比例风险模型下区间删失数据的参数回归模型研究

发布时间：2018-10-09 12:41

【摘要】：目前,生存分析中最常用的方法即COX比例风险模型,该模型在慢性流行病学研究中已有广泛的应用,而基于各种分布的参数型比例风险回归模型在生物学、医学、工程科学还有社会学、心理学、经济学、保险精算学和可靠性等领域有重要的工具性作用。本文主要针对区间删失两种类型(区间删失case I和区间删失case II)的数据,分别建立了广义指数COX比例风险模型,给出了不同的模型估计方法。这里选取广义指数分布,是因为该分布在很多方面能很好的弥补韦布尔分布和伽马分布的不足,针对危险率函数具有很强的灵活性,可以适用很多类型的危险率的数据进行建模分析。当然对于区间删失时间数据也有相对较好的更灵活的分析效果,并且在寿命试验和可靠性研究等很多领域中都有着重要的应用。重点从两方面进行创新性的研究,首先针对区间删失II型数据,基于广义指数分布,建立了广义指数比例风险回归模型,由于数据的复杂性,模型的极大似然估计方法不能给出明显的估计结果,应用Newton-Rapson算法进行比例风险回归模型的参数估计,通过设置各种情形的大量的模型研究,验证了所提出的模型及估计方法的有效性。并将此模型方法应用到31名艾滋病患者参加的艾滋病治疗临床试验数据的分析中。其次针对区间删失I型数据建立广义指数分布的比例风险回归模型,由于数据和似然函数的复杂性,故尝试使用带有先验信息的贝叶斯估计方法估计,分层给出的各参数后验分布没有显示表达式,应用了MCMC的各种算法进行抽样,得到参数的贝叶斯估计。并设计了大量的模拟实验,验证了提出的模型和算法的有效性。并将此模型和贝叶斯估计算法应用到实际数据是144只雄性RFM小鼠肺肿瘤的致瘤性实验数据的分析中。
[Abstract]:At present, COX proportional risk model, which is the most commonly used method in survival analysis, has been widely used in chronic epidemiology, while parametric proportional risk regression model based on various distributions has been applied in biology and medicine. Engineering science also plays an important instrumental role in sociology, psychology, economics, actuarial insurance and reliability. In this paper, the generalized exponential COX proportional risk model is established for two types of interval censored data (interval censored case I and interval-censored case II), and different estimation methods are given. The generalized exponential distribution is chosen here because it can make up for the deficiency of Weibull distribution and gamma distribution in many aspects. Many types of hazard rate data can be applied for modeling and analysis. Of course, the interval censored time data also has a relatively better and more flexible analysis results, and has important applications in many fields such as life test and reliability research. The innovative research is focused on two aspects. Firstly, based on generalized exponential distribution, a generalized exponential proportional risk regression model is established for interval-censored II data. Because of the complexity of the data, a generalized exponential proportional risk regression model is established. The maximum likelihood estimation method of the model can not give obvious estimation results. The Newton-Rapson algorithm is used to estimate the parameters of the proportional risk regression model. The validity of the proposed model and estimation method is verified. The model was applied to the analysis of clinical trial data of 31 AIDS patients. Secondly, the proportional risk regression model of generalized exponential distribution is established for interval censored I-type data. Because of the complexity of data and likelihood function, Bayesian estimation method with prior information is used to estimate the model. The posteriori distribution of each parameter given by stratification has not shown the expression. The Bayesian estimation of parameters is obtained by sampling by using various algorithms of MCMC. A large number of simulation experiments have been designed to verify the effectiveness of the proposed model and algorithm. The model and Bayesian estimation algorithm were used to analyze the tumorigenicity of lung tumors in 144 male RFM mice.
【学位授予单位】：长春工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：C81

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