A structural equation model to evaluate direct and indirect factors associated with a latent measure of mastitis in Belgian dairy herds

Please cite this article in press as: Detilleux, J., et al., A structural equation model to evaluate direct

ContentslistsavailableatSciVerseScienceDirect

Preventive

Veterinary

Medicine

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

A

structural

equation

model

to

evaluate

direct

and

indirect

factors

associated

with

a

latent

measure

of

mastitis

in

Belgian

dairy

herds

J.

Detilleux

a,∗

_,

_L.

_Theron

b

_,

_J.-M.

_Beduin

b

_,

_C.

_Hanzen

b

a_{QuantitativeGeneticsGroup,DepartmentofAnimalProduction,FacultyofVeterinaryMedicine,UniversityofLiège,4000Liège,Belgium}

b_{LargeAnimalClinics,Obstr.etpath.delareprod.deséquidés,rumin.etporcs,FacultyofVeterinaryMedicine,UniversityofLiège,4000Liège,Belgium}

a

r

t

i

c

l

e

i

n

f

o

Articlehistory:

Received29March2010

Receivedinrevisedform12June2012 Accepted14June2012

Keywords: Mastitis

Structuralequationmodel Latentvariable

Riskfactors

a

b

s

t

r

a

c

t

Indairycattle,manyfarmingpracticeshavebeenassociatedwithoccurrenceofmastitis butitisoftendifficulttodisentanglethecausalthreads.Structuralequationmodelsmay reducethecomplexityofsuchsituations.Here,weappliedthemethodtoexaminethe linksbetweenmastitis(subclinicalandclinical)andriskfactorssuchasherd demograph-ics,housingconditions,feedingprocedures,milkingpractices,andstrategiesofmastitis preventionandtreatmentin345dairyherdsfromtheWalloonregionofBelgium.During theperiodJanuary2006toOctober2007,upto110differentherdmanagementvariables wererecordedbytwosurveyorsusingaquestionnaireforthefarmmanagersandduringa farmvisit.Monthlysomaticcellcountsofalllactatingcowswerecollectedbythelocaldairy herdimprovementassociation.Structuralequationmodelswerecreatedtoobtainalatent measureofmastitisandtoreducethecomplexityoftherelationshipsbetweenfarming practices,betweenindicatorsofherdmastitisandbetweenboth.Robustmaximum likeli-hoodestimateswereobtainedfortheeffectsoftheherdmanagementvariablesonthelatent measureofherdmastitis.Variablesassociateddirectly(p<0.05)withthelatentmeasureof herdmastitisweretheadditionofureaintherations;thepracticesofmachinestripping, ofpre-andpost-milkingteatdisinfection;thepresenceofcowswithhyperkeratoticteats, ofcubiclesforhousingandofdirtylinersbeforemilking;thetreatmentofsubclinicalcases ofmastitis;andtheageoftheherd(latentvariableforaverageageandparityofcows, andpercentageofheifersintheherd).Treatmentofsubclinicalmastitiswasalsoan inter-mediateintheassociationbetweenherdmastitisandpost-milkingteatdisinfection.The studyillustrateshowstructuralequationmodelprovidesinformationregardingthelinear relationshipsbetweenriskfactorsandalatentmeasureofmastitis,distinguishesbetween directrelationshipsandrelationshipsmediatedthroughintermediateriskfactors,allows theconstructionoflatentvariablesandteststhedirectionalhypothesesproposedinthe model.

© 2012 Elsevier B.V. All rights reserved.

1. Introduction

Publicconcernaboutfarmanimalwelfarehassteadily grown during recent years and many indicators have been proposed to evaluate its state in terms of the 5

∗ Correspondingauthor.Tel.:+3243664129;fax:+3243664122. E-mailaddress:jdetilleux@ulg.ac.be(J.Detilleux).

freedoms,amongwhichthefreedomfromdisease(Dalmau et al., 2009). In dairy practice, disorders of the udder areamongthemostfrequentclinicalconditions encoun-tered(Fourichonetal.,2001).Forexample,itwasfound in 2 independent surveys of Belgian dairy herds that 40%of quartermilksamplesfromsubclinicallyinfected cowscontainedmastitispathogens(Detilleuxetal.,1999;

Piepers etal., 2007).Given this highprevalence,

scien-tists have searched for and identified a great number 0167-5877/$–seefrontmatter © 2012 Elsevier B.V. All rights reserved.

Please cite this article in press as: Detilleux, J., et al., A structural equation model to evaluate direct of risk factors for the developmentof clinical mastitis.

Theseincludefactorsattheherd,cowandquarterlevels

(Breenetal.,2009).

In this study, we restricted ourselves to the study of factorsat theherd level. Factorssuch asinadequate nutrition,poormilkinghygiene,deficientmilking proce-duresorincreasedexposureoftheherdtoenvironmental pathogensmayincreasetheriskofclinicalandsubclinical mastitis(deVliegheretal.,2004;Haltiaetal.,2006;Nyman

etal.,2007;Schukkenetal.,1991).Butallthese

characteris-ticsareinterrelatedsoitisdifficulttodistinguishbetween spuriousandfactualassociations,orbetweendirectand mediatedeffects. To reducethe complexity ofsuch sit-uations,it ispossibletousestructural equationmodels (SEM) with latent variables (Bollen, 2002).Within this methodology,observedvariablesmaybeconsideredasthe expressionofasmallnumberoflatentconstructsthat can-notbedirectlymeasuredbutareinferredfromtheobserved variables.Inoursetting,thiswouldsuggestthatobserved herdcharacteristicsandmastitisindicatorscanbe aggre-gatedinafewnumbersofunderlyingconcepts.Then,the covarianceorcorrelationmatrices(orboth)betweenlatent constructsandobservedvariables,andbetweenlatent con-structs,aremodeledasafunctionofasetofparameters.It isthenpossibletotest alternativehypothesesaboutthe relationshipsbetweenthesevariables.Forexample, rela-tionshipsbetweensomaticcellcountsandmilkyieldhave beenexploredwiththismethod(delosCamposetal.,2006; Wuetal.,2008).TheSEMhandlescollinearityamong inde-pendentvariablesandcontrolsspuriousinflationoftypeI errorwhichconstitutesariskinmultipleunivariate anal-yseswhentestingcomplexrelationships(Pugesek,2003). AnotherinterestingfeatureoftheSEMconsistsinthe con-jointestimationofdirectandmediated(orindirect)effects

