带终止事件纵向数据的统计推断及纵向数据分析框架探讨

Longitudinal data is an important type of complicated data which usually appears in medical and economical studies. It became a popular research subject in recent years and there have been a large number of literatures studying on analyzing and modeling of such data set. In practice, there usually exists some terminal event(e.g., death),which is totally different from censoring. However,many existing literatures still treat it as censoring event. This is obviously inappropriate. In this project, we will consider the analyzing and modeling of longitudinal data with terminal events. Some complicated but useful models such as the single index model, the transformation model with unknown transformation function, are to be considered. The asymptotic properties of derived estimators will be established, proved and confirmed by simulations. At the same time,we will consider the problem of lifetime medical cost, and discuss the modeling and statistical inferences under longitudinal data structure. Besides,note that until now, related literatures about analysis of longitudinal data mainly do their research under these two frameworks: framework of clustered data and framework of point processes. However, there are no researches on the differences and merits and demerits between these two frameworks. In this project, first we will devote ourselves to summarizing the methodologies for analyzing and modeling of longitudinal data, and providing a systematic statement as well as comparison of these two frameworks, aiming at deriving some instructive conclusions.

纵向数据是医学、经济等领域中经常面临的一种重要的复杂数据类型，近年来逐渐成为研究热点，已有大量的文献对其分析和建模方法进行了研究。实践中，往往会存在终止事件(比如死亡)，它与删失事件有着本质区别。但是现有的许多文献还只是把它当做删失事件进行处理，这是不恰当的。本项目将对带终止事件的纵向数据进行一系列的分析和建模，将考虑单指标模型、转移函数未知的转移模型等模型，并证明和模拟所得估计量的渐近性质。同时，我们还将考虑终身医疗费用问题，对其在纵向数据框架下的建模与统计推断进行探讨。此外，目前关于纵向数据的相关文献主要在这两种框架下来进行研究：聚类数据框架与随机过程框架。但是这两种框架的区别以及优缺点并没有文献进行探讨。本项目将致力于对纵向数据分析和建模的方法进行总结，并对前述两种分析框架进行一个系统的阐述和比较，从而得出一些具有指导意义的结论。

本项目主要研究了带终止事件的纵向数据、面板计数数据和复发数据，讨论了一元和多元的病例-队列设计下估计的有效性问题，探讨和比较了纵向数据的分析框架。这些数据类型都是现代生物医学统计中非常重要的数据类型，对它们的分析方法的研究，具有重要的应用价值。 对于病例-队列设计，我们研究了一元情形下的可加可乘模型以及多元情形下的加性模型，提出了有效估计量，并证明了估计量的大样本性质。对于带终止事件的复发数据、面板计数数据以及纵向数据，我们分别进行了研究，提出了相应的估计方法和大样本理论。对于纵向数据的分析框架，我们从数据特征、模型假定、估计和证明方法以及可延展性等方面进行了详细比较，给出了一些有意思的结果，并通过数值模拟验证了这些结论。