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1、CHAPTER8JointModelingLongitudinalDataandSurvivalData8.1IntroductionAsshowninChapter7,survivaldataoftenariseinlongitudinalstudies.Inprac-tice,wemayneedtomodelatime-to-eventprocessandalongitudinalprocessjointly.Acommonsituationisinsurvivalmodelswithtime-dependentcovari-ates,inwhichcovariatedatamaybemi
2、ssingatfailuretimes,soalongitudinalmodelforthecovariatesisrequiredtoaddressmissingcovariatesorcovariatemeasurementerrors.Asanotherexample,inmodelinglongitudinaldatawithdropouts,wemayalsoneedtomodelthetimestodropoutortimestodeath,withtheobjectivesofavoidingpossiblebiasesintheestimationofthelongi-tudi
3、nalmodel,aswellasstudyingtheassociationbetweenthetimetoeventandcharacteristicsofthelongitudinaltrajectoriessuchasinitialslopesorin-tercepts.Inbothcases,jointmodelingofthelongitudinaldataandthesurvivaldataisrequired.Injointmodelingoflongitudinaldataandsurvivaldata,themainfocusmaybeeitherthelongitudin
4、almodel,orthesurvivalmodel,orbothmodels,dependingontheobjectivesofthestudies.Whenthemainfocusisononemodel,theothermodelisthensecondarysoitsparametersmaybeviewedasnuisanceparameters.Inthiscase,oneshouldfocusoncorrectspecicationofthemainmodelandsimplifythesecondarymodeltoreducethenumberofnuisancepara
5、metersandavoidpotentialparameternon-identiability.Ifbothmodelsareofprimaryinterest,wemayreducethenumberofothersecondaryparameterssuchastheassociationparameters.Injointmodelingoflongitudinaldataandsurvivaldata,weoftenhavethefollowingthreesituations:themainfocusisonmodelingsurvivaldata,withmodelingl
6、ongitudinaldatabeingsecondary.Thissituationmayarise,forexample,insurvival253254MIXEDEFFECTSMODELSFORCOMPLEXDATAmodelswithmeasurementerrorsormissingdataintime-dependentcovari-ates,wheremodelingthelongitudinalcovariateprocessesisonlyusedtoaddressmeasurementerrorsormissingdata(covariatedatamaybemissing
7、atfailuretimes);themainfocusisonmodelinglongitudinaldata,withmodelingsurvivaldatabeingsecondary.Thissituationmayarise,forexample,intheanalysisoflongitudinaldatawithinformativedropouts,whereasurvivalm