(Casal et al., 1990). Here, a direct effect will occurif a

putativeriskfactorinfluencesdirectlyonmastitis.Itisnot passedonthroughinterveningvariablesbutremainswhen allothervariablesinthemodelareheldconstant.Onthe otherhand,amediatedeffectwilloccurwhentheinfluence oftheriskfactoronmastitisisthroughone(ormore) inter-veningvariable.IfwedenoteYasthestateofmastitis,Xas theriskfactorandMastheinterveningvariable,thenthe pathX→M→YrepresentsthemediatedeffectbywhichX indirectlyaffectsYthroughM.Totaleffectsarethesumof directandmediatedeffects.Thecomparisonofdirectand mediatedeffectsmightallowustosubstituteintervening variablestomeasuresofmastitiswhenthesearedifficultto obtainoratahighcost.Thiscouldbethecaseifatreatment (X)wasclearingabacterialinfection(Y)bymodifyingsome biochemicalmilkprofile(M).Thisexampleillustrateshow itcouldbemorecost-effectivetoevaluatetheeffectofa treatmentbymeasuringthevariationofmilkcomponents bymodernrapidanalyticalmethods(M)thanbycounting coloniesonmicrobiologicalcultures(Y).Theidentification ofinterveningvariablesmayservealsotoclarifythenature oftherelationshipsbetweenmastitisandriskfactor.This issuereceivedrenewedinterestasawaytoaddressthe crit-icismsof‘blackbox’epidemiology(HafemanandSchwartz,

2009).

Theobjectiveof this paperis thustoapplytheSEM methodologytoevaluateand toquantifythedirectand

mediatedeffectsofherdcharacteristicsonmastitisindairy herdsfromtheWalloonregionofBelgium.

2. Materialsandmethods 2.1. Animalsandstudyarea

A random stratified sample of 349 dairy farms was surveyedbetweenJanuary2006andOctober2007inthe WalloonregionofBelgium.Thissamplerepresented25% ofproducersregisteredfornationalmilkrecording,fora totalof16,000cows.Asaruleofthumb,thesamplesize inSEMshouldbe10–20timesthenumberofexploratory variables,withaminimumof200(Hoe,2008).The strati-ficationwasbasedontheresultsofaprincipalcomponent analysisofthemanagementandherdcharacteristicsofall dairyherdspresentintheregion(n=1303).Thefirsttwo principal componentsweredividedinquartiles andthe herdswererandomlysampledwithineachofthese quar-tiles(16differentstrata)toensureallfarmcharacteristics wererepresented.

Up to110 differentfarming practices and indicators ofmastitiswererecordedineachfarmbytwosurveyors. Aquestionnairewasdesignedtocollectinformation dur-ingtheinterviewwiththefarmer,usingclosedquestions

(Delfosse et al.,2008). Farming practices includedherd

demographics(n=5),productiveandreproductive indica-tors(n=4),feedingprocedures(n=16),typesofhousing (n=12),strategies of mastitisprevention andtreatment (n=48),and milkingmethods(n=19).Sixdifferent indi-catorsofmastitiswereconsideredbasedonSCCbecause information on bacteriological findings and on clinical casesofmastitiswasnotobtainable.Theseindicatorswere ‘3-moSCC’,‘cowsactually withhighSCC’(numbersand percentages),‘cowspreviouslywithhighSCC’,‘lastSCC’, and‘cowsmilkedaside’.TheyaredescribedinTable1.

2.2. Statisticalanalysis

AfterageneralintroductiontoSEM,thestatistical anal-ysesforourspecificstudyarepresented.Theyconsisted intheidentificationofnoteworthyassociationsbetween mastitisindicatorsandfarmingpractices,thepreparation ofthedatafortheSEM(imputationandfactoranalysis),the establishmentoftheSEMitself(measurementand struc-turalsubmodels),andfinallytheestimationofthedirect, mediatedandtotaleffects.

2.2.1. IntroductiontoSEM

ASEMiscomposedoftwodifferentcomponents.The firstcomponentisthestructuralsubmodelwhere endoge-nous latentvariables areregressed onlatent predictors accordingto:

␩=B␩+␰+␰,

where_␩isavectorofendogenouslatentvariables,_␰isa vectorofexogenouslatentvariablesand ␨ isavectorof errorterms.Themodelcontrastsexogenous(i.e., indepen-dentfromthestatesofothervariables)fromendogenous variables.ItisfurtherassumedE(␰)=␬,var(␰)=,E(␨)=0,

Please cite this article in press as: Detilleux, J., et al., A structural equation model to evaluate direct

Table1

ShortdescriptionofindicatorsofhighSCCandpotentialriskfactorsnoteliminatedafterthepreliminaryunivariateanalyses.

