Cluster randomized trials (CRTs) are frequently used to evaluate interventions, yet conducting causal mediation analysis in these settings remains challenging, particularly when the mediator is measured at the cluster level and the number of clusters is small. Standard inference methods often rely on asymptotic assumptions that fail in finite-sample settings, leading to biased variance estimation and invalid confidence intervals. In this paper, we propose a robust inference framework for causal mediation analysis in CRTs. We utilize parametric Bayesian models for the outcome and mediator to ensure computational efficiency and interpretability. Crucially, to quantify uncertainty, we specify a novel similarity-weighted Bayesian bootstrap (SWBB) with a `distance' metric between clusters; this avoids the need for restrictive parametric assumptions and allows the model to borrow more information from `closer' clusters. By combining observed data models with causal assumptions, our approach accurately estimates natural direct and indirect effects even with limited clusters. Simulation studies demonstrate that our method achieves nominal coverage probability across diverse scenarios. We illustrate the practical utility of our approach by assessing mediation in a CRT in Kenya.

翻译：簇随机试验（CRTs）常被用于评估干预措施，然而在此类设计中进行因果中介分析仍具挑战性，尤其是当中介变量在簇层面测量且簇数量较小时。标准推断方法通常依赖渐近假设，但在有限样本情形下这些假设可能失效，从而导致方差估计有偏和置信区间无效。本文提出一种稳健的CRTs因果中介分析推断框架。我们采用结果变量和中介变量的参数化贝叶斯模型以保证计算效率和可解释性。关键在于，为量化不确定性，我们提出了一种新颖的相似性加权贝叶斯自助法（SWBB），该方法利用簇间"距离"度量，避免了对限制性参数假设的需求，并允许模型从"更近"的簇中借用更多信息。通过将观测数据模型与因果假设相结合，我们的方法即使在有限簇条件下也能准确估计自然直接效应和间接效应。模拟研究表明，该方法在不同场景下均能达到名义覆盖概率。我们通过评估肯尼亚一项CRT中的中介效应，展示了该方法的实际应用价值。