The Study Of Semiparametric Joint Models For Longitudinal And Survival Data

In many longitudinal clinical studies, it is common that both longitudinal mea-surements of a response variable and the time to some event of interest are recorded during follow-up. A typical example is the AIDS study where CD4count and viral load are collected longitudinally and the time to AIDS or death is also monitored. It is of scientific and clinical interest to relate such longitudinal quantities to a later time-to-event clinical endpoint such as patient survival. The research needs theories about longitudinal and survival data, which has some complications in the study. Our study has more theoretical and practical value.This thesis consists of four parts as follows:In Chapter1, we introduce first the background of the questions and the results which have been obtained in recent years. Following, we introduce in general the results that we obtain in this thesis.In Chapter2, we propose a method by using quasi gaussian estimation for the semi-parametrical longitudinal data models, which develop the methods for the analysis of repeated measures. More recent methodology, based on generalized linear models and quasi-likelihood estimation, has gained generalized estimating equations. But this also has theoretical problem. The method which we proposed by maximizing a working likelihood function avoids such theoretical problem. By using the classical methods, we obtain and prove the consistency and asymptotic normality on the proposed estimator.In Chapter3, we have studied a general class of additive-multiplicative model with accelerated hazard factor for survival data. This general class model includes some popular classes of models as subclasses. The model is different from Chen and Wang(2001)[11],the estimators for the vector of regression parameters include addi-tive effect of covariates. The resulting estimators are proven to be consistent and asymptotically normal under appropriate regularity condition. Weak convergence of the Breslow-type estimator for the cumulative baseline hazard function is also estab-lished. Our model is an extended model of Chen and Jewell(2001)[11], which may provide a tool to choose modelling more appropriate for a given data set.In Chapter4, We study joint modeling of survival and longitudinal data. In this paper, we study a general class of semiparametric likelihood approach to joint modeling of longitudinal and time-to-event data. The longitudinal data are assumed to follow a generalized semiparametric mixed effects model, and a proportional hazards model depending on the longitudinal random effects and other covariates is assumed for the survival endpoint. Interest may focus on the longitudinal data process, which is infor-matively censored, or on the hazard relationship. Our model is an extended model of many current model, which may provide a tool to choose modelling more appropriate for a given data set. We propose to obtain the maximum likelihood estimates of the parameters by an expectation maximization (EM) algorithm and estimate their stan-dard errors using a bootstraping method. We illustrate our approach with a concrete clinical trial example. Finally, we introduce some aspects which we can do a further study or promotion by the use of our methods in this thesis.