Semiparametric Bayesian inference for causal mediation in cluster randomized trials

2026-06-11

AI Summary

This study addresses the challenge of causal mediation analysis in cluster-randomized trials when cluster-level mediators are observed and the number of clusters is small, a setting in which conventional methods yield biased variance estimates and invalid confidence intervals due to reliance on large-sample asymptotics. To overcome this limitation, the authors propose a robust semi-parametric Bayesian inference framework that integrates a parametric Bayesian model with a novel Similarity-Weighted Bayesian Bootstrap (SWBB). The SWBB leverages inter-cluster distances to borrow information across clusters, thereby avoiding strong parametric assumptions. The method accurately estimates natural direct and indirect effects even with limited clusters. Extensive simulations demonstrate that the proposed approach achieves nominal coverage across diverse data-generating scenarios and has been successfully applied to a real-world cluster-randomized trial in Kenya.

Abstract

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.

Problem

• causal mediation
• cluster randomized trials
• finite-sample inference
• mediation analysis
• small number of clusters

Innovation

• causal mediation analysis
• cluster randomized trials
• Bayesian bootstrap
• semiparametric inference
• small cluster settings