  In microbiome and genomic studies, 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. The merit of the
procedure is illustrated through real data analysis and simulation studies.