Indicators Recording Descriptionandclassification

Somaticcellcounts

LastSCC DHI-records Log-transformedherdsomaticcellcount(SCC)atlastrecordingbeforethe

visit(log2(SCC/100,000)+3,whereSCCarecounts/ml)

3-moSCC DHI-records Arithmeticaverageoverthelast3monthsbeforethevisitoflog-transformed

herdSCC(log2(SCC/100,000)+3,whereSCCarecounts/ml)

CowsactuallywithhighSCC DHI-records Percentageandnmberofcowswith≥1monthlysample≥400,000cells/mlin thecurrentlactation

CowspreviouslywithhighSCC DHI-records Numberofcowswith≥1monthlysample≥400,000cells/mlintheprevious lactation

Cowsmilkedaside Visual/interview NumberofcowstreatedwithantibioticsandcowswithhighSCCforwhich

milkwasnotincludedinthetank

Herddemographics

Heifers DHI-records Percentageofnonlactatingprimiparouscows

Age DHI-records Arithmeticaverageageinmonthsofcowspresentatthefarmvisit

Parity DHI-records Arithmeticaverageparityofcowspresentatthefarmvisit

Lactatingcows DHI-records Numberoflactatingcows

Drycows DHI-records Numberofdrycows

Productiveindicators

Milk DHI-records Arithmeticaveragetest-daymilkoflactatingcowspresentatthefarmvisit

Milkfat DHI-records Arithmeticaveragetest-daymilkfatpercentageoflactatingcowspresentat

thefarmvisit

Milkprotein DHI-records Arithmeticaveragetest-dayproteinpercentageoflactatingcowspresentat

thefarmvisit

Milkquota DHI-records Totalintonnesoftheherdmilkquota

Milkingmethods

Preparationtime Visual/interview Timeinsecondsnecessarytopreparetheudderbeforemilking

Delay Visual/interview Timebetweentheendoftheudderpreparationandtheinstallationofthe

milkingmachine(s)

Handwashing Visual/interview Whetherornotmilker(s)washed(ornot)theirhandsaftermilkingeachcow

Milker Visual/interview Whetherornotonepersonmilkedthecows

Teatspre-dipping Visual/interview Whetherornotmilker(s)disinfectedteatsbeforemilking

Foremilkcheck Visual/interview Whetherornotmilker(s)examinedforemilkofeachquarterofeachcowprior

tomilking

Machinestripping Visual/interview Whetherornotmilker(s)appliedpressureontheclawattheendofmilkingto removepartofresidualmilk

Siliconelinertype Visual/interview Whetherornotlinersofthemilkingmachinewereinsilicone

Dirtyliner Visual Whetherornotlinersweredirtyinsideatthebeginningofmilking

Pulsatortype Visual/interview Whetherornotpulsatorwasusedperclaw

Hyperkeratosis Visual Percentageofcowswithlesion(s)ofhyperkeratosis

Clawspermilker Visual Numberofclawspermilker

Typesofhousing

Calvingpen Visual/interview Whetherornotthefarmhadapeninwhichcowsmaycalve

Cubicles Visual/interview Whetherornotlactatingcowswerehousedinafree-stalloncubicles

Gratedfloor Visual/interview Whetherornotlactatingcowswerehousedongratedfloor

Insidebarn Visual/interview Whetherornotlactatingcowswerehousedinsidebarns

Mastitispreventionandtreatment

Partialinsertion Visual/interview Whetherornotcowsreceivedantibioticswithashort(<4mm)orlong (>54mm)infusioncannulaatdrying

Treatmentifsubclinicalmastitis Visual/interview WhetherornotcowswithSCCabovethresholdand/orpositiveCMTwere infusedwithantibiotics

Treatmentifclots Visual/interview Whetherornotuddersofcowswithclotsinmilkwereinfusedwithantibiotics Treatmentifswelledudder Visual/interview Whetherornotcowswithswelledudderreceivedantibiotics(systematicand

intra-mammaryadministration)

Treatmentifbadstate Visual/interview Whetherornotcowswithclinicalmastitis(badgeneralstate)received antibiotics(systematicandintra-mammaryadministration)

Uddercleaning Visual/interview Whetherornotmilker(s)cleanedudderteatswithadryorhumidtissue

(paperorcloth)

Cupwashing Visual/interview Whetherornotmilker(s)washedthecupsofcowswithsubclinicalorclinical

mastitis

Teatspost-dipping Visual/interview Whetherornotmilker(s)disinfectedsystematicallyteatsbeforemilking

Dryperiod Interview Timeindaysofthedryperiod

Feedingprocedure

Please cite this article in press as: Detilleux, J., et al., A structural equation model to evaluate direct

η

1

y

1 λy 11

ν

1

y

₂ λy 12

ν

2

y

₃ λy 13

ν

3

η

2

y

4 λy 24

ν

4

y

₅ λy 25

ν

5

y

₆ λy 26

ν

6

β

12

ξ

1

x

₁ λx 11

ε

1

x

₂ λx 12

ε

2

γ

11

γ

12

ζ

1

ζ

2

Fig.1.Anexampleofastructuralequationmodelwith2endogenouslatentvariables(1and2),oneexogenouslatentvariable(1)and8observed

variables(y1toy3,y4toy6,x1andx2).Inthemeasurementsubmodel,regressioncoefficientsrelateobservedandlatentvariables(x₁₁,x₁₂,andy₁₁toy₂₆).

Inthestructuralsubmodel,directlinksbetweenlatentvariablesarerepresentedbytheregressioncoefficientsˇ12,11and21.Errorsarerepresentedby

thesymbols␯,␧,and␨.Seethetextformoredetails.

var(␨)=,andcov(␰,␨)=0.MatrixBcontainsrecursiveand simultaneouseffectsrelatingelementsof␩,andcontains regressioncoefficientsbetween␰and␩.Equivalently,the structuralmodelcanbewrittenas:

␩=(I−B)−1␰+(I−B)−1␨.

