1−Sp₁)(1−Sp₂)Sp₃−(1−Sp₁)b23−(1−Sp2)b13+Sp3b12) p(101)=P(T₁+,T₂−,T₃+)=(Se1(1−Se2)Se3−Se1a23−(1−Se2)a13−Se3a12)+ (1−)((1−Sp₁)(1−Sp₂)Sp₃−(1−Sp₁)b23−(1−Sp2)b13+Sp3b12) p(100)=P(T₁+,T₂−,T₃−)=(Se1(1−Se2)(1−Se3)+Se1a23−(1−Se2)a13−(1−Se3)a12) +(1−)((1−Sp₁)Sp₂Sp₃−(1−Sp₁)b23−Sp2b13−Sp3b12) p(011)=P(T₁−,T₂+,T₃+)=((1−Se1)Se2Se3+(1−Se1)a23−Se2a13−Se3a12)+ (1−)(Sp1(1−Sp2)(1−Sp3)+Sp1b23−(1−Sp2)b13−(1−Sp3)b12) p(010)=P(T₁−,T₂+,T₃−)=((1−Se1)Se3(1−Se3)−(1−Se1)a23−Se2a13−(1−Se3)a12) +(1−)(Sp1(1−Sp2)Sp3−Sp1b23+(1−Sp2)b13−Sp3b12) p(001)=P(T₁−,T₂−,T₃−)=((1−Se1)(1−Se3)Se3−(1−Se1)a23−(1−Se2)∗a13+Se3∗a12) +(1−)(Sp1Sp2(1−Sp3)+Sp1b23+Sp2∗b13+(1−Sp3)∗b12) p(000)=P(T₁−,T₂−,T₃−)=((1−Se1)(1−Se3)(1−Se3)+(1−Se1)a23+(1−Se2)a13+Se3∗a12) +(1−Se3)a12)+(1−)(Sp1Sp2Sp3+Sp1b23+Sp2∗b13+(Sp3)∗b12)

Representingtheconditionalcovariancebetweenpairs of tests among infected animals by a and among the non-infectedpopulationbyb(Table5),medianposterior estimateswereobtainedalongwiththeir95%CrI.In addi-tion,conditionalcorrelationswerecomputedasdescribed inGeorgiadisetal.(2003),Haleyetal.(2011)andBranscum etal.(2005).AccordingtoGeorgiadisetal.(2003),when theconditionalcorrelationsarelow(≤0.2),theestimates

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Table1

SourcesofpriorsusedforestimationofdiagnostictestcharacteristicsforbrucellosisingoatsandsheepinBangladesh.

References Species iELISA RBT SAT

Se Sp Se Sp Se Sp

Blascoetal.(1994) SG 1 1 91.8–92.5 1

Baumetal.(1995) SG 90.3–96.7 97.7–1

AbuharfeilandAbo-Shehada(1998) S 66.5–78.7 34.4–47.8

Burrieletal.(2004) SG 88.1–96.7 94.7–99.2 Nielsenetal.(2004) SG 82.1–96.6 96.4–98.4 64.7–85.3 99.0–99.9 Nielsenetal.(2005) G 94.5–97.5 99.3–99.9 Minasetal.(2005) S 92.7–96.3 1–1 67.0–74.1 99.3–1 EFSA-Q-2006 SG 94.5–95.8 99.1–99.3 91.6–93.4 99.8–1 Minasetal.(2008) SG 97.6–98.8 99.8–1 74.0–77.7 99.5–99.9 Ramirez-Pfeifferetal.(2008) SG 76.5–85.2 61.9–74.4 Guptaetal.(2010) G 30.1–79.2 50.6–90.4

SG:sheepandgoat;G:goatonly;S:sheeponly;iELISA:indirectELISA;RBT:RoseBengalTest;SAT:SlowAgglutinationTest;Se:sensitivity;Sp:speciﬁcity.

oftheconditionaldependenceandindependencemodels aresimilarwhereaswhenthecorrelationsarehigh(>0.2) theconditionaldependencemodelshouldbeconsidered.

