Causal mediation analysis in cluster-randomized trials (CRTs) is essential for explaining how cluster-level interventions affect individual outcomes, yet it is complicated by interference, post-treatment confounding, and hierarchical covariate adjustment. We develop a Bayesian nonparametric framework that simultaneously accommodates interference and a post-treatment confounder that precedes the mediator. Identification is achieved through a multivariate Gaussian copula that replaces cross-world independence with a single dependence parameter, yielding a built-in sensitivity analysis to residual post-treatment confounding. For estimation, we introduce a nested common atoms enriched Dirichlet process (CA-EDP) prior that integrates the Common Atoms Model (CAM) to share information across clusters while capturing between- and within-cluster heterogeneity, and an Enriched Dirichlet Process (EDP) structure delivering robust covariate adjustment without impacting the outcome model. We provide formal theoretical support for our prior by deriving the model's key distributional properties, including its partially exchangeable partition structure, and by establishing convergence guarantees for the practical truncation-based posterior inference strategy. We demonstrate the performance of the proposed methods in simulations and provide further illustration through a reanalysis of a completed CRT.

翻译：聚类随机试验（CRTs）中的因果中介分析对于解释聚类层面干预如何影响个体结局至关重要，但该分析因干扰效应、事后混杂以及层次协变量调整而变得复杂。我们开发了一个贝叶斯非参数框架，该框架同时处理干扰效应和位于中介变量之前的事后混杂因素。识别通过多元高斯连接函数实现，该函数用单一依赖参数替代跨世界独立性假设，从而产生对残余事后混杂的内在敏感性分析。在估计方面，我们引入了一种嵌套公共原子富集狄利克雷过程（CA-EDP）先验，该先验结合公共原子模型（CAM）在聚类间共享信息的同时捕捉聚类间与聚类内异质性，并采用富集狄利克雷过程（EDP）结构在不影响结局模型的情况下实现稳健的协变量调整。我们通过推导模型的关键分布性质（包括其部分可交换划分结构）并建立基于截断的后验推断策略的收敛保证，为所提出的先验提供了正式的理论支持。我们通过模拟研究展示了所提出方法的性能，并通过对一项已完成CRT的再分析进行了进一步阐释。