【作者】 严国义；

【导师】 刘禄勤；

【作者基本信息】 武汉大学 ， 概率论与数理统计， 2013， 博士

【摘要】 在临床医学研究中经常要对一个反应变量作纵向观测,同时又对另一感兴趣的事件发生的时间作记录。一个典型的例子就是在爱滋病的研究中既有CD4+和HIV病毒数量的纵向测量,也有爱滋病发作时间和病人死亡时间记录。在科学研究和临床试验中,我们往往对纵向观测量与事件发生的时间(比如病人死亡时间)之间的关系感兴趣,这种研究需要纵向数据和生存数据两方面的理论,有一定的复杂性,既有一定的理论意义又有实际应用价值。本文主要分为以下四个部分：第一章,我们介绍了本文研究工作的实际背景与解决相应问题的实际意义,概述了前人的研究方法和已有的成果,并综述了本文的主要工作。第二章,我们对纵向数据半参数回归模型采用拟高斯估计的方法,是对重复测量数据分析方法的一个推广。通常的一个广泛接受的经典方法是基于广义线性模型和拟似然估计的“广义估计方程”,但是该方法有某些理论上的缺陷。我们建议的方法是通过极大化一个工作似然函数从而避免了上述理论缺陷。在理论上,我们证明了所得估计的相合性和渐近正态性。第三章,我们研究了生存数据具有加速危险因子的加乘危险模型。本模型包含很多常见的生存分析的模型作为其特例,比如比例危险模型、加法模型、加乘危险模型和加速危险模型等。此模型与Chen和Wang(2000)[12]的区别在于本模型中的协变量被划分为三类,除了加速危险因子、乘性危险因子外还含有加性危险因子,从而回归模型中的回归参数相应分为反映协变量作用的加速危险的效应、乘法效应和加法效应,这样在评价协变量对反应变量的效用时能给出更好的解释。在适当的正则条件下证明了所得估计的相合性和渐近正态性；对累积基准危险率函数给出了Breslow-型估计,并给出了其弱收敛性的证明。我们建立的模型对生存数据的建模分析提供了一种新的选择。第四章研究了纵向数据与生存数据的半参数联合模型。假定纵向数据满足半参数混合效应模型,假定生存数据服从含有随机效应的比例危险模型。感兴趣的问题首先是纵向数据过程的刻画,同时也感兴趣生存时间与其他协变量之间的关系。该模型是现有很多模型的推广,对给定数据下的模型选择提供了新的方法。我们用B-样条方法将非参数项的估计转化为参数估计问题,用蒙特卡洛EM算法给出了参数的极大似然估计,并用bootstrap方法得到参数估计的标准差的估计。基于一个临床试验的实际例子说明了本模型的应用。最后,介绍了有待进一步研究的问题.更多还原

【Abstract】 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.更多还原