A case study of causal mediation using Bayesian nonparametrics and semiparametric corrections

Yuhua Zhang; Michael J. Daniels

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arXiv · 2606.20148

A case study of causal mediation using Bayesian nonparametrics and semiparametric corrections

Yuhua Zhang·Michael J. Daniels

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Abstract

We propose a Bayesian nonparametric approach using a truncated Enriched Dirichlet Process mixture (EDPM) model to estimate natural direct (NDE) and indirect (NIE) effects in causal mediation analyses in the presence of post-treatment confounders. We introduce an efficient cluster reallocation Metropolis-Hasting algorithm to improve mixing in the blocked Gibbs sampler. We implement a one-step posterior correction based on the efficient influence function for our setting. This post-processing step solves a critical problem in Bayesian nonparametrics: how to obtain reliable estimates and posteriors for a specific causal estimand of interest (the NDE and NIE) with excellent frequentist properties, such as correct coverage, from a model designed for complex joint distributions. We conduct simulation studies to assess our method's performance and apply it to evaluate causal mediation effects in a weight management clinical trial.

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Yuhua Zhang, Michael J. Daniels. 2026-06-18. A case study of causal mediation using Bayesian nonparametrics and semiparametric corrections. https://arxiv.org/abs/2606.20148

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