ThesecondcomponentoftheSEMcontainsthe mea-surementsubmodelsthatlinkthevectorfortheobservable exogenous(x)andendogenous(y)variablestotheir under-lying(latent)variables:

y-measurementsubmodel: y=y␩+␷,

x-measurementsubmodel: x=x␰+␧,

with E(



)=0, var(



)=y, E(␧)=0, var(␧)=x and

cov(



,␧)=0.Thus,theelementsofxareindicatorsofthe elementsof␰andtheelementsofyareindicatorsofthe elementsof␩. Ifx=I and␧=0,thenx=␰.Similarly, if

y=Iand



=0,theny=␩.

Combining the equations of the SEM, the y-measurementmodelcanberewrittenas:

y=x␦,

where =y(I−B)−1−1

x and ␦=y(I−B)−1[␨− −1x ␧]+␷.Through the matrix , a SEM providesa

wayofinterpretingtherelationshipbetweenobservable variables(x,y)asafunctionofregressionparametersof structural(Band)andmeasurement(xandy)

sub-models.Furthermore,theSEMreducestoa multivariate

multipleregressionmodelwhenB=0,andxandyare mea-suredwithouterror(i.e.,y= x+␨).Fig.1showsthepath diagramforahypotheticalSEM.

Whennodistinctionisdonebetweenexogenousand endogenous variables, we obtained the so-called ‘all-y’ notationforbothcomponentsoftheSEM:␮ =␮+␻for thestructuralsubmodelandz=␮+␪forthe measure-mentsubmodel,with:

␮=



␰ ␩



, =



0 0  V



, var(␻)=



 0 0 



, z=



x y



,  =



x y



, and var(␪)=



x 0 0 y



. Thematrix representsthedirecteffects between ele-ments of ␮.The mediated effects are 2 _{and the total}

effectsare+2_.

2.2.2. Identificationofnoteworthyassociations

AfteraBox–Coxtransformationofthecontinuous vari-ables that werenot normally distributed, we applied a batteryofunivariateanalyses(correlation,chi-squareand F-tests)andidentified that,outofall104farming prac-tices,35werepotentiallyassociated(p≤0.10)witheach otherandwithatleastoneofthe6indicatorsofmastitis. Thesevariableswerekeptforthefollowinganalysesand aredescribedinTable1.

Please cite this article in press as: Detilleux, J., et al., A structural equation model to evaluate direct 0 5 10 15 20 25 30 35 40 20 15 10 5 0 Eigenvalue of factor Number of factors

Fig.2. Screeplotforthefirst20factorsextractedfromthedata.

2.2.3. Multipleimputationandfactoranalysis

Missingdatawereimputed.TheMarkovchainMonte Carlo (MCMC) method algorithm was used to create 5 independent draws of missing data from multivari-ate normal distributions, and these draws were then averaged. The starting values for the MCMC algorithm wereposterior modes ofdistributions generated bythe expected-maximizationalgorithmfromuninformative Jef-freys prior (procedures MI and MIANALYZE of SAS®_).

Averages of imputed categorical data were rounded to thenearestintegervalue.Simulationstudiesondatawith binaryandordinalvariablesshowedresultsusingmultiple imputationbasedonthemultivariatenormaldistributions werenotlessrobustthanthosebasedonthemore flex-iblefullyconditionalspecification(LeeandCarlin,2010). However, dataon4 farmshad tobediscardedbecause informationonallvariablescollectedtodescribethetypes ofhousingwaslacking.

Next,weperformedafactoranalysistoidentifywhether factorswerecontributingtothecommonvarianceinthe 41variablesmeasuringmanagementpracticesandmastitis (procedureFactoronSAS®_{).Variableswerenot}

standard-izedfortheanalysisandthemaximumlikelihoodmethod waschosentoestimatefactorloadings,withsquared mul-tiple correlationofeach observed variableregressedon alltheothersasthepriorcommunalities.Theresults sug-gestedthat18outofthe41variablescouldbegroupedinto 5differentfactors.Indeed,the5thfactorwasthefirstone tohaveaneigenvaluebelow1anditcorrespondedtothe pointatwhichthecurvestartedbendingonthescreeplot (Fig.2).Theproportionofthecommonvarianceexplained bythe5factorswasgreaterthan80%.

Variablesofthese5factorsthathadloadings>0.3were consideredinthelatentvariablesoftheSEM(seebelow: measurementsubmodel).ThefirstlatentvariablewasAGE regrouping theobserved variables ‘Parity’, ‘Heifers’,and ‘Age’;thesecondonewasPRODregroupingthevariables ‘Milk’,‘Milkprotein’,‘Milkfat’,and‘Milkquota’;thethird wasNUMregrouping thevariables ‘Lactatingcows’ and ‘Drycows’;thefourthonewasMLKregroupingthe vari-ables‘Preparationtime’,‘Delay’,and‘Handwashing’;and thelastonewasMAMregrouping‘3-moSCC’,‘Numberof cowsactuallywithhighSCC’,‘Numberofcowsalreadywith

highSCC’,‘PercentageofcowsactuallywithhighSCC’,‘SCS atlastrecording’,and‘Numberofmilkedasidecows’.The remaining23variables wereconsideredasindependent riskfactorsintheSEM.

