广义线性模型下基于因变量抽样的一种半参数经验似然估计方法

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1、广义线性模型下基于因变量抽样的一种半参数经验似然估计方法广义线性模型下基于因变量抽样的一种半参数经验似然估计方法ASemiparametricEmpiricalLikelihoodEstimationforGeneralizedLinearModelsunderOutcomeDependent510Sampling#DingJieli*SchoolofMathematicsandStatistics,WuhanUniversity,Wuhan,430072Abstract:Epidemiologicstudiesuseoutcome-dependentsam

2、plingODSschemeswhere,inadditiontoasimplerandomsample,therearealsoanumberofsupplementsamplesthatarecollectedbasedonoutcomevariable.ODSschemeisacosteffectivewaytoimprovestudyefficiency.WedevelopaimumsemiparametricempiricallikelihoodestimationMSELEfordatafromODSdesignunderagenerallinearm

3、odelframework.Whatismore,weprovetheasymptoticpropertiesofMSELE.Keywords:Outcome-dependentsampling;Generalizedlinearmodels;Empiricallikelihood;Consistency;Asymptoticnormality.150IntroductionEpidemiologicobservationalstudiesthatrelatediseaseoccurrencetoindividualexposuresandothercharact

4、eristicsplayanimportantroleinunderstandingthedeterminantsofdiseases.Majorcostandeffectarerelativetotheassemblyofexposuremeasurementsforthelargecohort2025303540members.Case-controlmethodhasbecomeafundamentalstatisticaltoolinenvironmentalepidemiologytoreducethecost.Morecomplexsamplingd

5、esignscouldenhancetheefficiencyfurther.Well-knownsamplingschemesforsurvivaldataincludecase-cohortdesignandgeneralizedcase-cohortdesign.Case-cohortdesignisadvocatedespeciallywhenthefailurerateislowWhite,1982;Prentice,1986;CaiandZeng,2004.Ageneralizedcase-cohortdesignassemblesthecovaria

6、teinformationonlyforafractiontakenfromthecasesinsteadofallcasesoutsideofthesubcohortwhenthenumberoffailuresislargeCaiandZeng,2007;KangandCai,2009.Ageneralbiassamplingscheme,outcomedependentsamplingODS,hasbeenwidelyusedinrecentepidemiologicresearchestoenhancetheefficiencyandreducetheco

7、st.AnODSdesignisaretrospectivesamplingschemewhereoneobservestheexposurewithaprobabilitythatdependsontheobservedvalueoftheoutcomevariable.Therefore,suchadesignusuallyincludesasimplerandomsamplefromtheunderlyingpopulationandsomeadditionalsupplementalsampleswhicharedeterminedbythevalueso

8、foutc