  Causal mediation analysis aims to characterize an exposure's effect on an
outcome and quantify the indirect effect that acts through a given mediator or
a group of mediators of interest. With the increasing availability of
measurements on a large number of potential mediators, like the epigenome or
the microbiome, new statistical methods are needed to simultaneously
accommodate high-dimensional mediators while directly target penalization of
the natural indirect effect (NIE) for active mediator identification. Here, we
develop two novel prior models for identification of active mediators in
high-dimensional mediation analysis through penalizing NIEs in a Bayesian
paradigm. Both methods specify a joint prior distribution on the
exposure-mediator effect and mediator-outcome effect with either (a) a
four-component Gaussian mixture prior or (b) a product threshold Gaussian
prior. By jointly modeling the two parameters that contribute to the NIE, the
proposed methods enable penalization on their product in a targeted way.
Resultant inference can take into account the four-component composite
structure underlying the NIE. We show through simulations that the proposed
methods improve both selection and estimation accuracy compared to other
competing methods. We applied our methods for an in-depth analysis of two
ongoing epidemiologic studies: the Multi-Ethnic Study of Atherosclerosis (MESA)
and the LIFECODES birth cohort. The identified active mediators in both studies
reveal important biological pathways for understanding disease mechanisms.