2.2.4. Identificationofthemeasurementsubmodels Themeasurement submodel indicates howobserved variablesarelinkedtounderlyinglatentvariables.Using thesimple‘all-y’notation,all41observedvariables(z1to

z41)wererelatedto28latentvariables( 1to 28),with

1=MAMregroupingz1toz6, 2=AGEregroupingz7 to

z9, 3=PRODregroupingz10toz13, 4=NUMB

regroup-ingz14toz15, 5=MLKregrouping z16toz18,and 6 to

28aretheerror-freelatentvariablesforthe23remaining

riskfactors,i.e.,consideringz19toz41arerandomvariables

contaminatedbyerrors(19to41).Modelsfor 2

(vari-ableAGE)and 25 (=variable‘Dirtyliners’)aregiven as

examples:



z7 z8 z9



=



1 8 9



[ 2]+



7 8 9



and z25= 25+25,

withz7=‘Averageage’inmonths,z8=‘Averageparity’,and

z9=‘Percentageofheifers’.Thevalueof8 indicatesthe

extenttowhichz8dependsonAGE( 2),inunitsgivenby

thereference,chosenheretobez7.Theprocedurewas

sim-ilarforMAM(unit=somaticcellscore),PROD(units=kg milk),NUMB(units=numberoflactatingcows),andMLK (units=timeinsecondstopreparetheudder).Fixingone loadingisrequiredtoidentifytheparametersofthemodel. Anotherconstraintwouldconsistinfixingthevarianceof thelatentvariablealthoughSteiger(2002)arguedthislast constraintcaninteractwithothermodelconstraintsand interferewithsomehypothesistesting.Squaredmultiple correlationsbetweenlatentandeveryobservedvariable, denotedR2_{,wereusedtodeterminetheextenttowhich}

theobservedvariableadequatelymeasuresitsrespective underlyingconstruct.

2.2.5. Identificationofthestructuralsubmodels

Structuralsubmodelsindicatehowlatentvariablesare linkedtoeachother.Thepremises forconstructingthis partof theSEM werethat all 27 latentvariables could affectMAMandbethemselvesaffectedbylatentvariables otherthanMAMandthemselves.Thenforthemthlatent variable,wehave: [ m]= [ m,1 m,2 m,3 ... m,28]·

⎡

⎢

⎢

⎢

⎢

⎣

1 2 3 . . . 28

⎤

⎥

⎥

⎥

⎥

⎦

+[ωm] with m=1–28

Values for m,1 and m,m werefixed to0 for m=1–28.

Weassigned(inthetextbelow)thesymbolRFMAM_tothe

latentvariables forwhich partialregression coefficients with MAM (1,2, 1,3,..., or 1,28) were significantly

different from null (p<0.05). Having identified these RFMAM_{,wedenotedasRF,thelatentvariablesforwhich}

Please cite this article in press as: Detilleux, J., et al., A structural equation model to evaluate direct partialregressioncoefficients(m,2,m,3,...,orm,28with

m=2–28) with RFMAM _{were significantly different from}

null(p<0.05).VariablesotherthanRFMAM_andRFwerenot

includedinthefinalmodel.Thedirectionofthese relation-ships(fromRFtoRFMAM_{toMAM)wasbasedonourcurrent}

knowledgeofmastitis.Wemaythinkattheprocedureasa classicalbackwardstepwiseregressionanalysisbut,here, wewentfurtherbydeterminingwhethertheRFMAM_kept

attheend ofthebackward procedurewere themselves influencedbyRFvariables.

Thefinaltheoreticalmodelis:

MAM= n



k=1 1,kRFMAMk +ω1 with n≤28, and RFMAM_m = nm



k=1 m,kRFm+ωm for m=1,...,n.

2.2.6. Estimationoftheparametersandfitofthemodels Parameters of the final SEM were estimated with the“robust”maximumlikelihoodmethod(Boomsmaand

Hoogland,2001).Inthismethod,alsocalledthemaximum

likelihood–meanadjusted,parametersareestimatedby maximumlikelihood and standard errors areestimated fromtheasymptoticcovarianceandcorrelationmatrices. These“robustestimators”aresupposedtobemorerobust againstviolationsoftheassumptionsoflargesamplesize andnon-normalitythan regularestimators(Satorra and

Bentler,1988).Thematrices werebasedonthePearson

correlations for continuous variables and on the tetra-choricandthepolychoriccorrelationsforordinalindicators (LISREL®_{program2.8,JöreskogandSörbom,1996).}

Afterthemodelparameterswereestimated,thedegree towhichthemodelfitsthedatawasassessed.Fitindices, allprovidedbyLISREL,canbeclassifiedintoseveralclasses thatinclude (1) discrepancy functions,suchasthe root mean square error of approximation (RMSEA=squared averagedifferencesbetweenobservedandmodel-implied covariances),(2)teststhatcomparethetargetmodelwith thenullmodel,suchasthecomparativefitindex(CFI)or thenormedfitindex(NFI),(3)informationtheorygoodness offitmeasures,suchastheAkaikeInformationcriterion (AIC),and(4)noncentralityfitindices.AnRMSEAvalueof lessthan0.08suggestssatisfactoryfit,andavalueofless than0.05suggestsclosefit(BrowneandCudeck,1993).The indicesNFIandCFI,allnormallylieintherange0.0–1.0, withhighervalues indicatingbetterfit. Asa benchmark for good fit, the value0.90 is oftenused (Kline, 2005). Inadditiontoomnibusgoodness-of-fitmeasures(RMSEA, CFI,NFI,AIC),nullhypothesesthatindividualparameters oftheSEMaredifferentfromzeroweretestedthrough inspectionof the Waldstatistic (labeled t-value in LIS-REL),modificationindices(estimatesofthechangeinthe likelihood-ratio chi-squarestatisticfor themodel if the parameterisspecifiedasafreeparameter),and standard-izedresiduals(Bollen,1989;Kline,2005).Estimatesofthe parameterswereobtainedasifthevariancesofthe vari-ableswereunity(completestandardizationinLISREL).

