One of the major research questions regarding human microbiome studies is the feasibility of designing interventions that modulate the composition of the microbiome to promote health and cure disease. This requires extensive understanding of the modulating factors of the microbiome, such as dietary intake, as well as the relation between microbial composition and phenotypic outcomes, such as body mass index (BMI). Previous efforts have modeled these data separately, employing two-step approaches that can produce biased interpretations of the results. Here, we propose a Bayesian joint model that simultaneously identifies clinical covariates associated with microbial composition data and predicts a phenotypic response using information contained in the compositional data. Using spike-and-slab priors, our approach can handle high-dimensional compositional as well as clinical data. Additionally, we accommodate the compositional structure of the data via balances and overdispersion typically found in microbial samples. We apply our model to understand the relations between dietary intake, microbial samples, and BMI. In this analysis, we find numerous associations between microbial taxa and dietary factors that may lead to a microbiome that is generally more hospitable to the development of chronic diseases, such as obesity. Additionally, we demonstrate on simulated data how our method outperforms two-step approaches and also present a sensitivity analysis.
Microbiome `omics approaches can reveal intriguing relationships between the human microbiome and certain disease states. Along with the identification of specific bacteria taxa associated with diseases, recent scientific advancements provide mounting evidence that metabolism, genetics and environmental factors can all modulate these microbial effects. However, the current methods for integrating microbiome data and other covariates are severely lacking. Hence, we present an integrative Bayesian zero-inflated negative binomial regression model that can both distinguish differentially abundant …
An important task in microbiome studies is to test the existence of and give characterization to differences in the microbiome composition across groups of samples. Important challenges of this problem include the large within-group heterogeneities among samples and the existence of potential confounding variables that, when ignored, increase the chance of false discoveries and reduce the power for identifying true differences. We propose a probabilistic framework to overcome these issues by combining three ideas: (i) a phylogenetic tree-based decomposition of the cross-group comparison proble…
Detecting associations between microbial compositions and sample characteristics is one of the most important tasks in microbiome studies. Most of the existing methods apply univariate models to single microbial species separately, with adjustments for multiple hypothesis testing. We propose a Bayesian analysis for a generalized mixed effects linear model tailored to this application. The marginal prior on each microbial composition is a Dirichlet Process, and dependence across compositions is induced through a linear combination of individual covariates, such as disease biomarkers or the subj…
Dissecting Microbial Community Structure and Heterogeneity via Multivariate Covariate-Adjusted Clustering
University of Connecticut Health Center（康涅狄格大学健康中心）；Department of Biostatistics, University of Michigan（密歇根大学生物统计系）；Department of Statistics, University of Connecticut（康涅狄格大学统计学系）
BPEC is an R package for Bayesian Phylogeographic and Ecological Clustering which allows geographical, environmental and phenotypic measurements to be combined with DNA sequences in order to reveal clustered structure resulting from migration events. DNA sequences are modelled using a collapsed version of a simplified coalescent model projected onto haplotype trees, which subsequently give rise to constrained clusterings as migrations occur. Within each cluster, a multivariate Gaussian distribution of the covariates (geographical, environmental, phenotypic) is used. Inference follows tailored …
Department of Statistics, Texas A&M University（德克萨斯农工大学统计系）；Statistics Online Computational Resource, Computational Medicine & Bioinformatics, University of Michigan（密歇根大学计算医学与生物信息学统计在线计算资源）
Motivated by regression analysis for microbiome compositional data, this paper considers generalized linear regression analysis with compositional covariates, where a group of linear constraints on regression coefficients are imposed to account for the compositional nature of the data and to achieve subcompositional coherence. A penalized likelihood estimation procedure using a generalized accelerated proximal gradient method is developed to efficiently estimate the regression coefficients. A de-biased procedure is developed to obtain asymptotically unbiased and normally distributed estimates,…
The Dirichlet-multinomial (DM) distribution plays a fundamental role in modern statistical methodology development and application. Recently, the DM distribution and its variants have been used extensively to model multivariate count data generated by high-throughput sequencing technology in omics research due to its ability to accommodate the compositional structure of the data as well as overdispersion. A major limitation of the DM distribution is that it is unable to handle excess zeros typically found in practice which may bias inference. To fill this gap, we propose a novel Bayesian zero-…
Many biological high-throughput data sets, such as targeted amplicon-based and metagenomic sequencing data, are compositional in nature. A common exploratory data analysis task is to infer statistical associations between the high-dimensional microbial compositions and habitat- or host-related covariates. We propose a general robust statistical regression framework, RobRegCC (Robust Regression with Compositional Covariates), which extends the linear log-contrast model by a mean shift formulation for capturing outliers. RobRegCC includes sparsity-promoting convex and non-convex penalties for pa…
A network lasso enables us to construct a model for each sample, which is known as multi-task learning. Existing methods for multi-task learning cannot be applied to compositional data due to their intrinsic properties. In this paper, we propose a multi-task learning method for compositional data using a sparse network lasso. We focus on a symmetric form of the log-contrast model, which is a regression model with compositional covariates. The effectiveness of the proposed method is shown through simulation studies and application to gut microbiome data.
Environment-Robust Representation Learning with Empirical Bayes
Department of Statistics Columbia University（统计学系哥伦比亚大学）；Columbia University（哥伦比亚大学）；Departments of Statistics and Computer Science Columbia University（统计学与计算机科学系哥伦比亚大学）
Differential abundance tests in compositional data are essential and fundamental tasks in various biomedical applications, such as single-cell, bulk RNA-seq, and microbiome data analysis. However, because of the compositional constraint and the prevalence of zero counts in the data, differential abundance analysis in compositional data remains a complicated and unsolved statistical problem. This study introduces a new differential abundance test, the robust differential abundance (RDB) test, to address these challenges. Compared with existing methods, the RDB test is simple and computationally…
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. 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 lo…
