A Bayesian nonparametric approach for causal mediation with a post-treatment confounder

Area of Science:

• Causal inference
• Bayesian statistics
• Nonparametric methods

Background:

• Estimating causal mediation effects is crucial but challenging with post-treatment confounders.
• The Rural Lifestyle Intervention Treatment Effectiveness Trial (Rural LITE) presents such a challenge.

Purpose of the Study:

• To develop a Bayesian nonparametric method for causal mediation analysis with post-treatment confounders.
• To estimate natural direct effects (NDE) and natural indirect effects (NIE).

Main Methods:

• Specified an enriched Dirichlet process mixture (EDPM) for joint data distribution.
• Utilized extended sequential ignorability (SI) and Gaussian copula for identifiability.
• Employed data augmentation for handling missing data.

Main Results:

• The proposed method successfully estimates NDE and NIE.
• Simulation studies demonstrated the method's performance.
• Applied to Rural LITE trial, finding no strong evidence for mediation.

Conclusions:

• The new Bayesian method effectively addresses causal mediation with post-treatment confounders.
• The Rural LITE trial analysis suggests the potential mediator was not significant.