半参数加速失效时间模型及其在医学中的应用

发布时间：2018-05-16 05:17

本文选题：半参数加速失效时间模型 + Gehan统计量　；参考：《山西医科大学》2007年硕士论文

【摘要】： 在生存数据分析领域当中,半参数加速失效时间模型做为一种线性回归模型,它把生存时间的对数作为反应变量,而且误差项的分布也是未知的。在分析含有删失数据的生存资料时,半参数加速失效时间模型是Cox比例风险模型的一种很好的替代模型。在用加速失效时间模型处理删失数据时,许多人都研究基于秩的估计方法,秩估计量可以由最小化凸目标函数通过标准的线性规划的方法得到。但在用传统方法估计秩估计量的方差时有很大困难。这里介绍Zhou的一种经验似然的分析方法来对秩估计量做推断。这里的似然定义为误差变量的删失经验似然,用经验似然的方法进行假设检验,而且用它来为模型的回归系数建立可信区间。同时表明了在原假设下,对数经验似然比的限制分布是一个中心卡方分布,标准的卡方分布用来计算P值和建立可信区间。经验似然方法避免了估计方差,只需要计算删失经验似然的约束最大化即可,而这种方法的计算是很可靠的。因此,为了检验假设和计算P值,经验似然的方法需要解决最优化的问题。模拟分析和实例分析都显示了对数经验似然比的分布很好地接近卡方分布,而且展现出了比其它方法更多的优点。我们同时介绍了Arnost Komarek的一种加速失效时间模型的半参数估计方法。这种方法主要是利用惩罚B样条来光滑误差项。用了Eilers和Marx(1996)的光滑技术来表达误差项的密度函数,因为误差项密度是无限支撑的,所以用正态密度来替换B样条,其实正态密度是B样条的极限情形。样条系数和回归参数都可由惩罚最大似然的方法快速准确的计算得到。用“伪方差估计”的方法在基于惩罚最大似然的基础上做出准确的推断。这种方法可以在固定协变量时直接预测生存曲线,而且这种方法可以处理左删失、右删失和区间删失的生存数据。本课题模拟分析及实例分析使用R软件作为运算分析平台。
[Abstract]:In the field of survival data analysis, the semi-parametric accelerated failure time model is a linear regression model, which takes the logarithm of survival time as a response variable, and the distribution of the error term is unknown. In the analysis of survival data with censored data, the semi-parametric accelerated failure time model is a good substitute for Cox proportional risk model. When processing censored data with the accelerated failure time model, many people have studied the rank estimation method, which can be obtained by minimizing convex objective function through the standard linear programming method. However, it is difficult to estimate the variance of rank estimator by traditional method. This paper introduces an empirical likelihood analysis method of Zhou to infer rank estimators. Here the likelihood is defined as the erasure empirical likelihood of error variables. The empirical likelihood method is used to test the hypothesis, and it is used to establish the confidence interval for the regression coefficient of the model. It is also shown that the restricted distribution of logarithmic empirical likelihood ratio is a central chi-square distribution under the original assumption, and the standard chi-square distribution is used to calculate P value and establish confidence intervals. The empirical likelihood method avoids the estimation of variance and only needs to compute the constraint maximization of erasure empirical likelihood. The calculation of this method is very reliable. Therefore, in order to test the hypothesis and calculate P value, the empirical likelihood method needs to solve the optimization problem. Both simulation analysis and case analysis show that the distribution of logarithmic empirical likelihood ratio is close to the chi-square distribution and shows more advantages than other methods. We also introduce a half parameter estimation method for accelerated failure time model of Arnost Komarek. This method mainly uses the penalty B spline to smooth the error term. The density function of the error term is expressed by the smooth technique of Eilers and Marks 1996. Because the density of the error term is infinitely supported, the normal density is replaced by the B-spline. In fact, the normal density is the limit of the B-spline. The spline coefficients and regression parameters can be calculated quickly and accurately by the maximum likelihood penalty method. The method of pseudo-variance estimation is used to infer accurately based on the maximum likelihood of punishment. This method can directly predict the survival curve when the covariable is fixed, and this method can deal with the survival data of left, right and interval deletions. In this paper, R software is used as the platform of calculation and analysis.
【学位授予单位】：山西医科大学
【学位级别】：硕士
【学位授予年份】：2007
【分类号】：R311

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