  Mediation analysis with contemporaneously observed multiple mediators is an
important area of causal inference. Recent approaches for multiple mediators
are often based on parametric models and thus may suffer from model
misspecification. Also, much of the existing literature either only allow
estimation of the joint mediation effect, or, estimate the joint mediation
effect as the sum of individual mediator effects, which often is not a
reasonable assumption. In this paper, we propose a methodology which overcomes
the two aforementioned drawbacks. Our method is based on a novel Bayesian
nonparametric (BNP) approach, wherein the joint distribution of the observed
data (outcome, mediators, treatment, and confounders) is modeled flexibly using
an enriched Dirichlet process mixture with three levels: the first level
characterizing the conditional distribution of the outcome given the mediators,
treatment and the confounders, the second level corresponding to the
conditional distribution of each of the mediators given the treatment and the
confounders, and the third level corresponding to the distribution of the
treatment and the confounders. We use standardization (g-computation) to
compute causal mediation effects under three uncheckable assumptions that allow
identification of the individual and joint mediation effects. The efficacy of
our proposed method is demonstrated with simulations. We apply our proposed
method to analyze data from a study of Ventilator-associated Pneumonia (VAP)
co-infected patients, where the effect of the abundance of Pseudomonas on VAP
infection is suspected to be mediated through antibiotics.
