4DMadiganetalSafetyDatalinkprovidesanearlyexampleofaLODspeci callydesignedforsafetyPapersfocusingondrugsafetyincludeCurtisetal2008Jinetal2008Kulldor etal2008Li2009Norenetal2008an ID: 165300
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2D.Madiganetal.recentrelatedmethodologicaldevelopments.Methods:Literaturereview.Results:Theself-controlledcaseserieso ersseveraladvantagesforactivesurveillancefordrugsafetybutwealsooutlinesomekeylimitations.Wedescribeapproachesforaddressedsomeoftheselimitations.Conclusions:Theself-controlledcaseseriesmodelanditsexten-sionsmayprovetobeausefultoolforactivesurveillance.Con ictsofInterest:NoneWordCount:3912KeyPointsTheself-controlledcaseseries(SCCS)representsonepartic-ularmethodologythatmaybeusefulforactivesurveillanceofdrugsafety.SCCShasstrengthsandweaknesses.Modicationsofthebasicmodelcanaddresssomebutnotalloftheweaknesses.Furtherresearchisrequiredtoestablishtheoperatingchar-acteristicsofSCCS-basedactivesurveillance.KeywordsandPhrases:Drugsafety;Shrinkage;Poissonregression;Caseseries;1.INTRODUCTIONIncreasingscientic,regulatoryandpublicscrutinyfocusesontheobligationofthemedicalcommunity,pharmaceuticalindustryandhealthauthoritiestoensurethatmarketeddrugshaveacceptablebenet-riskproles.Thisisanintricateandongoingprocessthatbeginswithcarefullydesignedrandomizedclinicaltrialspriortoapprovalbutcontinuesafterregulatorymarketautho-rizationwhenthedrugisinwidespreadclinicaluse.Inthepost-approvalenvironment,surveillanceschemesbasedonspontaneousreportingsystems(SRS)representacornerstonefortheearlydetectionofnoveldrughazards.KeylimitationsofSRS-basedpharmacovigilanceincludeunder-reporting,du-plicatereporting,andtheabsenceofadenominatororcontrolgrouptopro-videacomparison.NewerdatasourceshaveemergedthatovercomesomeoftheSRSlim-itationsbutpresentmethodologicalandlogisticalchallengesoftheirown. 4D.Madiganetal.SafetyDatalinkprovidesanearlyexampleofaLODspecicallydesignedforsafety.PapersfocusingondrugsafetyincludeCurtisetal.(2008),Jinetal.(2008),Kulldor etal.(2008),Li(2009),Norenetal.(2008),andSchneeweissetal.(2009).3.THESELF-CONTROLLEDCASESERIESMETHODFarrington(1995)proposedtheself-controlledcaseseries(SCCS)methodinordertoestimatetherelativeincidenceofadverseeventstoassessvaccinesafety.ThemajorfeaturesofSCCSarethat(1)itautomaticallycontrolsfortime-xedcovariatesthatdon'tvarywithinapersonduringthestudyperiod,and(2)onlycases(individualswithatleastoneevent)needtobeincludedintheanalysis.WithSCCS,eachindividualservesastheirowncontrol.Inotherwords,SCCScomparesoutcomeeventratesduringtimeswhenapersonisexposedversusoutcomeeventratesduringtimeswhenthesamepersonisunexposed.Ine ect,thecases'unexposedtimeletsusinferexpectationsaboutwhatwouldhavehappenedduringtheirexposedtimehadtheynotbeenexposed.SCCSisoneofseveralself-controlledmethodsthattheepidemiologylit-eraturedescribes,manyofwhicharevariantsonthecase-crossovermethod(Maclure,1991).Howeverunlikethecase-crossovermethod,whichtypicallyrequiresthechoiceofacomparatortimeperiodtoserveasacontrol,SCCSmakesuseofallavailabletemporalinformationwithouttheneedforselection.EpidemiologicalapplicationsofSCCStendtofocusonsituationswithsmallsamplesizesandfewexposurevariablesofinterest.Incontrast,theproblemofdrugsafetysurveillanceinLODsmustcontendwithmillionsofindividualsandmillionsofpotentialdrugexposures.Thesizeoftheproblempresentsamajorcomputationalchallenge{ensuringtheavailabilityofanecientoptimizationprocedureisessentialforafeasibleimplementation.3.1.Onedrug,oneadverseeventWewillrstfocusonthecasewherethereisonedrug(e.g.Vioxx)andoneadverseevent(e.g.myocardialinfarction,MI)ofinterest.Tosetupthenotation,iwillindexindividualsfrom1toN.Eventsandexposuresinourdatabasesarerecordedwithdates,sotemporalinformationisavailabledowntothelevelofdays(indexedbyd).Let ibethenumberofdaysthatpersoniisobserved,with(i,d)beingtheirdthdayofobservation.Thenumberofeventsonday(i,d)isdenotedbyyid,anddrugexposureisindicatedbyxid,wherexid=1ifiisexposedtothedrugon(i,d),and0otherwise.SCCSassumesthatAEsariseaccordingtoanon-homogeneousPoissonprocess,wheretheunderlyingeventrateismodulatedbydrugexposure.We 6D.Madiganetal.Inordertoavoidestimatingthenuisanceparameter,wecanconditiononitssucientstatisticandremovethedependenceon i.UnderthePoissonmodelthissucientstatisticisthetotalnumberofeventspersonihasovertheirentireobservationperiod,whichwedenotebyni=Pdyid.Foranon-homogeneousPoissonprocess,niisaPoissonrandomvariablewithrateparameterequaltothecumulativeintensityovertheobservationperiod:nijxiPoisson( iXd=1id=e i iXd=1exid)Inourcasethecumulativeintensityisasum(ratherthananintegral)sinceweassumeaconstantintensityovereachday.Conditioningonniyieldsthefollowinglikelihoodforpersoni:Lci=P(yijxi;ni)=P(yijxi) P(nijxi)/ iYd=1exid Pd0exid0yidNoticethatbecauseniissucient,theindividuallikelihoodintheaboveexpressionnolongercontains i.Thisconditionallikelihoodtakestheformofamultinomial,butdi ersfromatypicalmultinomialregression.Herethenumberof\bins"(observeddays)variesbyperson,theparameterisconstantacrossdays,andthecovariatesxidvarybyday.Assumingthatpatientsareindependent,thefullconditionallikelihoodissimplytheproductoftheindividuallikelihoods.Lc/NYi=1 iYd=1exid Pd0exid0yidEstimationofthedruge ectcannowproceedbymaximizingthecondi-tionallog-likelihoodtoobtain^CMLE.Winkelmann(2008)showedthatthisestimatorisconsistentandasymptoticallyNormalinthePoissoncase.Itisclearfromtheexpressonforthelikelihoodthatifpersonihasnoobservedevents(yi=0),theywillhaveacontributionofLci=1.Conse-quently,personihasnoe ectontheestimation,anditfollowsthatonlycases(ni1)needtobeincludedintheanalysis.SCCSdoesawithin-personcomparisonoftheeventrateduringexposuretotheeventratewhileunexposed,andthusthemethodis\self-controlled".Intuitivelyitfollowsthatifihasnoevents,theycannotprovideanyinfor-mationabouttherelativerateatwhichtheyhaveevents.ThattheSCCSanalysisreliessolelyondatafromcasesisasubstantialcomputationaladvan-tage{sincetheincidencerateofmostAEsisrelativelylow,typicalSCCSanalyseswillutilizeonlyamodestfractionofthetotalnumberofpatients. 