A Bayesian Nonparametric Approach to Mediation and Spillover Effects with Multiple Mediators in Cluster-Randomized Trials

Cluster randomized trials (CRTs) with multiple unstructured mediators present significant methodological challenges for causal inference due to within-cluster correlation, interference among units, and the complexity introduced by multiple mediators. Existing causal mediation methods often fall short in simultaneously addressing these complexities, particularly in disentangling mediator-specific effects under interference that are central to studying complex mechanisms. To address this gap, we propose new causal estimands for spillover mediation effects that differentiate the roles of each individual’s own mediator and the spillover effects resulting from interactions among individuals within the same cluster. We establish identification results for each estimand and, to flexibly model the complex data structures inherent in CRTs, we develop a new Bayesian nonparametric prior—the Nested Dependent Dirichlet Process Mixture—designed to flexibly capture the outcome and mediator surfaces at different levels. We conduct extensive simulations across various scenarios to evaluate the frequentist performance of our methods, compare them with a Bayesian parametric counterpart and illustrate our new methods in an analysis of a completed CRT. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.存在多个非结构化中介变量的整群随机试验（Cluster Randomized Trials, CRTs），由于群内相关性、个体间干扰以及多中介变量带来的复杂性，给因果推断带来了显著的方法学挑战。现有的因果中介分析方法往往难以同时应对这些复杂情形，尤其在干扰情境下拆解中介变量特异性效应这一研究复杂机制的核心问题上表现欠佳。为填补这一研究空白，本文针对溢出中介效应提出全新的因果估计量（causal estimand），用以区分个体自身中介变量的作用与同一集群内个体间交互产生的溢出效应。本文推导了各因果估计量的识别结果；为灵活建模整群随机试验中固有的复杂数据结构，本文提出一种全新的贝叶斯非参数先验——嵌套依赖狄利克雷过程混合模型（Nested Dependent Dirichlet Process Mixture），旨在灵活捕捉不同层级的结果与中介变量曲面。本文通过多场景下的大规模模拟实验评估所提方法的频率学派性能，并与贝叶斯参数化同类方法进行对比，同时通过一项已完成的整群随机试验的实例分析展示新方法的应用效果。本文的补充材料可在线获取，其中包含可用于复现本研究工作的标准化材料说明。