AllmodelswerecomparedusingtheDICandposterior predictivep-values.Tobeconsideredsigniﬁcantly differ-ent,thereductioninDICbetweenanytwomodelsshould bemorethan3units(Spiegelhalteretal.,2002;Kostoulas etal.,2006;Néretteetal.,2008).Insituationswherethe dif-ferenceinDICwassmallerthan3units,themodelswere assumed to be similarand selection was based on par-simony(thesmallerthe numberof effectiveparameters estimated(pD)thebetter)(Spiegelhalteretal.,2002). 2.5. Priordistributionsforparameters

Basedona review of the literature, limited informa-tionwasavailableregardingthetrueprevalenceandtest sensitivitiesandspeciﬁcitiesforbrucellosisamongsmall ruminants in Bangladesh. Therefore, prior information from other similar studies were used. A very impor-tant source of priorinformation wasthe EFSAreport of 2006 (EFSA-Q-2006) in which a thorough meta-analytic approach was used to estimate priors of Se and Sp for RBT, iELISA and SAT in sheep and goats. Based on sev-eralstudiesobtainedfromtheliterature,ameta-analysis wasperformedusing“metandi”inStata12.1(Harbordand Whiting,2009).Toperformmetandi,aminimumoffour studiesisrequired.However,forSAT,onlytwostudieswere availabletherefore,themeta-analysiswasperformedfor RBT andiELISA. In addition,mentandirequires that the numberoftruepositives,truenegatives,falsepositivesand falsenegativesbeknowforeachstudy.Thiswasnot avail-ableforthemeta-analyticstudybasedontheEFSAreport sothepriorswerecombined:thelowestlimitwasusedas thelowerboundandthehighervalueastheupperbound inuniformdistributions.Thesamesetofpriorsforthe sen-sitivityandspeciﬁcitywereusedbothforsheepandgoats data.Thepriorintervalestimatesusedinuniform distri-butionsfortheSeandSpwere(0.870,0.986)and(0.962, 1.00)foriELISA(0.670,0.934)and(0.915,1.00)forRBTand (0.301,0.967)and(0.977,1)forSATrespectively.

The priors used for the prevalence of brucellosis in goatsandsheepinBangladeshwerebasedonlocal preva-lencereports0.7–14.6%ingoats(Mustafa,1984;Rahman etal.,1988,2011a,b)and0–4.8%insheep(Mustafa,1984;

Amin,2003;Uddin,2006;Rahmanetal.,2011a,b).Theprior sourcesforsensitivitiesandspeciﬁcitiesofthethree sero-logicaltestsusedfortheBayesiananalysisinthisstudyare summarizedinTable1.Priorinformationonthe8 covari-anceparameters(4forinfectedand4forthenon-infected individuals)werenotavailablesoinitialvalueswere gen-erated inR 2.14.2based onthe rangeof possiblevalues of thesensitivitiesandspeciﬁcitieslistedinTable1(see

AppendixB).

2.6. Modeldiagnostics

All models were run using three chains, a burn-in period of 50,000 iterations and another 100,000 itera-tions toobtaintheposterior estimates.Traceplots were used to explore how fast the chain explores the poste-riordistribution(Ntzoufras,2011).Amoreformaltestfor convergence,theBrooks,GelmanandRubinconvergence statisticwasusedtoassess modelconvergence (Gelman andRubin,1992).TheWinBUGScodesusedarepresented inAppendicesAandB.

2.7. Sensitivityanalysesofselectedmodels

Theinﬂuenceofthepriorinformationontheestimates of the diagnostic test characteristicswereveriﬁedusing sensitivityanalysis(Branscumetal.,2005;Kostoulasetal., 2006;Praudetal.,2012).Thiswasdonebyusingstandard uniformpriorsandslightperturbations(instepsof10%or 15%)ofthepriorintervals(Haleyetal.,2011).Thefollowing setsofpriorswereconsidered:

• Uniformprior(UP) forprevalence (Pr)andinformative priors(IP)forsensitivities(Se)andSpeciﬁcities(Sp) • UPforPrandforSeandIPforSp

• UPforPrandforSpandIPforSe • IPforPrandUPforSeandSp • IPforPrandforSeandUPforSp • IPforPrandforSpandUPSe • Perturbationsofthepriorinterval

Foreachsetofalternativepriordistributionsconsidered forthemodelparameters,themodelwasrunwiththesame numberofchainsandsimilardiagnosticswereperformed.

