  We consider Bayesian high-dimensional mediation analysis to identify among a
large set of correlated potential mediators the active ones that mediate the
effect from an exposure variable to an outcome of interest. Correlations among
mediators are commonly observed in modern data analysis; examples include the
activated voxels within connected regions in brain image data, regulatory
signals driven by gene networks in genome data and correlated exposure data
from the same source. When correlations are present among active mediators,
mediation analysis that fails to account for such correlation can be
sub-optimal and may lead to a loss of power in identifying active mediators.
Building upon a recent high-dimensional mediation analysis framework, we
propose two Bayesian hierarchical models, one with a Gaussian mixture prior
that enables correlated mediator selection and the other with a Potts mixture
prior that accounts for the correlation among active mediators in mediation
analysis. We develop efficient sampling algorithms for both methods. Various
simulations demonstrate that our methods enable effective identification of
correlated active mediators, which could be missed by using existing methods
that assume prior independence among active mediators. The proposed methods are
applied to the LIFECODES birth cohort and the Multi-Ethnic Study of
Atherosclerosis (MESA) and identified new active mediators with important
biological implications.
