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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.
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Multisample estimation of bacterial composition matrices in metagenomics data
Summary Metagenomics sequencing is routinely applied to quantify bacterial abundances in microbiome studies, where bacterial composition is estimated based on the sequencing read counts. Due to limited sequencing depth and DNA dropouts, many rare bacterial taxa might not be captured in the final sequencing reads, which results in many zero counts. Naive composition estimation using count normalization leads to many zero proportions, which tend to result in inaccurate estimates of bacterial abundance and diversity. This paper takes a multisample approach to estimation of bacterial abundances in order to borrow information across samples and across species. Empirical results from real datasets suggest that the composition matrix over multiple samples is approximately low rank, which motivates a regularized maximum likelihood estimation with a nuclear norm penalty. An efficient optimization algorithm using the generalized accelerated proximal gradient and Euclidean projection onto simplex space is developed. Theoretical upper bounds and the minimax lower bounds of the estimation errors, measured by the Kullback–Leibler divergence and the Frobenius norm, are established. Simulation studies demonstrate that the proposed estimator outperforms the naive estimators. The method is applied to an analysis of a human gut microbiome dataset.
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- Award ID(s):
- 1811868
- PAR ID:
- 10166376
- Date Published:
- Journal Name:
- Biometrika
- Volume:
- 107
- Issue:
- 1
- ISSN:
- 0006-3444
- Page Range / eLocation ID:
- 75 to 92
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1093/biomet/asz062
