The Cox regression models and their Bayesian extensions are widely used for time-to-event analysis. However, standard Bayesian approaches typically require baseline hazard modeling, and their full conditional distributions lack closed-form expressions, resulting in computational inefficiency and increased vulnerability to bias from baseline hazard misspecification. To address these issues, we propose GS4Cox, a fully Gibbs sampler for Bayesian Cox regression models with four elements: (i) generalized Bayesian framework for avoiding baseline hazard specification, (ii) composite partial likelihood and (iii) Pólya-Gamma augmentation for closed-form expressions of full conditional distributions, and (iv) affine posterior calibration via the open-faced sandwich adjustment for location and scale adjustment of the posterior distribution. We prove asymptotic unbiasedness of the generalized Bayes estimator under composite partial likelihood and propose an affine posterior transformation that yields higher-order asymptotic agreement with the maximum partial likelihood estimator, while the posterior covariance matches the asymptotic target covariance. We demonstrated that GS4Cox consistently outperformed existing sampling methods through numerical and real-data experiments.

翻译：Cox回归模型及其贝叶斯扩展在时间-事件分析中应用广泛。然而，标准贝叶斯方法通常需要对基线风险进行建模，其完全条件分布缺乏闭式表达式，导致计算效率低下且易受基线风险误设偏差的影响。为解决这些问题，我们提出GS4Cox——一种针对贝叶斯Cox回归模型的完全吉布斯采样器，包含四个核心要素：(i) 避免基线风险设定的广义贝叶斯框架；(ii) 复合偏似然与(iii) Pólya-Gamma增强技术，用于获得完全条件分布的闭式表达式；(iv) 通过开放式三明治调整进行仿射后验校准，实现后验分布的位置与尺度调整。我们证明了基于复合偏似然的广义贝叶斯估计量的渐近无偏性，并提出一种仿射后验变换方法，使其与最大偏似然估计量具有高阶渐近一致性，同时后验协方差与渐近目标协方差相匹配。通过数值模拟与真实数据实验，我们证明GS4Cox在性能上持续优于现有采样方法。