High-dimensional log-error-in-variable regression with applications to microbial compositional data analysis
针对微生物组成数据回归中零计数和协变量随机性问题，提出一种高维对数变量误差回归方法，无需主观插补零值，能校正测序数据的过度离散，并提供理论误差界。
Summary 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. 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 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.