带辅助协变量的Ⅰ型区间删失数据的回归分析

发布时间：2018-01-16 03:00

本文关键词：带辅助协变量的Ⅰ型区间删失数据的回归分析　出处：《武汉大学》2017年硕士论文　论文类型：学位论文

【摘要】：生存分析是从医学、生物学、经济学等学科研究的大量实际问题中提取出来,并侧重于解决生存数据的统计推断问题的一门学科。生存分析的理论和应用研究一直以来都受到社会各界的广泛关注。如今,其应用已渗透到诸如医学、药学、生物学、保险精算学、可靠性工程、经济学以及人口统计学等领域。人们在对数据跟踪与采集过程中往往会因为研究期限的限制,与研究个体失去联系等客观原因使得观察被迫终止,从而引起删失。不同的删失机制下一般会产生不同类型的删失数据,其中区间删失是生存分析中一种重要的数据删失方式。迄今为止,对删失数据的基础理论绝大多数都建立在右删失数据的基础之上。由于区间删失机制与右删失机制之间的本质差别,区间删失数据是一种更具挑战性的数据类型。另一方面,研究可能会因为经费紧张或技术困难等原因而出现部分缺失的或不具备精确观测值的协变量,只能得到一些辅助协变量的信息,在这种情况下,统计推断工作要借助这些辅助变量信息来完成。许多学者已成功地将协变量的辅助信息用于右删失数据的统计推断。那么如何将协变量的辅助信息用到区间删失数据的统计推断?本文首先对生存分析中常见的删失数据类型以及常见的半参数模型进行了介绍,其次介绍了辅助信息缺失数据的统计处理方法,最后,我们针对带辅助协变量的I型区间删失数据的回归分析问题提出了两种参数估计方法,并给出了估计量的极限分布理论。大量的数据模拟分析和一个实例分析都表明这两种估计方法是有效性。
[Abstract]:Survival analysis is extracted from a large number of practical problems in medicine, biology, economics and other disciplines. The theory and application of survival analysis have been widely concerned by all walks of life. Nowadays, its application has penetrated into medicine and pharmacy. In the fields of biology, actuarial science, reliability engineering, economics, and demographics, people tend to be limited by the duration of their research in the process of tracking and collecting data. The objective reasons such as losing contact with the individual make the observation stop and cause the deletion. Under different deletion mechanisms different types of censored data are usually produced. Interval deletion is an important data deletion method in survival analysis. Most of the basic theories on censored data are based on right-censored data, because of the essential difference between interval delete mechanism and right censored mechanism. Interval-censored data is a more challenging type of data. On the other hand, research may be due to financial constraints or technical difficulties caused by some missing or do not have accurate observations of covariables. You can only get some information about auxiliary covariables, in this case. Many scholars have successfully applied the auxiliary information of covariables to the statistical inference of right-censored data. So how to use the auxiliary information of covariables to use interval censored information? Statistical extrapolation of the data? In this paper, we first introduce the common types of censored data and the common semi-parametric model in survival analysis, and then introduce the statistical processing method of the missing data of auxiliary information. We propose two parameter estimation methods for regression analysis of type I interval censored data with auxiliary covariables. The limit distribution theory of the estimator is given. A large number of data simulation and an example analysis show that these two estimation methods are effective.
【学位授予单位】：武汉大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.1

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