Recurrent events often serve as key endpoints in clinical studies but may be prematurely truncated by terminal events such as death, creating selection bias and complicating causal inference. To address this challenge, we develop a Bayesian nonparametric framework to address potential selection bias due to truncation by death within the continuous-time principal stratification framework. We introduce causal estimands for recurrent events in the presence of a terminal event and derive a partial identification result for the estimand under a dual-frailty framework, enabling transparent sensitivity analysis for non-identifiable parameters. We then propose a flexible Bayesian nonparametric prior, the enriched dependent Dirichlet process, specifically designed for joint modeling of recurrent and terminal events, addressing a limitation where standard Dirichlet process priors create random partitions dominated by recurrent events, yielding poor predictive performance for terminal events. Simulations are carried out to show that our method has superior performance compared to existing methods. We apply the proposed new Bayesian nonparametric methods to infer the causal effect of a structured exercise program on rehospitalizations, which are subject to truncation by death.

翻译：在临床研究中，复发事件常作为关键终点，但可能被死亡等终末事件提前截断，从而产生选择偏倚并使因果推断复杂化。为应对这一挑战，我们在连续时间主分层框架内开发了一种贝叶斯非参数框架，以处理因死亡截断导致的潜在选择偏倚。我们针对存在终末事件情形下的复发事件提出了因果估计量，并在双重脆弱性框架下推导了该估计量的部分可识别性结果，从而能够对不可识别参数进行透明的敏感性分析。随后，我们提出了一种灵活的贝叶斯非参数先验——增强型相依狄利克雷过程，该先验专门为复发事件与终末事件的联合建模而设计，解决了标准狄利克雷过程先验因随机划分受复发事件主导而导致终末事件预测性能不佳的局限性。仿真研究表明，与现有方法相比，我们的方法具有更优的性能。我们将所提出的新型贝叶斯非参数方法应用于推断结构化运动计划对再住院（受死亡截断影响）的因果效应。