Bayesian Variable Shrinkage and Selection in Compositional Data Regression: Application to Oral Microbiome.

Area of Science:

• Microbiology
• Statistical Modeling
• Bioinformatics

Background:

• Microbiome studies yield complex compositional data (e.g., taxa counts) that are non-negative, bounded, and sum to one.
• The Dirichlet-Multinomial (D-M) regression is a common framework for modeling such data with covariates.
• Efficient variable selection is crucial for identifying key associations in high-dimensional microbiome data.

Purpose of the Study:

• To present a Bayesian approach for Dirichlet-Multinomial compositional data analysis.
• To compare the performance of continuous shrinkage priors (horseshoe, horseshoe+) against Bayesian lasso for variable selection.
• To identify significant associations between covariates and taxonomic abundance in microbiome data.

Main Methods:

• Bayesian estimation and inference under the D-M regression framework.
• Comparative evaluation of horseshoe, horseshoe+, and Bayesian lasso priors.
• Utilized Hamiltonian Monte Carlo for posterior sampling and generated credible intervals.
• Applied methods to synthetic data for simulation studies and real oral microbiome data (NYC-Hanes study).

Main Results:

• Continuous shrinkage priors demonstrated excellent recovery and estimation accuracy in sparse parameter settings.
• The horseshoe and horseshoe+ priors showed strong performance in identifying significant covariate-taxa associations.
• The approach was successfully illustrated on oral microbiome data.

Conclusions:

• Bayesian continuous shrinkage priors offer an effective strategy for variable selection in D-M compositional microbiome data.
• The proposed methods enhance the ability to identify key drivers of microbial community composition.
• An RStan implementation is available for broader application.