In Bayesian inference for the Cox proportional hazards model, modeling the baseline hazard function is challenging. Recently, direct Bayesian inference using the partial likelihood is considered in the framework of general Bayesian inference. In terms of posterior computation, several studies have examined sampling algorithms under the Cox model. In this study, we propose two Gibbs sampling algorithms for Bayesian inference in the Cox proportional hazards model, motivated by a rank-ordered data representation and based on the Plackett--Luce and generalized Plackett--Luce models with P'{o}lya--Gamma data augmentation, referred to as PL-Cox and GPL-Cox, respectively. The two proposed methods offer practical advantages, as they do not require correction of posterior samples, naturally handle tied event times, and are readily extensible to shared frailty models. In simulation study, we considered multiple survival model settings, including continuous and discrete survival time models, as well as scenarios with varying degrees of ties, and found that the PL-Cox model exhibited relatively stable performance. In analyses of a large real dataset, the proposed methods remained computationally feasible, and the GPL-Cox model showed more favorable computational scalability than the PL-Cox model. In analyses of real data incorporating shared frailty, both methods demonstrated good computational efficiency.

翻译：在Cox比例风险模型的贝叶斯推断中，基线风险函数的建模颇具挑战性。近年来，研究者已在广义贝叶斯推断框架下采用偏似然函数进行直接贝叶斯推断。针对后验计算问题，多项研究探讨了Cox模型下的采样算法。本研究提出两种用于Cox比例风险模型贝叶斯推断的吉布斯采样算法，其动机源于秩次排序数据表示，并基于引入Pólya-Gamma数据增广的Plackett-Luce模型与广义Plackett-Luce模型，分别称为PL-Cox模型与GPL-Cox模型。这两种方法的实用优势在于：无需校正后验样本、能自然处理结事件时间、且易于扩展至共享脆弱模型。模拟研究考虑了多种生存模型设定，包括连续与离散生存时间模型，以及不同结比例的场景，发现PL-Cox模型表现出相对稳健的性能。在对大型真实数据集的分析中，所提方法仍保持计算可行性，且GPL-Cox模型较PL-Cox模型展现出更优的计算可扩展性。在纳入共享脆弱性结构的真实数据分析中，两种方法均表现出良好的计算效率。