【作者】 刘吉彩；

【导师】 刘焕彬；

【作者基本信息】 上海师范大学 ， 概率论与数理统计， 2010， 硕士

【摘要】 在医学,生物学,经济学等研究过程中,研究的个体有时会重复地经历某一事件或者多次的失效,这种事件称为复发事件.复发事件是广泛存在的,然而复发事件数据的结构往往是很复杂的.因为这些事件之间常常存在一定的相依性和有序性.越来越多的学者正致力于解决这方面的问题,并且获得了许多有意义的结果.复发事件数据根据研究对象的种类一般可以分为两种类型.当只对一种可反复发生的事件感兴趣时,这时得到的数据称为单类型复发事件数据.然而,有时研究的个体可能会同时经历多种不同类型的复发事件且类别之间存在相关性,这时我们必须同时研究各类事件,这样得到的数据称为多类型复发事件数据.对于复发事件,我们常常感兴趣的是研究协变量对复发事件的影响程度.历史上,许多学者提出了各种不同的回归模型来研究协变量对单类型复发事件的影响.本文主要讨论的是多类型复发事件在间隔时间数据下的三种危险率回归模型.首先介绍复发事件的一些背景,综述了单类型复发事件在间隔时间数据下的比例危险率模型,可加危险率模型以及可乘可加危险率模型；接着我们提出多类型复发事件的比例危险率模型,同时给出模型中参数以及非参数函数的估计方法,建立这些估计的渐近性质并且进行模拟研究；其次我们提出多类型复发事件的可加危险率模型,给出了模型中参数以及非参数函数的估计方法,研究了这些估计的渐近性质；再次我们提出多类型复发事件的可乘可加危险率模型,给出了模型中参数以及非参数函数的估计方法,讨论了这些估计的渐近性质.更多还原

【Abstract】 In many application areas, subjects may usually experience multiple events or failure over time, which have been termed recurrent events. Recurrent event date often arises in many applica-tion areas, such as, medical science, biology and economics. However, the structure of recurrent event dates is usually complex. Because there exist correlation and sequence between different events. Recently, more and more researchers exert their efforts to solve these difficulties and gain many significant results.The recurrent event dates which record the recurrent time of each event of interest, includes two types. The first type termed single recurrent events is that only one type of recurrent events is of considered. However, in many settings, subjects may experience several types of recurrent events, and these types are dependent on each other. This case is naturally considered, in which dates have been called multiple type recurrent event.For recurrent events, we are interested in assessing the effect of covariates on the recurrent events. There have been many regression models to be proposed. In this thesis, we mainly dis-cussed three models for multiple type recurrent gap times. In Chapter 2, the proportional hazards model has been put forward which is the generalized form of Cox model, methods and asymp-totic properties for inferences on this model are established and some results from simulation are presented. In Chapter 3, we study additive hazards model for multiple type recurrent gap times. Asymptotic properties for estimators of parameter are established. In Chapter 4, the additive-multiplicative hazards model for multiple type recurrent gap times are investigated. Asymptotic properties of the proposed parameter estimators are developed.更多还原