Estimation for Generalized Linear Mixed Model Via Multiple Imputations

This dissertation, "Estimation for Generalized Linear Mixed Model via Multiple Imputations" by On-yee, Tang, 鄧安怡, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Abstract of the thesis entitled ESTIMATION FOR GENERALIZED LINEAR MIXED MODEL VIA MULTIPLE IMPUTATIONS submitted by TANG On Yee for the degree of Master of Philosophy at The University of Hong Kong in February 2005 This thesis addresses the estimation of generalized linear mixed model in two par- ticular areas, namely analysis of zero-inated count data and survival analysis with long-term survivors. Analysis of count data is pervasive in many empirical applications. However, the count data encountered often exhibit a larger pro- portion of zeros than expected according to the Poisson distribution, making it inappropriateforanalysisusingastandardPoissonregressionmodel. Inthiscase, it is common to assume a mixture model which incorporates random e(R)ects into the Poisson regression model to accommodate the excessive zeros. More general random e(R)ects with the non-central chi-square distribution with zero degrees of freedom were proposed to model the extra variation induced by subject-specicheterogeneity. Theuseofthisspecialdistributionnotonlyprovidesmoreexibility on the relationship between covariates and random e(R)ects, but also demonstrates its superior merits and usefulness in analysis of clustered or multivariate count data. In practice, independence between observations cannot always be assumed. Correlated zero-inated count data are often encountered when they are collected on clusters of individuals or when repeated measurements are made on the same subject. In this case, each subject is regarded as a cluster. To further accommo- date the level of association among the zero-inated response counts within the same cluster, namely the intra-cluster correlation, the proposed model was ex- tended to incorporate a cluster-specic frailty, where the intra-cluster correlation can be measured either in terms of a correlation coecient or characterized by a dependence parameter. Multivariate zero-inated count data arise naturally when more than one rare event of interest, that are originally related, are observed simultaneously. To account for both preponderance of zeros and dependence between multivariate responses, a multivariate extension of the proposed model was suggested. In ad- dition to random e(R)ects which describe the subject-specic heterogeneity in the proposedmodel, agammafrailtywasintroducedtoaccommodatethedependence between multivariate response counts. Another topic deals with modeling the proportion of immunes or surviving fraction in a population. Recently, there has been a recurring interest in modelingsurvival data which hypothesize subpopulations of individuals highly susceptible tosometypesofadverseeventswhileotherindividualsareassumedtobeatmuch lessrisk. Itiscommontoassumeabinaryrandome(R)ecttomodelthesusceptibility ofeachindividual. Toanalyzethistypeofcensoreddatawithlong-termsurvivors, amixturemodelwasrevisited. Itcombinesabinaryregressionformulationforthe probabilityofoccurrenceofaneventandtheCox'sproportionalhazardsregression model for the time to occurrence of the event if it does. Simple multiple imputation algorithms were proposed to perform estimation for the above analyses. It is simple, easy to implement and has the merit of a straightforward variance estimation. Its computational and analytical simplicity were validated by simulation studies and illustrated by real data applications. DOI: 10.5353/th_b3068765 Subjects: Linear models (S