Bayesian Mixed Effects Models for Zero-inflated Compositions in Microbiome Data Analysis

TL;DR

This paper introduces a Bayesian mixed effects model with Dirichlet Process priors for analyzing zero-inflated microbiome compositions, capturing covariate effects and residual variability in a unified framework.

Contribution

It develops a novel Bayesian approach tailored for zero-inflated microbiome data, incorporating latent factors and a Dirichlet Process prior for improved association detection.

Findings

Effective in modeling zero-inflated data

Revealed associations between covariates and microbial compositions

Performs well in simulation and real data analysis

Abstract

Detecting associations between microbial compositions and sample characteristics is one of the most important tasks in microbiome studies. Most of the existing methods apply univariate models to single microbial species separately, with adjustments for multiple hypothesis testing. We propose a Bayesian analysis for a generalized mixed effects linear model tailored to this application. The marginal prior on each microbial composition is a Dirichlet Process, and dependence across compositions is induced through a linear combination of individual covariates, such as disease biomarkers or the subject's age, and latent factors. The latent factors capture residual variability and their dimensionality is learned from the data in a fully Bayesian procedure. The proposed model is tested in data analyses and simulation studies with zero-inflated compositions. In these settings, within each sample, a large proportion of counts per microbial species are equal to zero. In our Bayesian model a priori the probability of compositions with absent microbial species is strictly positive. We propose an efficient algorithm to sample from the posterior and visualizations of model parameters which reveal associations between covariates and microbial compositions. We evaluate the proposed method in simulation studies, and then analyze a microbiome dataset for infants with type 1 diabetes which contains a large proportion of zeros in the sample-specific microbial compositions.