Bayesian compositional generalized linear models for analyzing microbiome data.The crucial impact of the microbiome on human health and disease has gained significant scientific attention.  Researchers seek to connect microbiome features with health conditions, aiming to predict diseases and develop personalized medicine strategies.  However, the practicality of conventional models is restricted due to important aspects of microbiome data.  Specifically, the data observed is compositional, as the counts within each sample are bound by a fixed-sum constraint.  Moreover, microbiome data often exhibits high dimensionality, wherein the number of variables surpasses the available samples.  In addition, microbiome features exhibiting phenotypical similarity usually have similar influence on the response variable.  To address the challenges posed by these aspects of the data structure, we proposed Bayesian compositional generalized linear models for analyzing microbiome data (BCGLM) with a structured regularized horseshoe prior for the compositional coefficients and a soft sum-to-zero restriction on coefficients through the prior distribution.  We fitted the proposed models using Markov Chain Monte Carlo (MCMC) algorithms with R package rstan.  The performance of the proposed method was assessed by extensive simulation studies.  The simulation results show that our approach outperforms existing methods with higher accuracy of coefficient estimates and lower prediction error.  We also applied the proposed method to microbiome study to find microorganisms linked to inflammatory bowel disease (IBD).  To make this work reproducible, the code and data used in this article are available at https://github.com/Li-Zhang28/BCGLM.
R
We fitted the proposed models using Markov Chain Monte Carlo (MCMC) algorithms with R package rstan. 
rstan