8D.Madiganetal.interactionsandavectoroftime-varyingcovariateszidcanbewrittenasid=e i+0xid+Pr6=s rsxidrxids+ 0zidwhere denotesatwo-wayinteractionbetweendrugsrands.Remark1.Inpractice,manyadversee ectscanoccuratmostonceinagivendaysuggestingabinaryratherthanPoissonmodel.Onecanshowthatadoptingalogisticmodelyieldsanidenticalconditionallikelihoodto(1).Thisequivalenceallowsshiftingtoalogisticmodelwithfollow-uptruncatedattheoutcomeevent,whenthateventistheonsetofanenduringconditionthatpermanentlychangesexposurepropensity(seeDiscussionbelow.)Remark2.Itisstraightforwardtoshowthattheconditionallikelihoodin(1)islog-concave.3.3.BayesianSelf-ControlledCaseSeriesWehavenowsetupthefullconditionallikelihoodformultipledrugs,soonecouldproceedbyndingconditionalmaximumlikelihoodestimatesofthedrugparametervector.Howeverintheproblemofdrugsafetysurveil-lanceinLODstherearemillionsofpotentialdrugexposurepredictors(tensofthousandsofdrugmaine ectsalongwithdruginteractions).Thishighdimensionalityleadstopotentialoverttingundertheusualmaximumlikeli-hoodapproach,soregularizationisnecessary.WetakeaBayesianapproachbyputtingaprioroverthedruge ectpa-rametervectorandperforminginferencebasedonposteriormodeestimates.Therearemanychoicesofpriordistributionsthatshrinktheparameteresti-matestowardzeroandaddressovertting.Inparticular,wefocusonthe(1)Normalpriorand(2)Laplacianprior.(i)Normalprior.HereweshrinktheestimatestowardzerobyputtinganindependentNormalprioroneachoftheparametercomponents.TakingtheposteriormodeestimateswouldbeanalogoustoaridgePoissonregression,placingaconstraintontheL2-normoftheparametervector.(ii)Laplaceprior.Underthischoiceofprioraportionoftheposteriormodeestimateswillshrinkallthewaytozero,andtheircorrespondingpredictorswille ectivelybeselectedoutofthemodel.ThisisequivalenttoalassoPoissonregression,wherethereisaconstraintontheL1-normoftheparametervectorestimate.Ecientalgorithmsexistforndingposteriormodes,renderingourap-proachtractableeveninthelarge-scalesetting.Inparticular,wehaveadaptedthecyclic-coordinatedescentalgorithmofGenkinetal.(2007)totheSCCScontext.Anopen-sourceimplementationisavailableathttp://omop.fnih.org. 10D.Madiganetal.increaseanindividual'sfutureeventrisk.LetNi(t)recordthenumberofeventsthatpersonihasexperiencedupuntiltimet.Assume,asbefore,thatihasnitotaleventsduringtheirobservationperiodandthattheseeventsoccurattimesti1tini.Itisconvenienttodeneacountingprocess,suchasNi(t),intermsofitsintensityfunctioni(tjxi(t)).Thisfunctiongivestheinstantaneousprobabilitythataneventoccursattimet,giventhehistoryoftheprocessandcovariates.UndertheSCCSmodel,thePoissonintensityforiattimetisi(tjxi(t))=e i+0xi(t)(4)aswaspreviouslydescribed.PD-SCCSextendsthismodelbyincorporatingNi(t�),thenumberofeventsthatihasexperienceduptobutnotincludingtimet,asanadditivee ectontheindividualbaselinee i.ThePD-SCCSintensityfunctiontakestheformi(tjxi(t))=(e i+Ni(t�))e0xi(t)(5)whereistheparameterthatcontrolsthelevelofdependencebetweenevents.BasedonpluggingthePD-SCCSintensity(5)intothelikelihoodexpressionforageneralintensity-basedprocess,onecanseethatthetotalnumberofeventsniissucientforthenuisanceparameter i.AsintheSCCSmodel,conditioningonniremoves ifromthelikelihoodexpression.Symmetryargumentsyieldaclosedformfortheconditionallikelihood,whichinthede-nominatorrequiresintegratingoverallpossiblewaysforitohavenieventsduringtheirobservationperiod.Inferenceforandisbasedonthiscon-ditionallikelihood.Sincetheintensityfunctionmustbenon-negative,theeventdependenceparameterisrestrictedto&#x-306;0.Inthecasethat=0,thePD-SCCSintensitymodelin(5)reducestothatoftheSCCSmodelin(4).4.3.RelaxingtheIndependenceAssumptionsIII:Exposures.Asdiscussedabove,theSCCSmodelassumesthateventsarecondition-allyindependentofsubsequentexposures.Farringtonetal.