删失失效时间数据的回归分析

发布时间：2018-01-08 14:14

本文关键词：删失失效时间数据的回归分析　出处：《吉林大学》2017年博士论文　论文类型：学位论文

【摘要】：近年来,删失数据的统计分析引起了学者的广泛关注,这种数据存在于很多科学研究领域,包括医学、人口学和社会学等.本文的研究内容主要分为三个方面,分别为带相依删失时间的1型区间删失数据的回归分析、半参数转换frailty模型下多元1型区间删失数据的回归分析和半参数转换模型下双重删失数据的回归分析.首先,针对带相依删失时间的1型区间删失失效时间数据,我们提出使用frailty模型来刻画删失时间和失效时间的相关关系.其中,我们使用单调样条函数来逼近失效时间模型中的基线累积风险函数并提出一种基于泊松随机变量的EM算法来得到参数的极大似然估计.此时得到的估计量具有相合性、渐近正态性和有效性.数值模拟和来自小鼠肿瘤实验的实例均验证了该模型及相应估计方法的实际应用价值.其次,我们讨论了半参数转换frailty模型下多元1型区间删失数据的回归分析问题.我们通过frailty的拉普拉斯变换将转换frailty模型变换为带有两重frailty的比例风险模型,并提出一种基于泊松随机变量的EMM算法来进行参数估计.其中,在期望步,我们联合使用概率积分变换和高斯正交方法来计算关于frailty的条件期望.此时得到的估计量具有相合性、渐近正态性和有效性.我们通过数值模拟验证了该估计方法的合理性,并将所提出的模型及相应估计方法应用于关于衣原体和淋病的实际数据中.最后,我们研究了半参数转换模型下双重删失数据的回归分析问题.我们通过frailty的拉普拉斯变换将转换模型变换为比例风险frailty模型以简化估计问题,同时提出一种基于泊松随机变量的EM算法进行参数估计,并证明了估计量的渐近性质,包括相合性、渐近正态性和有效性.我们通过数值模拟验证了估计的效果和精确性,并将提出的模型拟合了关于艾滋病的临床试验数据.
[Abstract]:In recent years, the statistical analysis of censored data has attracted wide attention of scholars. This kind of data exists in many fields of scientific research, including medicine, demography and sociology. The research content of this paper is mainly divided into three aspects. The regression analysis of type 1 interval censored data with dependent censored time was presented. Regression analysis of multivariate 1-type interval censored data under semi-parametric conversion frailty model and double-censored data regression under semi-parametric transformation model. First. For the data of type 1 interval censored failure time with dependent censored time, we propose to use frailty model to describe the correlation between censored time and failure time. We use the monotone spline function to approximate the baseline cumulative risk function in the failure time model and propose an EM algorithm based on Poisson random variables to obtain the maximum likelihood estimation of the parameters. Consistency. The asymptotic normality and validity. The numerical simulation and the examples from mouse tumor experiments verify the practical application value of the model and the corresponding estimation method. Secondly. In this paper, we discuss the regression analysis of interval censored data of multivariate type 1 under semi-parametric converted frailty model. We transform the frailty model by frailty's Laplace transform. Is a proportional risk model with double frailty. A EMM algorithm based on Poisson random variables is proposed to estimate the parameters. We use probabilistic integral transform and Gao Si orthogonal method to calculate the conditional expectation of frailty. Asymptotic normality and validity. The rationality of the proposed method is verified by numerical simulation, and the proposed model and the corresponding estimation method are applied to the actual data on chlamydia and gonorrhea. Finally. We study the regression analysis of double censored data under semi-parametric transformation model. We transform the transformation model into proportional risk frailty model by Laplace transform of frailty to simplify the estimation. The problem. At the same time, an EM algorithm based on Poisson random variables is proposed to estimate the parameters, and the asymptotic properties of the estimator, including consistency, are proved. Asymptotic normality and validity. The effectiveness and accuracy of the estimation are verified by numerical simulation and the data of clinical trials on AIDS are fitted by the proposed model.
【学位授予单位】：吉林大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：O212.1

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