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Abstract A critical task in microbiome data analysis is to explore the association between a scalar response of interest and a large number of microbial taxa that are summarized as compositional data at different taxonomic levels. Motivated by fine‐mapping of the microbiome, we propose a two‐step compositional knockoff filter to provide the effective finite‐sample false discovery rate (FDR) control in high‐dimensional linear log‐contrast regression analysis of microbiome compositional data. In the first step, we propose a new compositional screening procedure to remove insignificant microbial taxa while retaining the essential sum‐to‐zero constraint. In the second step, we extend the knockoff filter to identify the significant microbial taxa in the sparse regression model for compositional data. Thereby, a subset of the microbes is selected from the high‐dimensional microbial taxa as related to the response under a prespecified FDR threshold. We study the theoretical properties of the proposed two‐step procedure, including both sure screening and effective false discovery control. We demonstrate these properties in numerical simulation studies to compare our methods to some existing ones and show power gain of the new method while controlling the nominal FDR. The potential usefulness of the proposed method is also illustrated with application to an inflammatory bowel disease data set to identify microbial taxa that influence host gene expressions.
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Regression Models for Compositional Data: General Log-Contrast Formulations, Proximal Optimization, and Microbiome Data Applications
Compositional data sets are ubiquitous in science, including geology, ecology, and microbiology. In microbiome research, compositional data primarily arise from high-throughput sequence-based profiling experiments. These data comprise microbial compositions in their natural habitat and are often paired with covariate measurements that characterize physicochemical habitat properties or the physiology of the host. Inferring parsimonious statistical associations between microbial compositions and habitat- or host-specific covariate data is an important step in exploratory data analysis. A standard statistical model linking compositional covariates to continuous outcomes is the linear log-contrast model. This model describes the response as a linear combination of log-ratios of the original compositions and has been extended to the high-dimensional setting via regularization. In this contribution, we propose a general convex optimization model for linear log-contrast regression which includes many previous proposals as special cases. We introduce a proximal algorithm that solves the resulting constrained optimization problem exactly with rigorous convergence guarantees. We illustrate the versatility of our approach by investigating the performance of several model instances on soil and gut microbiome data analysis tasks.
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- Award ID(s):
- 1818946
- PAR ID:
- 10164672
- Date Published:
- Journal Name:
- Statistics in Biosciences
- ISSN:
- 1867-1764
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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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.more » « less
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/s12561-020-09283-2
