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 for 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.

翻译：在包含多重非结构化中介变量的聚类随机试验中，由于存在聚类内相关性、单元间干扰以及多重中介变量引入的复杂性，因果推断面临显著的方法学挑战。现有的因果中介分析方法往往难以同时处理这些复杂性问题，特别是在存在干扰的情况下解析中介特异性效应——这对于研究复杂机制至关重要。为填补这一空白，我们提出了针对溢出中介效应的新因果估计量，该估计量能够区分个体自身中介变量的作用与同一聚类内个体间相互作用产生的溢出效应。我们为每个估计量建立了可识别性结果，并为灵活建模聚类随机试验固有的复杂数据结构，开发了一种新的贝叶斯非参数先验——嵌套依赖狄利克雷过程混合模型——该模型旨在灵活捕捉不同层次的结果变量与中介变量曲面。我们在多种情境下进行了广泛的模拟研究，以评估所提方法的频率学派性能，并将其与贝叶斯参数化模型进行对比，最后通过一项已完成的聚类随机试验分析展示了新方法的应用。