Bayesian variable selection for multivariate zero-inflated models: Application to microbiome count data

Abstract

Microorganisms play critical roles in human health and disease. They live in diverse communities in which they interact synergistically or antagonistically. Thus for estimating microbial associations with clinical covariates, such as treatment effects, joint (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. Analysis of microbial count data also requires special attention because data commonly exhibit zero inflation, i.e., more zeros than expected from a standard count distribution. 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. Though there has been much work on 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 ("excess zero") 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 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 (of 44) species associated with HIV infection.

Keywords: Bayesian variable selection; Markov chain Monte Carlo; Microbiome sequencing data; Multivariate analysis; Zero-inflated models.

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Figures

Fig. 1.

Observed and estimated correlations among counts of 44 microbial species in the Pediatrics HIV/AIDS Cohort Study (PHACS): (a) empirical correlations calculated by cor(); (b) Posterior median of ; (c) Posterior median of , calculated based on posterior samples of from the proposed multivariate zero-inflated Poisson (MZIP) model fit.

Fig. 2.

Analysis of Pediatric HIV/AIDS Cohort Study (PHACS) data: marginal posterior inclusion probabilities for the HIV status covariate in relation to excess zeros and counts of 44 microbial species as estimated via the proposed multivariate zero-inflated Poisson (MZIP) model. We adjust for participants age, a potential confounder, but do not perform variable selection on it. “NOI” stands for “not otherwise identified.”