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Table2

Cross-classiﬁed test results for brucellosis in goats and sheep of BangladeshbasedoniELISA,RBT,andSAT.

iELISA RBT SAT Goat Sheep

1 1 1 2 8 1 1 0 1 3 1 0 1 0 0 1 0 0 29 5 0 1 1 0 9 0 1 0 2 6 0 0 1 4 6 0 0 0 598 1007 Total 636 1044

iELISA:indirectELISA;RBT:RoseBengalTest;SAT:SlowAgglutination Test;1:Positive;0:Negative.

3. Results

3.1. Dataexploration

ThestudywasconductedinitiallybetweenSeptember 2007andAugust2008forbothsheepandgoatsandlater betweenJanuary2010andMay2010forsheep.Themean age for goats was 1.6±0.06 (mean±se) years ranging from0.17to8yearswhereasthemeanbodyweightwas 10.0±0.19(mean±se)kgrangingfrom2to30kg.About 95%ofgoatswereoftheBlackBengalbreedandtherest wereof Jamuanparibreed oforigin. Sixty-sixpercent of thesampledgoatswerefemale.Themedianherdsizeof goatswas2rangingfrom1to18.Themeanageofsheep was2.1±0.0.04(mean±se)yearsrangingfrom0.08to8 yearswhereasthe meanbody weightof was14.6±0.15 (mean±se)kg ranging from 2to 40kg. All sheepwere oftheindigenoustypeand77%ofthemwerefemale.The medianherdsizeofsheepwas5andrangedfrom1to75. Thecrossclassiﬁedtestresultsofthethreeserologicaltests onthe636seraofgoatsand1044seraofsheepareshown inTable2.Two(0.3%)outofatotalof636goatswere posi-tiveforallthreetestsand94%(598/636)weretestnegative. Similarly8(0.8%)outofthetotalof1044sheepwere posi-tiveforallthreetestsand96.5%(1007/1044)werenegative forallthreetests(Table2).

Table4

Medianposteriorestimatesofprevalence,sensitivityandspeciﬁcityof iELISA,RBTandSATforthediagnosisofbrucellosisingoatsinBangladesh.

Test Variable Median 95%Credibility

interval Prevalence 1.0 0.7,1.8 iELISA Se 92.9 87.3,98.3 Sp 96.5 96.2,97.3 RoseBengal Se 80.2 67.7,92.7 Sp 99.6 98.9,99.9 SlowAgglutination Se 57.1 31.7,91.4 Sp 99.3 98.4,99.8

3.2. Modelselectionandposteriorestimates

ThepriorsusedintheBayesiananalyseswerethesame forthemodelsforbothgoatsandsheep.Forthedatafor goats,theDICfortheconditionalindependencemodelwas 26.09.None of themodels withconditionaldependence termsledtoasignificantreduction(ofgreaterthan3)in DIC(Table3).Inaddition,allthemedianestimatesofthe conditionalcorrelationswerecloseto0.2.Theconditional independence modelwastherefore selectedas a plausi-blemodelforthedataforgoats.Themedianestimatesof thetrueprevalenceofcaprinebrucellosis,sensitivity,and specificityofthethreetestsaresummarizedinTable4.The trueprevalenceofcaprinebrucellosisinBangladeshwas updatedto1% with 95%CrIof 0.7–1.8.The highest sen-sitivity(92.8%and95%CrI87.3–98.3)withcorresponding lowestspecificity(96.5%and95%CrI96.2–97.3)was esti-matedforiELISAamonggoats.ThespecificityofbothRBT andSATweregreaterthan99.2%andthesensitivityofRBT washigher(80.2%)thanthatofSAT(57.3%)amonggoats.

