刘红伟,张甜甜,刘媛媛,李长平,胡良平.生存资料回归模型分析——生存资料参数回归模型分析基础[J].四川精神卫生杂志,2020,33(1):33-38.Liu Hongwei,Zhang Tiantian,Liu Yuanyuan,Li Changping,Hu Liangping,Regression analysis of the parametric models for the survival data——the basis of the parametric regression model analysis of the survival data[J].SICHUAN MENTAL HEALTH,2020,33(1):33-38

生存资料回归模型分析——生存资料参数回归模型分析基础

Regression analysis of the parametric models for the survival data——the basis of the parametric regression model analysis of the survival data

投稿时间：2020-01-06

DOI：10.11886/scjsws20200106004

中文关键词: 生存分析参数回归拟合优度检验似然比检验 Weibull分布 Log-logistic分布

英文关键词:Survival analysis Parametric regression Goodness-of-fit tests Likelihood-ratio tests Weibull distribution Log-logistic distribution

基金项目:国家自然科学基金项目（项目名称：贝叶斯生存分析方法在肝细胞癌肝移植患者预后预测中的应用研究，项目编号：81803333）

作者	单位	邮编
刘红伟	天津医科大学公共卫生学院，天津 300070	300070
张甜甜	天津医科大学公共卫生学院，天津 300070	300070
刘媛媛	天津医科大学公共卫生学院，天津 300070	300070
李长平	天津医科大学公共卫生学院，天津 300070 世界中医药学会联合会临床科研统计学专业委员会，北京 100029	100029
胡良平	世界中医药学会联合会临床科研统计学专业委员会，北京 100029 军事科学院研究生院，北京 100850	100850

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中文摘要:

本文目的是介绍生存资料参数回归模型有关的基础知识。首先，介绍了构建三个常见的生存资料参数回归模型的基本原理，包括指数分布回归模型、Weibull分布回归模型和Log-logistic分布回归模型；其次，介绍了基于图示法判断生存时间服从何种概率分布的方法；最后，介绍了基于最大似然估计法求解参数回归模型中的参数和两个参数回归模型拟合优度的比较。得到如下结论 ①当资料中的生存时间服从特定概率分布时，应选用相应的参数回归模型；②图示法可用于粗略判断生存时间服从何种概率分布；③似然比检验可用于包含不同参数数目的两个参数回归模型之间拟合优度的比较。

英文摘要:

The purpose of this paper was to introduce the fundamental knowledge of the parametric models for the survival data. Firstly, the basic principles of three common parametric models for the survival data were given, including exponential distribution regression model, Weibull distribution regression model and Log-logistic distribution regression model. Secondly, the method of judging the probability distribution of survival time based on graphs was introduced. Finally, the solution for the parameters in the parametric regression model based on maximum likelihood estimation and the comparison between the goodness of fit of the two parametric regression models was introduced. The results of the article showed that: ① when the data followed the specific distribution, the corresponding parametric regression model should be applied； ② graphical methods could be use to judge rouphly the survival time followed what kind of the probability distribution； ③ likelihood ratio test could be used to compare the effects of the goodness of fit between two parametric regression models with different numbers of parameters.

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