The Cox regression model and its Bayesian extensions are widely used in survival analysis. However, standard Bayesian approaches require modeling of the baseline hazard, and their full conditional distributions lack closed-form expressions. Therefore, the Metropolis-Hastings sampling algorithm is typically employed, whose efficiency is highly sensitive to the choice of proposal distribution. To address these issues, we propose the GS4Cox, an efficient Gibbs sampling algorithm for the Cox regression model based on four key components: (i) general Bayesian framework, (ii) composite partial likelihood, (iii) P\'olya-Gamma augmentation scheme, and (iv) finite corrections. Our experiments on both synthetic and actual datasets demonstrate that the GS4Cox algorithm outperforms existing sampling methods in terms of convergence speed and sampling efficiency.

翻译：Cox回归模型及其贝叶斯扩展在生存分析中应用广泛。然而，标准的贝叶斯方法需要对基线风险进行建模，且其完全条件分布缺乏闭式表达式。因此，通常采用Metropolis-Hastings采样算法，其效率对建议分布的选择高度敏感。为解决这些问题，我们提出了GS4Cox——一种基于四个关键组成部分的Cox回归模型高效吉布斯采样算法：(i) 通用贝叶斯框架，(ii) 复合偏似然，(iii) Pólya-Gamma数据增广方案，以及(iv) 有限样本校正。我们在合成数据集和真实数据集上的实验表明，GS4Cox算法在收敛速度和采样效率方面均优于现有的采样方法。