2.2.7. Total,directandindirecteffects

Thelaststepintheanalysesconsistedindetermining, forthefinalSEM,thedirect,mediatedandtotaleffecton MAM.Usingthenotationpresentedintheintroduction,X istheriskfactororRFMAM_{,YistheMAMandMisan}

inter-mediateriskfactorinthepathwayfromXtoY.Thedirect effectsofXonYwereestimatedbythecorresponding ele-mentsofthematrix,i.e.,partialregressioncoefficients. Themediatedeffectswereobtainedfrom2_,asthe

prod-uctoftheestimatedregressioncoefficientofXonMtimes theestimatedregressioncoefficientMonY.Themediated effectofXonYcanalsobeestimatedbystandardregression methods,asthedifferencebetweenestimatedregression coefficientofXonY(X→Y)andestimateddirecteffectofX onY(X_|M→Y).Thetwomethodswillleadequivalent esti-mateswhennolatentvariableisused,nodataismissing andcovariatesarethesameinallequations.Asimulation studyillustratedthesuperiorityofSEM(Iacobuccietal., 2007).TheSobeltest(Sobel,1982)wasusedtotestthe nullhypothesisthatthemediatedeffectisnull.

3. Results

DescriptivestatisticsaregiveninTable2forthe345 farmsusedintheanalyses.Theaveragenumberoflactating cowswas50perherd,rangingfrom15to165.Theaverage numberofheiferswas6perherdandrangedfrom0to30. Milkquotavariedfrom105to1380tonnes,withanaverage of378tonnes.Farmsomaticcellscoreatlastcheckranged from1.60to5.20andtheaverageoverthelast3months from2.85to3.89.Managementpracticesdifferedbetween farmsbutthemajorityofproducersfollow recommenda-tionstopreventmastitis:theycheckedforemilkforearly signsofinfection(78%),cleanedtheudderbeforemilking (78%),practisedpost-milkingteatdisinfection(64%)and mostofthemtreatedcowswithclinicalmastitis(>90%). Theydippedteatsbeforemilking(7%),strippedmachine (37%)andwashedthecups(34%).Onaverage,20%of sam-pledcowspresentedsignsofhyperkeratosisandonly29% offarmshadcowswithoutsignsofit.

Completelystandardizedestimatesoftheparameters of the final SEM are given in Table3 for the measure-mentandinFig.3forthefinalstructuralsubmodels.The goodness-of-fit statistics (RMSEA<0.01; NFI=0.95, and CFI=1.0)suggestedclosefitofthefinalmodel.InTable3, we see that 66% of the variance in the average parity number(z8)isexplainedbythelatentvariableAGE( 2).

Theestimated valuefor8 is 0.81 meaningthatz8 will

increase by 0.81 in terms of standard deviations when AGEincreasesbyonestandarddeviation.The‘t-value’of 20.4suggests8 exceedsthecriticalvalueof2.58atthe

significance level of 1% (p<0.01). Parity was positively associatedwiththeunderlyingAGEandthecoefficientfor thepercentageofheiferswas,logically,negative.Looking at MAM, thestandardized coefficients showedthatSCC at last check and animals with high SCC(number and percentage)weremorehighlycorrelatedwithMAMthan cowsmilkedaside.ThevariableMLKwaspositivelyrelated withthetimenecessarytocleantheudderbeforemilking andthepracticetowashhandaftermilking.Finally,herd

Please cite this article in press as: Detilleux, J., et al., A structural equation model to evaluate direct

Table2

Percentageofherdscharacterizedbythepresence(vs.absence)ofabinaryriskfactor(percent);meanandstandarderror(SE)forquantitativeriskfactor; averageof3-moSCCforherdswith(yesherds)orwithout(noherds)theriskfactor;percentageofherdswithnoinformationontheriskfactor(Pmiss).

Riskfactors Mean(SE) Percent Yesherds Noherds Pmiss

IndicatorofhighSCC

3-moSCC 3.40(0.01) 0.0

CowsactuallywithhighSCC 13.76(0.44) 2.3

CowspreviouslywithhighSCC 6.18(0.25) 2.3

Cowsmilkedaside 1.70(0.11) 0.3

LastSCC 3.22(0.03) 2.3 Herddemographics Heifers 33.03(0.53) 2.3 Age 52.65(0.36) 2.3 Parity 2.65(0.02) 2.3 Lactatingcows 50.48(1.19) 0.0 Drycows 6.16(0.26) 1.4 Productiveindicators Milk 24.12(0.28) 2.3 Milkfat 4.06(0.02) 2.3 Milkprotein 3.33(0.01) 2.3 Milkquota 377.99(10.5) 2.6 Milkingmethods Preparationtime 12.39(0.70) 0.6 Delay 75.17(4.18) 0.6 Handwashing 41.2 3.40(0.01) 3.39(0.01) 2.6 Milker 24.6 3.39(0.02) 3.42(0.03) 0.1 Teatspre-dipping 7.0 3.46(0.04) 3.40(0.01)* _0.3 Foremilkcheck 78.0 3.41(0.01) 3.37(0.02) 0.0 Machinestripping 37.4 3.43(0.02) 3.38(0.01)* _0.3

Siliconelinertype 13.0 3.39(0.03) 3.40(0.01) 0.0

Dirtyliner 7.8 3.51(0.03) 3.39(0.01)* _0.3

Pulsatortype 19.1 3.43(0.03) 3.39(0.01) 0.6

Hyperkeratosis 19.62(0.83) 8.3

Clawspermilker 6.64(0.17) 0.9

Housing Calvingpen 34.8 3.36(0.02) 3.42(0.01) 3.5 Cubicles 45.2 3.37(0.01) 3.43(0.01)* _1.1 Gratedfloor 47.5 3.38(0.01) 3.41(0.01) 1.1 Insidebarn 85.8 3.40(0.02) 3.42(0.03) 1.1 Mastitistreatment Subclinicalmastitis 27.8 3.40(0.02) 3.40(0.01) 1.1

Ifpresenceofclotsinmilk 61.2 3.38(0.04) 3.40(0.01) 0.0

Ifswelledudder 93.3 3.40(0.01) 3.41(0.07) 0.3

Ifbadgeneralstate 94.2 3.39(0.02) 3.40(0.01) 1.4

Mastitisprevention Partialinsertion 55.6 3.41(0.01) 3.39(0.01) 0.0 Uddercleaning 78.5 3.39(0.01) 3.44(0.02) 0.0 Cupwashing 33.9 3.39(0.02) 3.41(0.01) 0.9 Post-dipping 64.1 3.38(0.01) 3.44(0.02)* _0.3 Dryperiod 50.05(0.49) 0.1 Feedingprocedure Ureainfeed 10.4 3.46(0.03) 3.39(0.01) 1.7

*_{Significantdifferencebetweenyesandnoherds(t-test;p<0.05).}

average production was strongly associated withPROD contrarytofatandproteinpercentages.

