In Bayesian semi-parametric analyses of time-to-event data, non-parametric process priors are adopted for the baseline hazard function or the cumulative baseline hazard function for a given finite partition of the time axis. However, it would be controversial to suggest a general guideline to construct an optimal time partition. While a great deal of research has been done to relax the assumption of the fixed split times for other non-parametric processes, to our knowledge, no methods have been developed for a gamma process prior, which is one of the most widely used in Bayesian survival analysis. In this paper, we propose a new Bayesian framework for proportional hazards models where the cumulative baseline hazard function is modelled a priori by a gamma process. A key feature of the proposed framework is that the number and position of interval cutpoints are treated as random and estimated based on their posterior distributions.

在时间到事件数据的贝叶斯半参数分析中，对于给定的时间轴有限分区的基线危险函数或累积基线危险函数采用非参数过程先验。然而，提出构建最佳时间分区的一般准则是有争议的。虽然已经进行了大量研究以放宽对其他非参数过程的固定分割时间的假设，但据我们所知，还没有为伽马过程先验开发方法，这是贝叶斯中最广泛使用的方法之一。生存分析。在本文中，我们为比例风险模型提出了一个新的贝叶斯框架，其中累积基线风险函数是先验建模的通过伽马过程。所提出的框架的一个关键特征是区间分割点的数量和位置被视为随机的，并根据它们的后验分布进行估计。