Bayesian compositional generalized linear mixed models for disease prediction using microbiome data

The primary goal of predictive modeling for compositional microbiome data is to better understand and predict disease susceptibility based on the relative abundance of microbial species. Current approaches in this area often assume a high-dimensional sparse setting, where only a small subset of microbiome features is considered relevant to the outcome. However, in real-world data, both large and small effects frequently coexist, and acknowledging the contribution of smaller effects can significantly enhance predictive performance. To address this challenge, we developed Bayesian Compositional Generalized Linear Mixed Models for Analyzing Microbiome Data (BCGLMM). BCGLMM is capable of identifying both moderate taxa effects and the cumulative impact of numerous minor taxa, which are often overlooked in conventional models. With a sparsity-inducing prior, the structured regularized horseshoe prior, BCGLMM effectively collaborates phylogenetically related moderate effects. The random effect term efficiently captures sample-related minor effects by incorporating sample similarities within its variance-covariance matrix. We fitted the proposed models using Markov Chain Monte Carlo (MCMC) algorithms with rstan. The performance of the proposed method was evaluated through extensive simulation studies, demonstrating its superiority with higher prediction accuracy compared to existing methods. We then applied the proposed method on American Gut Data to predict inflammatory bowel disease (IBD). To ensure reproducibility, the code and data used in this paper are available at https://github.com/Li-Zhang28/BCGLMM .