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 developed a novel likelihood extension for the Cox proportional hazards model based on the modeling of rank-ordered data. Furthermore, we propose two Gibbs sampling algorithms that combine the full likelihood based on the Plackett--Luce and generalized Plackett--Luce models with Pólya--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 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 real data with many ties, the GPL-Cox model fit the dataset substantially better than the PL-Cox model. In analyses of real data incorporating shared frailty, both methods demonstrated good computational efficiency. The R package \texttt{BayesPLCox}, which implements the PL-Cox and GPL-Cox methods, is publicly available.

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具有挑战性。近期，学者们在通用贝叶斯推断框架下探讨了直接使用部分似然进行贝叶斯推断的方法。在后验计算方面，多项研究考察了Cox模型下的采样算法。本研究基于排序数据的建模，提出了一种Cox比例风险模型的新型似然扩展方法。此外，我们提出了两种吉布斯采样算法，分别结合基于Plackett-Luce模型和广义Plackett-Luce模型的完全似然与Pólya-Gamma数据增广技术，并将其命名为PL-Cox和GPL-Cox。这两种方法具有实用优势：无需校正后验样本，且易于扩展至共享脆弱性模型。在模拟研究中，我们考虑了包括连续和离散生存时间模型、以及不同结比例场景在内的多种生存模型设定，发现PL-Cox模型展现出相对稳定的性能。在含有大量结的实际数据分析中，GPL-Cox模型对数据集的拟合效果显著优于PL-Cox模型。在包含共享脆弱性的实际数据分析中，两种方法均表现出良好的计算效率。实现PL-Cox与GPL-Cox方法的R软件包\texttt{BayesPLCox}已公开可用。