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In microbiome and genomic studies, the regression of compositional data hasbeen a crucial tool for identifying microbial taxa or genes that are associatedwith clinical phenotypes. To account for the variation in sequencing depth, theclassic log-contrast model is often used where read counts are normalized intocompositions. However, zero read counts and the randomness in covariates remaincritical issues. In this article, we introduce a surprisingly simple,interpretable, and efficient method for the estimation of compositional dataregression through the lens of a novel high-dimensional log-error-in-variableregression model. The proposed method provides both corrections on sequencingdata with possible overdispersion and simultaneously avoids any subjectiveimputation of zero read counts. We provide theoretical justifications withmatching upper and lower bounds for the estimation error. The merit of theprocedure is illustrated through real data analysis and simulation studies.

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