(2009)presentaningeniousrelaxationofthisassumptionusingacounterfactualmodelingapproach.Theirapproachappliestothespecicsituationwheretheriskreturnstoitsbaselinelevelattheendofeachriskperiod,wheretheeventofinterestisnon-recurrent,andwheretheoccurenceoftheeventprecludesfutureexposures.HerewesketchtheFarringtonetal.approachusingasimpliedversionoftheirrunningexample.Considerasituationinwhicheachindividualcanhaveuptotwoexposures.Forindividuali,againdenoteby(ai;bi]theobservationperiodanddenotebyci1andci2theactualexposuretimes,shouldtheyoccur. 12D.Madiganetal.5.DISCUSSIONWehavedescribedself-controlledcaseseriesmethodsforpost-approvaldrugsafetyriskestimation,someBayesianandsomenot.Keyadvantagesoftheself-controlledcaseseriesapproachinclude:SCCSadjustsforalltime-invariantmultiplicativeconfounders,Estimationrequiresonlycases,andAregularized/BayesianimplementationofSCCSscalestolargedatabaseswiththepotentialtoadjustforlargenumbersoftime-varyingcovariates.ThemainproblemswiththeSCCSapproachconcerntheunderlyinginde-pendenceassumptions,inparticular,theassumptionthateventsarecondi-tionallyindependent,andtheassumptionthattheexposuredistributionandtheobservationperiodmustbeindependentofeventtimes.Wedescribedapproachestocircumventtheseassumptionsandthesemaybeusefulinsomeapplications.Furthermore,sinceSCCSestimatestheexposure-outcomeassociationincases,itignoresdataonindividualsinthestudypopulationthatdidnotexpe-riencetheoutcomeevent.Forexample,theremaybeseasonalitydrivingboththeexposureandtheoutcome,whereseasonisanimportanttime-varyingco-variate.Toadjustforseasonality,itishelpfultoaddressboth(a)therelationbetweenseasonandtheexposure,and(b)therelationbetweenseasonandtheoutcome.WhileSCCScanincorporatetimevaryingcovariates,ignoringSentinel'srichdataonthenon-caseslimitsourpowertoaddress(a).Inan-otherpaperinthisissue,wediscusshowanalysesofdatafromnon-casescansupplementcase-basedanalysesWenotethatonepossibleapproachtodealingwiththeexposureindepen-denceissueistotruncateobservationtimeafterthersteventoccurrence.ThisviolatesotherSCCSassumptionsbutmaystillbeusefulinpractice.Fig-ure2showsestimatesforanumberofdrug-outcomepairswithandwithouttruncation.Clearlythetruncationdoesaltersomeestimatedrelativeriskssubstantiallyandfutureworkwillevaluatetheempiricalperformanceofthisapproach.Real-lifeLODsarenoisyandhavethepotentialtointroduceallsortsofartifactsandbiasesintoanalyses.Forexample,conditionsandthedrugsprescribedtotreattheconditionsareoftenrecordedsimultaneouslyatasinglevisittothedoctor,eventhoughtheconditionactuallypredatedthevisit.Thiscanintroduce\confoundingbyindication"-thedrugusedtotreataconditioncanappeartobecausedbythecondition.ManysuchchallengesexistanditremainstobeseenwhetherornotfalsepositiveswillrenderriskidenticationinLODsimpractical. 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