Sinha D
Department of Mathematics and Statistics, University of New Hampshire, Durham 03824-3591, USA.
Biometrics. 1998 Dec;54(4):1463-74.
This article deals with the semiparametric analysis of multivariate survival data with random block (group) effects. Survival times within the same group are correlated as a consequence of a frailty random block effect. The standard approaches assume either a parametric or a completely unknown baseline hazard function. This paper considers an intermediate solution, that is, a nonparametric function that is reasonably smooth. This is accomplished by a Bayesian model in which the conditional proportional hazards model is used with a correlated prior process for the baseline hazard. The posterior likelihood based on data, as well as the prior process, is similar to the discretized penalized likelihood for the frailty model. The methodology is exemplified with the recurrent kidney infections data of McGilchrist and Aisbett (1991, Biometrics 47, 461-466), in which the times to infections within the same patients are expected to be correlated. The reanalysis of the data has shown that the estimates of the parameters of interest and the associated standard errors depend on the prior knowledge about the smoothness of the baseline hazard.
本文探讨了具有随机区组（组）效应的多变量生存数据的半参数分析。由于脆弱的随机区组效应，同一组内的生存时间相互关联。标准方法要么假设参数化的，要么完全未知的基线风险函数。本文考虑一种中间解决方案，即一个相当平滑的非参数函数。这通过一个贝叶斯模型来实现，其中条件比例风险模型与基线风险的相关先验过程一起使用。基于数据的后验似然以及先验过程类似于脆弱模型的离散惩罚似然。该方法以McGilchrist和Aisbett（1991年，《生物统计学》47卷，461 - 466页）的复发性肾脏感染数据为例进行说明，其中同一患者内的感染时间预计是相关的。对数据的重新分析表明，感兴趣参数的估计值及其相关标准误差取决于关于基线风险平滑度的先验知识。
