【作者】 王洁；

【导师】 冯艳钦；

【作者基本信息】 武汉大学 ， 统计学， 2022， 硕士

【摘要】 生存分析是统计学中一门重要的分支学科,主要研究生存现象和失效时间数据以及相关的统计分析与推断,自上个世纪开始发展以来就得到了广泛的应用.本文首先对生存分析中集群当前状态数据的模型检验问题相关的研究背景与国内外研究现状进行了概述,并介绍了不完全数据类型、基本函数以及常见的半参数回归模型,之后重点研究了加法风险模型对集群当前状态数据的拟合优度检验方法.其中,对集群当前状态数据,我们主要考虑具有信息的集群容量.为此,本文首先介绍了带有潜在变量的加法风险模型,并建立了回归参数的加权估计方程.其次,本文基于鞅残差提出了加法风险模型的拟合优度检验方法,并建立了相关的渐近性质.最后,我们进行了大量的数值模拟,评估该检验方法在有限样本下的性能以及有效性,同时将提出的检验方法应用于一个致瘤性研究的真实数据集,验证了其在实际场景下的应用价值与准确性.更多还原

【Abstract】 Survival analysis is an important branch of statistics,which mainly studies survival phenomenon and failure time data as well as related statistical analysis and inference.It has been widely used since its development in the last century.This paper firstly summarizes the research background and research status of model testing of clustered current status data in survival ananlysis,and introduces incomplete data types,basic functions and common semi-parametric regression models,and then focuses on the goodness-of-fit test method of the additive hazards model to the clustered current status data.Among them,for clustered current status data,we mainly consider the case where cluster sizes are informative.For this problem,this paper first introduces an additive hazards model with the latent variable,and establishes a weighted estimation equation for the regression parameter.Secondly,this paper proposes a goodness-of-fit test method for additive hazards model based on martingale-based residuals.Relevant asymptotic properties are established.Finally,we conduct extensive numerical simulations to evaluate the performance and effectiveness of the test method under a limited sample size.At the same time,the proposed test method is applied to a real data set of tumorigenicity research,showing its application value and accuracy in practical scenarios.更多还原