High-dimensional Log-Error-in-Variable Regression with Applications to Microbial Compositional Data Analysis

In microbiome and genomic study, the regression of compositional data has been a crucial tool for identifying microbial taxa or genes that are associated with clinical phenotypes. To account for the variation in sequencing depth, the classic log-contrast model is often used where read counts are normalized into compositions. However, zero read counts and the randomness in covariates remain critical issues. In this article, we introduce a surprisingly simple, interpretable, and efficient method for the estimation of compositional data regression through the lens of a novel high-dimensional log-error-in-variable regression model. The proposed method provides both corrections on sequencing data with possible overdispersion and simultaneously avoids any subjective imputation of zero read counts. We provide theoretical justifications with matching upper and lower bounds for the estimation error. We also consider a general log-error-in-variable regression model with corresponding estimation method to accommodate broader situations. The merit of the procedure is illustrated through real data analysis and simulation studies.