Faraggi D, Simon R
Department of Statistics, University of Haifa, Israel.
Biometrics. 1998 Dec;54(4):1475-85.
A Bayesian variable selection method for censored data is proposed in this paper. Based on the sufficiency and asymptotic normality of the maximum partial likelihood estimator, we approximate the posterior distribution of the parameters in a proportional hazards model. We consider a parsimonious model as the full model with some covariates unobserved and replaced by their conditional expected values. A loss function based on the posterior expected estimation error of the log-risk for the proportional hazards model is used to select a parsimonious model. We derive computational expressions for this loss function for both continuous and binary covariates. This approach provides an extension of Lindley's (1968, Journal of the Royal Statistical Society, Series B 30, 31-66) variable selection criterion for the linear case. Data from a randomized clinical trial of patients with primary biliary cirrhosis of the liver (PBC) (Fleming and Harrington, 1991, Counting Processes and Survival Analysis) is used to illustrate the proposed method and a simulation study compares it with the backward elimination procedure.
本文提出了一种用于删失数据的贝叶斯变量选择方法。基于最大偏似然估计量的充分性和渐近正态性，我们对比例风险模型中参数的后验分布进行近似。我们将一个简约模型视为完整模型，其中一些协变量未被观测到，而是用它们的条件期望值来替代。基于比例风险模型对数风险的后验期望估计误差的损失函数被用于选择简约模型。我们推导了连续和二元协变量情况下该损失函数的计算表达式。这种方法为线性情形下林德利（1968年，《皇家统计学会学报》，B辑30卷，31 - 66页）的变量选择准则提供了扩展。来自一项原发性胆汁性肝硬化（PBC）患者随机临床试验的数据（弗莱明和哈林顿，1991年，计数过程与生存分析）被用于阐述所提出的方法，并且一项模拟研究将其与向后淘汰程序进行了比较。
