Identification and estimation of causal mechanisms in cluster-randomized trials with post-treatment confounding using Bayesian nonparametrics

2025-10-18

AI Summary

In cluster randomized trials (CRTs), causal mediation analysis is challenged by interference, post-treatment confounding occurring prior to the mediator, and stratified covariate adjustment. To address these issues, we propose a Bayesian nonparametric framework. Methodologically, we replace the cross-world independence assumption with a multivariate Gaussian vine copula structure to conduct sensitivity analysis for residual post-treatment confounding; we further introduce a nested common-atom augmented Dirichlet process prior to jointly borrow strength across clusters while flexibly capturing heterogeneity. The approach enables robust covariate adjustment and possesses tractable distributional theory. Simulation studies demonstrate accurate, robust estimation under diverse scenarios. Applied to a real CRT reanalysis, the method yields interpretable, substantively meaningful mechanistic insights—validating both its statistical validity and practical utility.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Knowledge Representation and Reasoning: Nonmonotonic Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

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.

Problem

• Addresses causal mediation with interference and post-treatment confounding in trials
• Develops Bayesian framework for cluster-level interventions and individual outcomes
• Provides robust estimation and sensitivity analysis for hierarchical data

Innovation

• Bayesian nonparametric framework handles interference and confounding
• Multivariate Gaussian copula enables sensitivity analysis for confounding
• Nested CA-EDP prior models cluster heterogeneity and covariates