For the data for sheep, all models that included the conditional covariance between RBT and SAT yielded significantly lower DICs (33.47–35.13) compared to the conditional independence model (52.3). Among these potentialcandidatemodels,themodelwiththelowestDIC and forwhichthemagnitudesof theconditional covari-ance(betweeniELISAandRBTandbetweenRBTandSAT) wereconsiderablygreaterthan0.2wasselected.Basedon the finalmodel,the trueprevalenceofovinebrucellosis, sensitivity,specificityanddependencecoefficientsofthe

Table3

Comparisonofmodeldiagnosticparametersforconditionalindependenceanddifferentconditionaldependencemodelsusedtoestimatetrueprevalence ofbrucellosisinsmallruminantsandsensitivityandspeciﬁcityofthreediagnostictests.

Models Goat Sheep

Post. pD DIC Post. pD DIC

Conditionalindependence 0.55 2.30 26.09 1.00 4.54 52.3

Conditionaldependence(CD)betweeniELISAandRBT 0.62 3.03 26.43 1.00 4.82 53.46

CDbetweeniELISAandSAT 0.63 3.10 27.30 1.00 5.03 52.87

CDbetweenRBTandSAT 0.61 3.33 27.60 0.49 5.19 34.10

CDbetweeniELISAandRBTandbetweeniELISAandSAT 0.69 3.24 27.75 0.99 5.33 54.97

CDbetweeniELISAandSATandbetweenRBTandSAT 0.66 3.48 28.68 0.53 5.14 35.15

CDbetweeniELISAandRBTandbetweenRBTandSAT 0.64 3.35 27.74 0.48 5.10 33.50

CDamongalltestsforinfectedanimals 0.57 3.02 25.65 0.99 4.44 46.88

CDamongalltestsfornon-infectedanimals 0.71 3.47 29.37 0.64 5.50 37.61

CDamongalltests 0.69 3.54 28.90 0.52 4.98 34.53

iELISA:indirectELISA;RBT:RoseBengalTest;SAT:SlowAgglutinationTest;Boldmodelswereusedtoestimateprevalenceandtestcharacteristicsfor goatandsheeprespectively;pD:thenumberofparameterseffectivelyestimatedbythemodel;Post.:Postpredictivep-value;DIC:DevianceInformation Criterion.

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Table5

Bayesianmedianposteriorestimatesofprevalence,conditionalcorrelations,sensitivityandspeciﬁcityofiELISA,RBTandSATforthediagnosisofbrucellosis insheepinBangladesh.

Test Variable Median 95%Credibilityinterval

Prevalence 1.2 0.6,2.2 iELISA Se 92.0 87.2,98.2 Sp 99.5 98.7,99.9 RoseBengal Se 82.8 68.1,92.9 Sp 98.3 97.4,99.0 SlowAgglutination Se 72.0 43.6,94.5 Sp 98.6 97.8,99.2 Dependencecoefﬁcient

BetweeniELISAandRBTamonginfectedsheep a12 0.18 0.0,0.46

BetweenRBTandSATamonginfectedsheep a23 0.53 0.32,0.72

BetweeniELISAandRBTamongnon-infectedsheep b12 0.29 −0.11,0.82

BetweenRBTandSATamongnon-infectedsheep b23 0.40 −0.13,0.87

aijstandsfortheconditionalcorrelationbetweentestiandtestjamonginfectedsubjectsandbijstandsfortheconditionalcorrelationbetweentesti

andtestjamongnon-infectedsubjects.

threetestcombinationsareasshowninTable5.Thetrue prevalence of ovine brucellosis in Bangladesh was esti-mated tobe 1.2% with 95% CrI of 0.6–2.2.All the three tests were highly speciﬁc in sheep (≥98.3%). The most sensitive testwasthe iELISAwhereasthe least sensitive wasSAT.Therewasevidenceofconsiderableconditional dependence between RBT and SAT among infected and non-infectedsheep(Table5).

