A Bayesian Non-parametric Approach for Causal Mediation with a Post-treatment Confounder
Mike Daniels, Professor and Chair, Andrew Banks Family Endowed Chair, Department of Statistics, University of Florida
We propose a new Bayesian non-parametric (BNP) method for estimating the causal effects of mediation in the presence of a post-treatment confounder. We specify an enriched Dirichlet process mixture (EDPM) to model the joint distribution of the observed data (outcome, mediator, post-treatment confounder, treatment, and baseline confounders). For identifiability, we use the extended version of the standard sequential ignorability as introduced in Hong et al. (2022, Biometrics). The observed data model and causal identification assumptions enable us to estimate and identify the causal effects of mediation, i.e., the natural direct effects (NDE), and indirect effects (NIE). Our method enables easy computation of NDE and NIE for a subset of confounding variables and addresses missing data through data augmentation under the assumption of ignorable missingness. We conduct simulation studies to assess the performance of our proposed method. Furthermore, we apply this approach to evaluate the causal mediation effect in the Rural LITE trial, demonstrating its practical utility in real-world scenarios.
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