Forthestructuralsubmodel(Fig.3),completely stan-dardized coefficientsshowedthat AGE,additionofurea in the rations, presence of dirty liners, machine strip-ping, presence of cows with hyperkeratosis, pre- and post-milking teat disinfection, treatment of subclinical casesofmastitisandhousingofmilkingcowsoncubicles are directly correlated with MAM. The estimates were negativewhenhyperkeratoriccowswereobservedinthe farm,whenfarmersdisinfectteatsaftermilkingandwhen

lactating cows were housed in a free-stall on cubicles, andpositivefortheothers.Someoftheriskfactorwith significant links with MAM were also associated with othervariables,forexamplewithMLK(post-milkingteat disinfection,dirtyliners),withNUMB(hyperkeratosisand machine strip),or withboth PROD and NUMB(urea in feed,cubicles,dirtyliners,AGE).Treatmentforsubclinical mastitis and post-dipping were positively associated. Variables such as partial insertion, foremilk check and uddercleaning wereassociated withMLKbut not with MAM.

Please cite this article in press as: Detilleux, J., et al., A structural equation model to evaluate direct PROD 0.15 (0.02) 0.41 (0.01) -0.04(0.01) -0.08 (0.02) 0.07(0.02) 0.09 (0.01) Presence of hyperkeratosis MAM Pre-milking teat disinfecon Machine stripping Urea in feed MLK Dirty liners Treatment of subclinical mastitis Foremilk check Partial insertion Udder cleaning Post-milking teat disinfecon AGE NUMB Cubicles 0.06 (0.02) 0.13 (0.03) 0.18(0.03) -0.12 (0.02) 0.13 (0.03) 0.10 (0.04) -0.07 (0.02) _-0.05(0.02) 0.31 (0.04) 0.01 (0.00) 0.07(0.01) 0.09(0.02) -0.10 (0.00) 0.09 (0.002) 0.05 (0.01) 0.12 (0.02) 0.13 (0.02) 0.05 (0.01)

Fig.3.Finalstructuralmodeldescribingthedirect(straightline)andindirect(dashedline)linksbetweenthelatentstateofudderhealth(MAM)andrisk factors.Seethetextformoredetails.

Direct and mediated relationships were observed in theassociation‘post-milkingteatdisinfection–treatment of subclinical mastitis – MAM’ (Fig. 3), in which treat-mentof subclinicalmastitiswasanintermediate in the pathwayfromteatdisinfectiontoMAM.Thepartofthe totalassociation(−0.11SCS;SE=0.02)betweenMAMand teat disinfectionthat was mediated throughsubclinical treatmentwasestimatedat+0.01 SCS(SE=0.003).And, althoughthismediatedeffectwassmall,itwassignificantly differentfromnull(p<0.05).

4. Discussion

Among the numerous reports on the relationships betweenherdcharacteristicsandmastitis,thisoneis par-ticularin that it approachedmastitis asa composite of severalcontributoryindicators,representedbyMAM.The MAMcanbeunderstoodasaherdvariableevaluatingherd mastitisthatisonlyobservedthroughmultipleindicators, eachcapturingdifferentaspectsofit.Statementsaboutthe associationsbetweenMAMandriskfactorsaretherefore morecomprehensiveandlessspecificthanthosemadefor eachindividualmastitisindicator.Themethodologyisnot adequatetofindmanagementstrategieseffectiveagainst particularmammarypathogensbutitissuitedtostudies, likeours,withtheobjectiveofidentifyingfactors influenc-ingherdmastitisinaglobalmanner,giventhattrendsin

mastitishavechangedoverthelast50yearsandthat differ-entmastitispathogensarepredominantindifferentherds, regionsandcountries(ZadoksandFitzpatrick,2009).

Lookingatthecompletelystandardizedregression coef-ficients,allexpressedin unitsof standarddeviation,we observedthemostinfluentialvariableonMAM wasthe presence vs.absenceofdirtyliners ( 25).Indeed, MAM

increasedby0.18(SE=0.03)whenlinersweredirty(Fig.1). Thepresencevs.absenceofdirtylinerswasitselfincreased by 0.05 (SE=0.01) when NUMB increased by one stan-dard deviation. Among other RFMAM _{with standardized}

direct effectsonMAM greaterthan0.10, wealsofound dietary urea (+0.13, SE=0.03) and the practice of pre-dipping(+0.13,SE=0.03).Note,however,thatcontroversial reportswereretrievedintheliteratureasinSterketal.

(1978)whoobservedapositiverelationshipbetweenurea

andmastitisandinErbetal.(1976)inwhichnorelationship wasdiscovered.

Thepracticeofpost-milkingteatdisinfectionwas nega-tivelyassociatedwithMAM,withadirectstandardizedlink of−0.12(SE=0.02).Thiswasexpectedgiventhenumerous previousstudiesthatdemonstratedthebeneficialimpact ofpost-milkingteatdisinfectiononclinicaland subclini-calmastitis(Barkemaetal.,1998).But,thepracticewas alsoassociatedwithMAMthroughitslinkwiththe vari-able‘treatmentforsubclinicalcase’.Thismediatedeffect was estimated at +0.01 (SE=0.00) and wasin opposite

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Table3

Measurementmodelsforthefinalstructuralequationmodel:robust max-imumlikelihoodestimate(withthestandarderrorsinparentheses)ofthe effectsoneachlatentconstruct(AGE,PROD,MAM,MLK,andNUMB)along withthe‘t-value’(Waldstatisticwithcriticalvalueof2.58atp<0.01 sig-nificancelevel)andthesquaredmultiplecorrelation(R2_{).Seethetextfor}

moredetails.

