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