  Microorganisms play critical roles in human health and disease. It is well
known that microbes live in diverse communities in which they interact
synergistically or antagonistically. Thus for estimating microbial associations
with clinical covariates, multivariate statistical models are preferred.
Multivariate models allow one to estimate and exploit complex interdependencies
among multiple taxa, yielding more powerful tests of exposure or treatment
effects than application of taxon-specific univariate analyses. In addition,
the analysis of microbial count data requires special attention because data
commonly exhibit zero inflation. To meet these needs, we developed a Bayesian
variable selection model for multivariate count data with excess zeros that
incorporates information on the covariance structure of the outcomes (counts
for multiple taxa), while estimating associations with the mean levels of these
outcomes. Although there has been a great deal of effort in zero-inflated
models for longitudinal data, little attention has been given to
high-dimensional multivariate zero-inflated data modeled via a general
correlation structure. Through simulation, we compared performance of the
proposed method to that of existing univariate approaches, for both the binary
and count parts of the model. When outcomes were correlated the proposed
variable selection method maintained type I error while boosting the ability to
identify true associations in the binary component of the model. For the count
part of the model, in some scenarios the the univariate method had higher power
than the multivariate approach. This higher power was at a cost of a highly
inflated false discovery rate not observed with the proposed multivariate
method. We applied the approach to oral microbiome data from the Pediatric
HIV/AIDS Cohort Oral Health Study and identified five species (of 44)
associated with HIV infection.
