Finite sample inference for Cox models is an important problem in many settings, such as clinical trials. Bayesian procedures provide a means for finite sample inference and incorporation of prior information if MCMC algorithms and posteriors are well behaved. On the other hand, estimation procedures should also retain inferential properties in high dimensional settings. In addition, estimation procedures should be able to incorporate constraints and multilevel modeling such as cure models and frailty models in a straightforward manner. In order to tackle these modeling challenges, we propose a uniformly ergodic Gibbs sampler for a broad class of convex set constrained multilevel Cox models. We develop two key strategies. First, we exploit a connection between Cox models and negative binomial processes through the Poisson process to reduce Bayesian computation to iterative Gaussian sampling. Next, we appeal to sufficient dimension reduction to address the difficult computation of nonparametric baseline hazards, allowing for the collapse of the Markov transition operator within the Gibbs sampler based on sufficient statistics. We demonstrate our approach using open source data and simulations.

翻译：Cox模型的有限样本推断在临床试验等多种场景中是一个重要问题。若马尔可夫链蒙特卡洛算法与后验分布具有良好性质，贝叶斯方法可提供有限样本推断及先验信息整合的途径。另一方面，估计方法还需在高维场景中保持推断特性。此外，估计方法应能直接纳入约束条件与多水平建模（如治愈模型与脆弱模型）。为应对这些建模挑战，我们针对一类广泛适用的凸集约束多水平Cox模型，提出一种均匀遍历吉布斯采样器。我们发展了两种关键策略：首先，通过泊松过程揭示Cox模型与负二项过程之间的内在关联，将贝叶斯计算简化为迭代高斯采样；其次，借助充分降维方法处理非参数基准风险函数的复杂计算，基于充分统计量实现吉布斯采样器内马尔可夫转移算子的坍缩。我们通过开源数据集与模拟研究验证了所提方法的有效性。