Estimate(SE) ‘t-Value’ R2

AGE Parity 0.81(0.04) 20.39 0.66 Heifers −0.60(0.10) −6.54 0.36 Age 1(ref) PROD Milkprotein −0.06(0.01) −13.9 0.00 Milfat 0.02(0.01) 3.37 0.00 Quota 1(ref) Milk 0.27(0.12) 2.31 0.09 MAM 3-moSCC 1(ref)

CowsactuallywithhighSCC 0.46(0.02) 22.19 0.25

CowsactuallywithhighSCC(%) 0.55(0.02) 21.90 0.35 CowspreviouslywithhighSCC 0.46(0.04) 12.63 0.25

Cowsmilkedaside 0.24(0.02) 14.72 0.07

LastSCC 0.71(0.03) 21.90 0.76

MLK

Delay 0.46(0.04) 5.98 0.20

Handwashing 0.24(0.04) 5.44 0.04

Preparationtime 1(ref)

NUMB

Lactatingcows 1(ref)

Drycows 0.21(0.08) 2.80 0.07

directiontothedirect link,sotheestimatedtotaleffect

wasestimatedat−0.11(SE=0.02),lowerthanthedirect

effect.Eveniftheyarenotspectacular,theseresults

illus-trate thepotentialimportanceofdecomposingthetotal

relationshipintoitsdirectandindirectcomponents.For

example,ifthemediatedlinkhadbeengreaterthanthe

directlink,post-dippingwouldhavebeenincorrectly

asso-ciatedwithnomastitisbystandardregressiontechniques

althoughitstotaleffectwouldhavebeennotprotective.

OtherRFMAM_{haddirectstandardizedeffectslowerthan}

0.10. Forexample,MAM waslowerin farmsthathouse

lactatingcowsinwinterinatie-stall(−0.08,SE=0.02)

sim-ilarlytotheassociationfoundwithlowclinicalmastitis

incidence(KjæstadandSimensen,2001)andherdaverage

SCC(Kösteretal.,2006).ThelatentvariableAGEhada

pos-itiveeffectonMAMlikeinotherstudiesthatshowedan effectofincreasinglactationnumberonSCC(Busatoetal., 2000).Anotherexamplewastheslightnegativeassociation betweenthepresenceofhyperkeratosisandMAM.Others foundsevereteatlesionsisassociatedwithincreasedrisk ofclinicalmastitisandhigherSCC(Neijenhuisetal.,2001). Conversely,Gleeson(2004)foundnocorrelationbetween teathyperkeratosisscoreandSCCwhenteatswere disin-fectedaftermilking.

Somelatentvariables,suchasPRODandNUMB, influ-encedMAMonlyindirectly,throughtheirlinkswithother interveningvariables.Forexample,theyinfluencedMAM through theireffectonthepresence ofcubicles. Inthis survey,farmsthathouselactatingcowsinwinterina tie-stallwereindeedlargerandhadagreatermilkquota:the averagemilkquotawas462,100kgfor59.5lactatingcows

infarmswithcubicles,tobecomparedtothe308,800kg ofmilkquotaand theaveragenumber of43.1lactating cowsinfarmswithoutcubicles.TheNUMBalsoinfluenced MAMthroughitseffectonthepresenceofhyperkeratosis. Theaveragepercentageofcowswithhyperkeratosiswas higherinlargerfarms:infarmswithmorethan50 lactat-ingcows,21.7%ofcowspresentedlesionsofhyperkeratosis for17.8%infarmswithlessthan50lactatingcows.Haskell

etal.(2009)arguedalsothattherelationshipbetweenherd

sizeandSCCmaybeindirect.

SomelatentvariableshadnoeffectonMAM.For exam-ple,thelatentvariabledescribingthetime necessaryto preparetheudder(MLK),hadnoeffectonMAMbutKiiman

etal.(2005)observedhighbulktankSCCwhenthetotal

udderpreparationwasshort(averageof30s).Thepractice ofexaminingforemilktofacilitateearlydetectionof clin-icalmastitisobservedin78.2%ofthefarmswasalsonot associatedwithMAM.Interestingly,Jayaraoetal.(2004)

observedthatbulktankSCCwashigherinherdsthat prac-ticefore-strippingbeforemilkingthaninherdsthatdonot.

5. Conclusions

Thisstudydescribedastructuralequationmodelwith latentvariablestounderstandtherelativeinfluenceofrisk factorsonalatentmeasureofthestateofmastitisinherds fromaparticularregionofBelgium.Variablesassociated directlywiththelatentmeasureofherdmastitiswerethe additionofureaintherations;thepracticesofmachine stripping,ofteatdisinfectionbeforeandaftermilking;the presenceofcowswithhyperkeratoticteats,offree-stallon cubiclestohouselactatingcowsandofdirtylinersbefore milking;thetreatmentofsubclinicalcasesofmastitis;and anlatentmeasureoftheageoftheherd.Teatdisinfection aftermilkinginfluencedalsothelatentmeasureofherd mastitisthroughitsassociationwiththetreatmentof sub-clinicalcasesofmastitis.

Acknowledgments

ThisstudywassupportedbyEADGENE(European Ani-malDiseaseGenomicsNetworkofExcellenceforAnimal HealthandFoodSafety).Theauthorswishedalsotothank theOSAMteamthatcollectandstorethedata.

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