In observational studies, unmeasured confounders present a crucial challenge in accurately estimating desired causal effects. To calculate the hazard ratio (HR) in Cox proportional hazard models for time-to-event outcomes, two-stage residual inclusion and limited information maximum likelihood are typically employed. However, these methods are known to entail difficulty in terms of potential bias of HR estimates and parameter identification. This study introduces a novel nonparametric Bayesian method designed to estimate an unbiased HR, addressing concerns that previous research methods have had. Our proposed method consists of two phases: 1) detecting clusters based on the likelihood of the exposure and outcome variables, and 2) estimating the hazard ratio within each cluster. Although it is implicitly assumed that unmeasured confounders affect outcomes through cluster effects, our algorithm is well-suited for such data structures. The proposed Bayesian estimator has good performance compared with some competitors.

翻译：在观察性研究中，未测量混杂因素的存在对准确估计目标因果效应构成了关键挑战。针对时间-事件结局的Cox比例风险模型，通常采用两阶段残差纳入法和有限信息最大似然法来计算风险比（HR）。然而，这些方法在风险比估计的潜在偏倚和参数识别方面存在公认的困难。本研究提出了一种新颖的非参数贝叶斯方法，旨在估计无偏风险比，以解决先前研究方法存在的缺陷。我们提出的方法包含两个阶段：1）基于暴露变量和结局变量的似然性进行聚类检测；2）在每个聚类内估计风险比。尽管该方法隐含假设未测量混杂因素通过聚类效应影响结局，但我们的算法恰好适用于此类数据结构。与若干现有方法相比，所提出的贝叶斯估计量表现出良好的性能。