Compositional variable selection in quantile regression for microbiome data with false discovery rate control

Advancement in high‐throughput sequencing technologies has stimulated intensive research interests to identify specific microbial taxa that are associated with disease conditions. Such knowledge is invaluable both from the perspective of understanding biology and from the biomedical perspective of therapeutic development, as the microbiome is inherently modifiable. Despite availability of massive data, analysis of microbiome compositional data remains difficult. The nature that relative abundances of all components of a microbial community sum to one poses challenges for statistical analysis, especially in high‐dimensional settings, where a common research theme is to select a small fraction of signals from amid many noisy features. Motivated by studies examining the role of microbiome in host transcriptomics, we propose a novel approach to identify microbial taxa that are associated with host gene expressions. Besides accommodating compositional nature of microbiome data, our method both achieves FDR‐controlled variable selection, and captures heterogeneity due to either heteroscedastic variance or non‐location‐scale covariate effects displayed in the motivating dataset. We demonstrate the superior performance of our method using extensive numerical simulation studies and then apply it to real‐world microbiome data analysis to gain novel biological insights that are missed by traditional mean‐based linear regression analysis.