3.3. Sensitivityanalysesresults

Theresultsofthesensitivityanalysesofthemodelsfor goatsandsheepareshowninTables6and7respectively.

The conditional independence model for goats and a conditional dependence model for sheep were usedfor thesensitivityanalyses.Themodeldiagnosticparameters indicatedthatthedifferentsetofpriorsyieldedreasonable fittothedata. Thetrueprevalence ofcaprineaswellas ovinebrucellosisandspecificitiesofallthreetestsobtained from the different models of sensitivity analyses were similar to those of the selected models since their 95% credibility intervals overlapped. Whereas the estimated specificitieswerethesameasthoseoftheselectedmodels regardlessofthesetofpriorsused,thesensitivitieswere observedtovaryandyieldedwiderconfidenceintervals. However, since the 95% credibilityintervals overlapped,

Table6

Medianposteriorestimatesofprevalence,sensitivityandspeciﬁcityofiELISA,RBTandSATbasedonasensitivityanalysisoftheconditionalindependence modelusedtoestimatetrueprevalenceofcaprinebrucellosisanddiagnostictestcharacteristics.

Models&tests Post. pD DIC Prevalence(95%CrI) Sensitivity(95%CrI) Speciﬁcity(95%CrI)

UPforPrevandIPforSeandSp 0.55 2.89 25.92 0.6(0.2,1.6)

ELISA 93.0(87.3,98.3) 96.5(96.2,97.3)

RBT 81.2(67.8,92.8) 99.6(98.8,99.9)

SAT 60.1(32.1,92.9) 99.3(98.4,99.8)

UPforPrevandSpandIPforSe 0.40 3.65 25.32 0.6(0.2,1.5)

ELISA 93.0(87.3,98.3) 95.3(93.5,96.8)

RBT 81.7(67.9,92.9) 99.6(98.8,99.9)

SAT 62.1(32.3,93.5) 99.3(98.4,99.8)

IPforPrevandUPforSeandSp 0.57 3.42 27.97 1.1(0.7,3.3)

ELISA 69.6(23.9,98.5) 95.5(93.6,97.2)

RBT 62.5(15.3,98.1) 99.7(98.9,100)

SAT 46.0(10.2,90.8) 99.3(98.5,99.9)

IPforPrevandSeandUPforSp 0.39 3.06 25.57 0.9(0.7,1.7)

ELISA 92.8(87.3,98.3) 95.4(93.5,96.9)

RBT 80.9(67.7,92.8) 99.6(98.9,99.9)

SAT 59.0(31.9,92.1) 99.3(98.4,99.8)

IPforPrevandSpandUPforSe 0.70 2.07 28.03 1.3(0.7,5.0)

ELISA 71.1(26.1,98.5) 96.6(96.2,98.0)

RBT 51.1(10.2,97.0) 99.7(98.9,100)

SAT 37.5(6.9,87.1) 99.3(98.5,99.9)

Perturbationexample:10%decreaseof lowerlimitsofSeandSp

0.39 3.13 25.69 0.9(0.7,1.8)

ELISA 88.0(77.6,98.1) 95.4(93.5,96.8)

RBT 85.3(77.4,93.0) 99.6(98.9,99.9)

SAT 56.6(23.4,91.9) 99.3(98.4,99.8)

UP:uniformprior;IP:informativeprior;Prev:prevalence;Se:sensitivities;Sp:speciﬁcities;CrI:credibilityinterval;iELISA:indirectELISA;RBT:Rose BengalTest;SAT:SlowAgglutinationTest;Post.:Post.pred.p-value;pD:thenumberofparameterseffectivelyestimatedbythemodel;DIC:Deviance InformationCriterion.

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Table7

Medianposteriorestimatesofprevalence,sensitivityandspeciﬁcityofiELISA,RBTandSATbasedonasensitivityanalysisofaconditionaldependence modelusedtoestimatetrueprevalenceofovinebrucellosisanddiagnostictestcharacteristics.

