基于加法模型的相依区间删失数据的回归分析
发布时间：2019-02-15 18:16
【摘要】：区间删失数据是生存分析中的一种常见且非常重要的数据类型,针对这种数据的现有研究大多假设了独立删失机制,也就是说删失时间与事件失效时间是独立的,但这种假设在现实问题中并不一定成立,此时忽略删失时间与事件失效时间之间的相依性很可能会造成分析结果的有偏甚至错误。已有文献采用Cox模型(也称比例风险模型)对相依区间删失数据进行研究。而加法风险模型是生存分析中除Cox模型以外的另一种重要模型,和Cox模型不同,在加法模型中,协变量对寿命变量的危险率的影响是以加法形式呈现,协变量效应直接刻画了危险率的绝对变化量。当前对加法模型的研究还不是很多,且大多数研究针对右删失数据或者独立删失机制下的区间删失数据。本文讨论了加法风险模型下相依区间删失数据的半参数回归问题,通过引入隐变量来刻画失效时间与删失时间两者之间的相关关系,并采用极大似然方法对参数进行估计。此外,本文还给出了估计量的渐近正态性的证明,并采用模拟试验来对文中算法的效果进行评估,数值模拟结果显示文中的估计算法是合理有效的。
[Abstract]:Interval censored data is a common and very important data type in survival analysis. Most of the existing researches on this kind of data assume independent deletion mechanism, that is to say, deletion time and event failure time are independent. However, this assumption is not always true in practical problems, and neglecting the dependence between censored time and event failure time may lead to bias or even error of the analysis results. Cox model (also called proportional risk model) has been used to study the censored data of dependent interval. In addition to the Cox model, the additive risk model is different from the Cox model. In the additive model, the influence of the covariable on the risk rate of the life variable is presented in the form of addition. The covariable effect directly characterizes the absolute variation of the risk rate. At present, there are not many researches on addition model, and most of the researches focus on right censored data or interval censored data under independent delete mechanism. In this paper, the semi-parametric regression problem of dependent interval censored data under additive risk model is discussed. Implicit variables are introduced to describe the correlation between failure time and censored time, and the maximum likelihood method is used to estimate the parameters. In addition, the asymptotic normality of the estimator is proved, and the effectiveness of the proposed algorithm is evaluated by simulation experiments. The numerical simulation results show that the proposed estimation algorithm is reasonable and effective.
【学位授予单位】：华中师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.1
本文编号：2423608
[Abstract]:Interval censored data is a common and very important data type in survival analysis. Most of the existing researches on this kind of data assume independent deletion mechanism, that is to say, deletion time and event failure time are independent. However, this assumption is not always true in practical problems, and neglecting the dependence between censored time and event failure time may lead to bias or even error of the analysis results. Cox model (also called proportional risk model) has been used to study the censored data of dependent interval. In addition to the Cox model, the additive risk model is different from the Cox model. In the additive model, the influence of the covariable on the risk rate of the life variable is presented in the form of addition. The covariable effect directly characterizes the absolute variation of the risk rate. At present, there are not many researches on addition model, and most of the researches focus on right censored data or interval censored data under independent delete mechanism. In this paper, the semi-parametric regression problem of dependent interval censored data under additive risk model is discussed. Implicit variables are introduced to describe the correlation between failure time and censored time, and the maximum likelihood method is used to estimate the parameters. In addition, the asymptotic normality of the estimator is proved, and the effectiveness of the proposed algorithm is evaluated by simulation experiments. The numerical simulation results show that the proposed estimation algorithm is reasonable and effective.
【学位授予单位】：华中师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.1
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相关硕士学位论文 前3条
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