多类型复发事件数据半参数模型的统计推断

【作者】 王文忠；

【导师】 沈思；

【作者基本信息】 中央民族大学 ， 概率论与数理统计， 2015， 硕士

【摘要】 在生物医学、机械工业、人口学和生态学等领域中,研究的个体对象在一定的时间内可能经历多次我们感兴趣的事件,例如机器发生故障,患者疾病的发作等,这种事件在生存分析中被称复发事件,相应的复发时间组成的数据称为复发事件数据。当只对一种事件类型的结果感兴趣时,得到的就是单类型复发事件数据,如果研究中感兴趣的事件类型结果不止一种时,得到的就是多类型复发事件数据。由于复发事件数据具有次序性和相依性,并且由于删失时间的存在,导致复发事件数据往往是很复杂的。自上世纪80年代起,越来越多的国内外学者致力于研究解决这方面的问题,也得到了许多具有实际意义的结果。关于复发事件数据,我们感兴趣的往往是协变量对于复发事件的影响程度,至今为止学者们提出了各种各样的回归模型来研究协变量对于复发事件的影响,学者们主要从复发事件的间隔时间和复发事件本身这两方面入手来研究复发事件数据。本文第一章首先介绍了复发事件的一些背景知识和常用概念以及生存分析在复发事件研究用到一些定义和基础知识和本文用到的基本模型和基本估计方法,第二章综述了学者们在不同的角度下对复发事件数据进行研究的一些成果,本文的第三章在Lin等人于2000年提出的模型的基础上,提出了一个在一定条件下可以作为不同事件类型在时刻t与参考事件类型的平均复发次数的比较的模型,并给出该模型的参数估计值,以及估计的渐进性质。更多还原

【Abstract】 In many application research region such as biomedicine, mechanical industry, demography and ecology, individuals may repeat experience many times of a certain event in a certain period of time which are we interested in, such as machine failure, with the onset of the disease, which was known as recurrent events in the survival analysis. Recurrent events data refers to the observation of individuals, which contain the recurrent time of interest. We can obtain single type recurrent data when we focus on single type event, and if we are interested in multiple types of recurrent events, and we can obtain those results of multi-type events data. Because there exist sequence and sequence between different events, and also with the existence of the censored time, leading to the structure of recurrent event data is usually very complex. More and more domestic and foreign scholars exert their effort to solve these difficulties and had gain many significant results, since 1980’s.According to recurrent event data, we are interested in assessing the effect of covariates on the recurrent events. There have been many kinds of regression models to be proposed to study the effect of covariates on the recurrent events. These models are mostly built based on two aspects, the intervals and the recurrent event data itself. In this thesis’ Charpterl we introduce some background knowledge and the concepts of recurrent events, and then introduce some basic definitions and knowledge of the model in survival analysis. In Chapter2 we summarize some results about recurrent events in recent research. Based on Lin et al in 2000’s models, we propose a model which can be used as a measure of average recurrent number of different event-type at time t, methods and asymptotic properties for inferences on this model are established and some results from simulation are presented.更多还原