mixed effects models with missing data

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1、CHAPTER4MixedEffectsModelswithMissingData4.1IntroductionInChapter3,wehavereviewedsomecommonlyusedmethodsforgeneralmissingdataproblems.Missingdatamethodsforregressionmodelsarere-viewedinLittleandRubin(2002),Ibrahimetal.(2005),andMolenberghsandKenward(2007),amongothers

2、.Thesereviewsmostlyfocusonmodelsforcross-sectionaldata.Inpractice,missingdataareespeciallycommoninlongi-tudinalstudies.Inthischapter,wedescribesomestatisticalmethodsforvariousmissingdataproblemsinmixedeffectsmodels,includingLME,GLMM,andNLMEmodels.Wewilldiscussmissing

3、datainsurvivalmodelsandfrailtymodelsinChapter7.Weconsiderthefollowingmissingdataproblemsinmixedeffectsmodels:missingcovariates,missingresponses,missingbothcovariatesandresponses,dropouts.Anadvantageofthelikelihoodmethodformixedeffectsmodelsisthatital-lowsunbalanc

4、eddataintheresponse,i.e.,thenumbersandschedulesoftheresponsemeasurementscanbedifferentacrossindividuals.Inotherwords,iftherearemissingdataintheresponseandthemissingdatamechanismisig-norable(e.g.,MARorMCAR),wecansimplyignorethesemissingresponsesandproceedwithlikelihoo

5、dinference.Ifthemissingdataintheresponseofamixedeffectsmodelarenon-ignorable,however,wemustassumeamissingdatamodelandincorporateitinlikelihoodinference.Missingdatamayalsooccurincovariates.Therearetwotypesofcovariatesinlongitudinalstudies:time-independentcovariatesand

6、time-dependentco-131132MIXEDEFFECTSMODELSFORCOMPLEXDATAvariates.Time-independentcovariatesareonlymeasuredonceinalongitudi-nalstudyortheirvaluesdonotchangeovertime,suchasbaselinecovariatesorgenderandrace.Time-dependentcovariatesaremeasuredrepeatedlyovertimeortheirvalu

7、eschangeovertime.Foramixedeffectsmodelwithtime-dependentcovariates,standardmodelspecicationsrequirethatallcovariatevaluesareavailableatthesametimesastheresponsemeasurements.How-ever,thisisoftennotthecaseinpracticesincesomecovariatevaluesmaynotbeavailableattherespons

8、emeasurementtimes.Thisleadstomissingdataintime-dependentcovariates,whichisaverycommonproblem.Time-independentcovariatesmayalsohavem