  Analyzing multivariate count data generated by high-throughput sequencing
technology in microbiome research studies is challenging due to the
high-dimensional and compositional structure of the data and overdispersion. In
practice, researchers are often interested in investigating how the microbiome
may mediate the relation between an assigned treatment and an observed
phenotypic response. Existing approaches designed for compositional mediation
analysis are unable to simultaneously determine the presence of direct effects,
relative indirect effects, and overall indirect effects, while quantifying
their uncertainty. We propose a formulation of a Bayesian joint model for
compositional data that allows for the identification, estimation, and
uncertainty quantification of various causal estimands in high-dimensional
mediation analysis. We conduct simulation studies and compare our method's
mediation effects selection performance with existing methods. Finally, we
apply our method to a benchmark data set investigating the sub-therapeutic
antibiotic treatment effect on body weight in early-life mice.