Models&tests Post. pD DIC Prevalence(95%CrI) Sensitivity(95%CrI) Speciﬁcity((95%CrI))

UPforPrevandIPforSeandSp 0.48 5.09 33.49 1.2(0.6,2.2)

ELISA 92.1(87.2,98.2) 99.5(98.7,99.9)

RBT 82.8(68.1,92.9) 98.3(97.4,99.0)

SAT 72.2(43.6.4,94.5) 98.6(97.8,99.2)

UPforPrevandSpandIPforSe 0.49 5.18 33.70 1.2(0.5,2.2)

ELISA 92.1(87.2,98.2) 99.5(98.7,99.9)

RBT 82.7(68.1,92.9) 98.3(97.3,99.0)

SAT 72.0(43.6,94.5) 98.5(97.7,99.2)

IPforPrevandUPforSeandSp 0.49 4.43 31.84 2.1(0.8,4.3)

ELISA 52.7(25.1,94.3) 99.5(98.7,100)

RBT 75.0(37.0,99.0) 98.8(97.6,99.9)

SAT 66.4(35.2,96.6) 99.1(98.0,99.9)

IPforPrevandSeandUPforSp 0.49 5.21 33.77 1.2(0.5,2.2)

ELISA 92.1(87.2,98.2) 99.5(98.7,99.9)

RBT 82.8(68.1,92.9) 98.3(97.3,99.0)

SAT 72.0(43.7,94.5) 98.5(97.7,99.2)

IPforPrevandSpandUPSe 0.49 4.41 31.79 2.1(0.8,4.3)

ELISA 52.7(25.0,94.3) 99.5(98.7,100)

RBT 75.2(37.2,98.9) 98.8(97.7,99.9)

SAT 65.5(35.3,96.7) 99.1(99.1,99.9)

Perturbationexample:10%decreaseof lowerlimitsofSeandSp

0.50 5.11 33.45 1.3(0.6,2.5)

ELISA 85.5(77.4,97.7) 99.5(98.7,100)

RBT 80.1(59.6,92.8) 98.3(97.4,99.1)

SAT 70.5(41.4,94.3) 98.6(97.7,99.3)

UP:uniformprior;IP:informativeprior;Prev:prevalence;Se:sensitivities;Sp:speciﬁcities;CrI:credibilityinterval;iELISA:indirectELISA;RBT:Rose BengalTest;SAT:SlowAgglutinationTest;Post.:Post.pred.p-value;pD:thenumberofparameterseffectivelyestimatedbythemodel;DIC:Deviance InformationCriterion.

theobserveddifferenceswerenotstatisticallyimportant (Tables6and7).Forexample,thetruemedianprevalence of goats and sheep were 1.0% (95% CrI: 0.7–1.8%) and 1.2%(95%CrI:0.6–2.2%)respectivelyandtherangesofthe medianprevalenceobtainedinsensitivityanalyses respec-tivelyforgoatandsheeprangedfrom0.6–5%to0.5–4.3% respectively.Decreasing the lowerlimits ofall the prior intervalsby10%ledtoonlyslightandstatistically unimpor-tantchangesintheestimatedparametervaluesandtheir 95%CrIntervalsinthemodelsforbothgoatsandsheep. 4. Discussion

Inthis study, the trueprevalence and diagnostic test characteristics for brucellosis in goats and sheep were determined using a Bayesian analysis framework. More than90% of the goats in the country wereof the Black Bengalbreed. Thestudy areahad thehighest density of smallruminants(>300km2₎_in _Bangladesh₍_Anonymous, 2005) and about 95% of the goats sampled wereof the BlackBengalbreed.Thesheepsamplecoveredalmostall the divisions exceptKhulna divisionof Bangladesh. The breedofsampledsheepwasindigenouswhichis predomi-nantalloverBangladesh(Bhuiyan,2006).However,astudy based on micro-satellite markers by Khan et al. (2009)

