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1、doi:10.1111/j.1467-9469.2006.00526.x©BoardoftheFoundationoftheScandinavianJournalofStatistics2006.PublishedbyBlackwellPublishingLtd,9600GarsingtonRoad,OxfordOX42DQ,UKand350MainStreet,Malden,MA02148,USA,2006RegressionAnalysisforMultistateModelsBasedonaPseudo-valueApproach,wi
2、thApplicationstoBoneMarrowTransplantationStudiesPERK.ANDERSENDepartmentofBiostatistics,UniversityofCopenhagenJOHNP.KLEINDivisionofBiostatistics,MedicalCollegeofWisconsinABSTRACT.Typically,regressionanalysisformultistatemodelshasbeenbasedonregressionmodelsforthetransitionint
3、ensities.Thesemodelsleadtohighlynonlinearandverycomplexmodelsfortheeffectsofcovariatesonstateoccupationprobabilities.Wepresentatechniquethatmodelsthestateoccupationortransitionprobabilitiesinamultistatemodeldirectly.Themethodisbasedonthepseudo-valuesfromajackknifestatisticc
4、onstructedfromnon-parametricestimatorsfortheprobabilityinquestion.Thesepseudo-valuesareusedasoutcomevariablesinageneralizedestimatingequationtoobtainestimatesofmodelparameters.Weexaminethisapproachanditspropertiesindetailfortwospecialmultistatemodelprobabilities,thecumulati
5、veincidencefunctionincompetingrisksandthecurrentleukaemia-freesurvivalusedinbonemarrowtransplants.Thelatteristheprobabilityapatientisaliveandineitherafirstorsecondpost-transplantremission.Thetechniquesareillustratedonadatasetofleukaemiapatientsgivenamarrowtransplant.Wealsodi
6、scussextensionsofthemodelthatareofcurrentresearchinterest.Keywords:bonemarrowtransplantation,competingrisks,generalizedestimatingequations,multistatemodel,pseudo-observations,stateoccupationprobability,transitionprobability1.IntroductionMultistatemodelsariseinanumberofconte
7、xtsinbothengineeringandmedicalsciences.Inengineeringapplicationsmultistatemodellingoccursintheanalysisofcoherentsystems.Inmedicalapplications,themotivationforthisarticle,multistatemodelsariseinattemptingtounderstandcomplexdiseaseortreatmentprocesses.Asurveyofproblemsinmulti
8、statemodelsisfoundinAndersen&Keiding(2002).Inmoststudiesofmultistatemodelsweareint