Annals of Applied Statistics

Bayesian mixed effects models for zero-inflated compositions in microbiome data analysis

Boyu Ren, Sergio Bacallado, Stefano Favaro, Tommi Vatanen, Curtis Huttenhower, and Lorenzo Trippa

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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 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.

Article information

Source
Ann. Appl. Stat., Volume 14, Number 1 (2020), 494-517.

Dates
Received: October 2018
Revised: August 2019
First available in Project Euclid: 16 April 2020

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1587002684

Digital Object Identifier
doi:10.1214/19-AOAS1295

Mathematical Reviews number (MathSciNet)
MR4085103

Zentralblatt MATH identifier
07200181

Keywords
Truncated dependent Dirichlet processes latent factor model type 1 diabetes

Citation

Ren, Boyu; Bacallado, Sergio; Favaro, Stefano; Vatanen, Tommi; Huttenhower, Curtis; Trippa, Lorenzo. Bayesian mixed effects models for zero-inflated compositions in microbiome data analysis. Ann. Appl. Stat. 14 (2020), no. 1, 494--517. doi:10.1214/19-AOAS1295. https://projecteuclid.org/euclid.aoas/1587002684


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Supplemental materials

  • Source code for “Bayesian mixed effects models for zero-inflated compositions in microbiome data analysis”. R source code for replicating results in this paper and data files for the microbiome dataset.
  • Supplement to “Bayesian mixed effects models for zero-inflated compositions in microbiome data analysis”. We provide the proof of the proposition for model identifiability in the general setting. We also include additional supporting plots and tables for the simulation studies and data application.