describedGarolesheepofSatkhiradistrict(withinKhulna division)asanindependentsheepbreedinBangladesh.So, theprevalenceestimatedinthisstudyisbasedona repre-sentativesampleofgoatsandsheepandwouldthereforebe

applicabletothegoatsandsheep(exceptKhulnadivision) populationsofBangladesh.About1%ofgoatsand1.2%of sheepofBangladeshwerefoundtobeserologicallypositive forbrucellosis.Theprevalenceofbrucellosisingoatsand sheeparewithintherangeofpreviouslyreportedapparent prevalence.However,throughthisstudyweobtainedthe trueprevalencealongwiththeirtrueprobabilityinterval (credibilityintervalcontainsthetrueparameterwith95% certainty)(Mustafa,1984;Rahmanetal.,1988;Enøeetal., 2000;Amin,2003;Uddin, 2006;Rahmanetal.,2011a,b). Therelativelyhigherseroprevalenceinsheepmaybedueto therelativelylargerherdsizesofsheepcomparedtogoats in Bangladesh. Largerherd sizes have been reported to besigniﬁcantlyassociatedwithbrucellosis seropositivity amonglivestock(Mikolonet al.,1998;Kabagambeetal., 2001;Solorio-Riveraetal.,2007).

InBangladesh,amonglivestockfarmersabout49%rear smallruminantseitheraloneorwithlargeruminantsand about53%farmerswhosharesamepremiseswithanimals are goat owners (Rahman et al., 2012). As small rumi-nantscomeinveryclosecontactwithhumans,brucellosis in goats and sheepshould becontrolled with the high-est priorityin orderto controlthis zoonosis in humans. In Bangladesh,goatsare averyvaluableassetespecially forthepoorpeople.They maturesexuallyquiteearly,at 6–8monthsofage,and breedaroundthe year.Theykid twiceayearandmeatand skinobtainedfromthe Black Bengalareofexcellentqualityandfetchhighprices,even inthelocalmarket.SheepofBangladesharealsoasproliﬁc

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asgoats.Smallruminantswithclinicalsignssuggestiveof brucellosis(abortion,retainedfetalmembrane,anestrous, etc.)areusuallysoldandeventuallyslaughteredby butch-ers. Moreover, around 15 million goats are slaughtered annuallyandofthemabout40%areperformedduringthe annualfestivalofEid-ul-Azha(Anonymous,2007).It has beenshownthat thelongerinfectedanimalsarein con-tactwiththe restof theherd,thegreaterthenumberof seropositive animals (Radostits et al., 2000). Large scale slaughteringofsmallruminantsformeatconsumptionmay reducethenumberofinfectedanimalsinthepopulation. These factors may be responsible for low prevalence in goats and sheepof Bangladesh.In such an intermediate (1–5%)prevalencescenarioofsmallruminantsbrucellosis inBangladesh,eradicationcanbeachievedmainlybytest and slaughterpolicy.However,pre-requisitesfor under-taking eradication programs such as: good organization offarmersandveterinaryservices,theimplementationof strictmovementcontrolmeasures,anefficient identifica-tionsystemoftheanimals,nochanceofsharingcommon grazingplacesandavailabilityoffinancialresourcesarenot yetat hand. Thecomplete understanding of the disease includingthe speciesand biovarsof Brucellainvolved in smallruminantsshouldalsobeknownforplanningcontrol programs(Anonymous,2006;Minas,2006).

