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March 2020 Bayesian mixed effects models for zero-inflated compositions in microbiome data analysis
Boyu Ren, Sergio Bacallado, Stefano Favaro, Tommi Vatanen, Curtis Huttenhower, Lorenzo Trippa
Ann. Appl. Stat. 14(1): 494-517 (March 2020). DOI: 10.1214/19-AOAS1295


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 and 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.


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Boyu Ren. Sergio Bacallado. Stefano Favaro. Tommi Vatanen. Curtis Huttenhower. Lorenzo Trippa. "Bayesian mixed effects models for zero-inflated compositions in microbiome data analysis." Ann. Appl. Stat. 14 (1) 494 - 517, March 2020.


Received: 1 October 2018; Revised: 1 August 2019; Published: March 2020
First available in Project Euclid: 16 April 2020

zbMATH: 07200181
MathSciNet: MR4085103
Digital Object Identifier: 10.1214/19-AOAS1295

Rights: Copyright © 2020 Institute of Mathematical Statistics


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Vol.14 • No. 1 • March 2020
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