Inthisstudy,theperformanceofiELISAandRBTwere relativelybetterthanthatofSATingoatsandsheep.The specificityestimatesofSATandRBTwereverysimilar.The sensitivitiesofiELISAandRBTweresimilarinbothsheep andgoats.However,thespecificityofiELISA(95.5%)was slightlyloweringoatscomparedtosheepwhereasthatof RBTwasslightly lower insheepcomparedtogoats. The increased specificity of iELISA in sheep was due to the highercut-offvaluesthanthatofgoats.Thesensitivityand specificity of iELISA estimated were in accordance with resultsfrom otherstudies(Abuharfeiland Abo-Shehada, 1998;Burrieletal.,2004).ThesensitivityofRBTingoats andsheepwere80.2%and82.8%respectivelyeventhough thespecificityofRBTin bothgoatsandsheepwasmore than98%.TheestimatedsensitivityandspecificityofRBT werecoherentwithfindingsfrompreviousstudies(Nielsen etal.,2004;Ramirez-Pfeifferetal.,2008).Thesensitivity andspecificityofSATingoatsandsheepwere57.1%,99.3% and 72.0%, 98.6%respectively. Thesensitivity and speci-ficity of SAT werealso in accordance with results from otherstudies(Baumetal.,1995;Guptaetal., 2010).The iELISAwasthemostsensitiveandspecifictestexplaining thefactthatacutelyinfectedanimalswerelesscommonin thepopulation.Theserologicalresponseobservedinthis studyincludesbothB.abortusandB.melitensisinfections butexcludesB.ovisasitsantibodydoesnotreactwith anti-genspreparedbySLPS.Theproportionofgoatsandsheep infected with B. abortus and B. melitensis in Bangladesh isnotyetknown.ButB.abortuswasdetectedfrom goat milkusingrealtimePCRassay(unpublisheddata).Among the three tests none was sensitive and specific enough tobeusedalone forthe diagnosisof caprinebrucellosis in Bangladesh.In themodelfor goats,the hypothesis of conditional dependence among the three tests was not important.Thismighthavebeenduetosmalland some-timeszero cellfrequenciesobservedforgoats. In sheep,

considerableconditionaldependencebetweeniELISAand RBTandbetweenRBTandSATamonginfectedaswellas non-infectedsheepwereobserved.TheiELISAisa quanti-tativetestwhichdetectsonlyIgG,SATquantiﬁesbothIgM andIgG(butmainlyIgM)andRBTqualitativelydetectsboth IgMandIgG(Christopheretal.,2010;Godfroidetal.,2010; Dı’azetal.,2011).TheconditionalcorrelationbetweenRBT and SATforsheepmaybeexplainedby thesimilarityof thetypeofantibodydetected.Theweakerconditional cor-relationbetweeniELISAandRBT amonginfectedaswell asnon-infectedsheepmaybeexplainedbythe factthat RBT alsopartiallydetectsIgG. Thesensitivityanalysisof theconditionalindependencemodelforgoatsanda con-ditional dependence model for sheep revealed that the resultscanbeconsideredtoberobust.Slightdifferences inprevalenceandsensitivitieswereobservedbutthe dif-ferenceswerenotstatisticallyimportantasthecredibility intervals of the estimates overlapped with those of the prevalenceandsensitivitiesoftheserologicaltestsinthe chosenmodelsforgoatsandsheep(Tables4–7).

5. Conclusion

Thisstudyistheﬁrsttoevaluatetheaccuracyof brucel-losisdiagnostictestsamongsheepandgoatsinBangladesh considering conditional dependence between the diag-nostic tests.An intermediate levelof true prevalence of brucellosisamonggoatsandsheeprespectivelywas esti-mated.Suchlowprevalencewillallowtestandslaughter policytocontrolthiszoonosisin smallruminants. There wasconsiderableconditionaldependencebetweeniELISA andRBTandbetweenRBTandSATimplyingthata com-binationofthethreeserologicaltestsmaybeaplausible choice unless other tests with veryhigh sensitivity and speciﬁcityarevalidated.Inmultiple testvalidation, con-ditionaldependenceshouldnotbeignoredwhenthetests areinfactconditionallydependent.

Acknowledgements

This studywas supported by the Belgian Directorate GeneralforDevelopmentCooperation(DGDC).Theauthors aregratefultotheInstituteofTropicalMedicine(ITM)for logisticandtechnicalsupport,the UniversityofLiegefor scientiﬁcguidance&thestaffofCODA-CERVAfortechnical assistance.

AppendixAandB. Supplementarydata

Supplementarydataassociatedwiththisarticlecanbe found,intheonlineversion,athttp://dx.doi.org/10.1016/ j.prevetmed.2012.11.029.

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