Latent Network Estimation and Variable Selection for Compositional Data Via Variational EM

A modeling framework for detecting and leveraging node-level information in Bayesian network inference

Bayesian graphical models are powerful tools to infer complex relationships in high dimension, yet are often fraught with computational and statistical challenges. If exploited in a principled way, the increasing information collected alongside the data of primary interest constitutes an opportunity to mitigate these difficulties by guiding the detection of dependence structures. For instance, gene network inference may be informed by the use of publicly available summary statistics on the regulation of genes by genetic variants. Here we present a novel Gaussian graphical modeling framework to identify and leverage information on the centrality of nodes in conditional independence graphs. Specifically, we consider a fully joint hierarchical model to simultaneously infer (i) sparse precision matrices and (ii) the relevance of node-level information for uncovering the sought-after network structure. We encode such information as candidate auxiliary variables using a spike-and-slab submodel on the propensity of nodes to be hubs, which allows hypothesis-free selection and interpretation of a sparse subset of relevant variables. As efficient exploration of large posterior spaces is needed for real-world applications, we develop a variational expectation conditional maximization algorithm that scales inference to hundreds of samples, nodes and auxiliary variables. We illustrate and exploit the advantages of our approach in simulations and in a gene network study which identifies hub genes involved in biological pathways relevant to immune-mediated diseases.

TARO: tree-aggregated factor regression for microbiome data integration

MOTIVATION

Although the human microbiome plays a key role in health and disease, the biological mechanisms underlying the interaction between the microbiome and its host are incompletely understood. Integration with other molecular profiling data offers an opportunity to characterize the role of the microbiome and elucidate therapeutic targets. However, this remains challenging to the high dimensionality, compositionality, and rare features found in microbiome profiling data. These challenges necessitate the use of methods that can achieve structured sparsity in learning cross-platform association patterns.

RESULTS

We propose Tree-Aggregated factor RegressiOn (TARO) for the integration of microbiome and metabolomic data. We leverage information on the taxonomic tree structure to flexibly aggregate rare features. We demonstrate through simulation studies that TARO accurately recovers a low-rank coefficient matrix and identifies relevant features. We applied TARO to microbiome and metabolomic profiles gathered from subjects being screened for colorectal cancer to understand how gut microrganisms shape intestinal metabolite abundances.

AVAILABILITY AND IMPLEMENTATION

The R package TARO implementing the proposed methods is available online at https://github.com/amishra-stats/taro-package.

Analysis of Microbiome Data

The microbiome represents a hidden world of tiny organisms populating not only our surroundings but also our own bodies. By enabling comprehensive profiling of these invisible creatures, modern genomic sequencing tools have given us an unprecedented ability to characterize these populations and uncover their outsize impact on our environment and health. Statistical analysis of microbiome data is critical to infer patterns from the observed abundances. The application and development of analytical methods in this area require careful consideration of the unique aspects of microbiome profiles. We begin this review with a brief overview of microbiome data collection and processing and describe the resulting data structure. We then provide an overview of statistical methods for key tasks in microbiome data analysis, including data visualization, comparison of microbial abundance across groups, regression modeling, and network inference. We conclude with a discussion and highlight interesting future directions.

A Bayesian zero-inflated Dirichlet-multinomial regression model for multivariate compositional count data

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-inflated DM model for multivariate compositional count data with excess zeros. We then extend our approach to regression settings and embed sparsity-inducing priors to perform variable selection for high-dimensional covariate spaces. Throughout, modeling decisions are made to boost scalability without sacrificing interpretability or imposing limiting assumptions. Extensive simulations and an application to a human gut microbiome dataset are presented to compare the performance of the proposed method to existing approaches. We provide an accompanying R package with a user-friendly vignette to apply our method to other datasets.

Cultural transmission of move choice in chess

The study of cultural evolution benefits from detailed analysis of cultural transmission in specific human domains. Chess provides a platform for understanding the transmission of knowledge due to its active community of players, precise behaviours and long-term records of high-quality data. In this paper, we perform an analysis of chess in the context of cultural evolution, describing multiple cultural factors that affect move choice. We then build a population-level statistical model of move choice in chess, based on the Dirichlet-multinomial likelihood, to analyse cultural transmission over decades of recorded games played by leading players. For moves made in specific positions, we evaluate the relative effects of frequency-dependent bias, success bias and prestige bias on the dynamics of move frequencies. We observe that negative frequency-dependent bias plays a role in the dynamics of certain moves, and that other moves are compatible with transmission under prestige bias or success bias. These apparent biases may reflect recent changes, namely the introduction of computer chess engines and online tournament broadcasts. Our analysis of chess provides insights into broader questions concerning how social learning biases affect cultural evolution.

TARO: tree-aggregated factor regression for microbiome data integration

Motivation

Although the human microbiome plays a key role in health and disease, the biological mechanisms underlying the interaction between the microbiome and its host are incompletely understood. Integration with other molecular profiling data offers an opportunity to characterize the role of the microbiome and elucidate therapeutic targets. However, this remains challenging to the high dimensionality, compositionality, and rare features found in microbiome profiling data. These challenges necessitate the use of methods that can achieve structured sparsity in learning cross-platform association patterns.

Results

We propose Tree-Aggregated factor RegressiOn (TARO) for the integration of microbiome and metabolomic data. We leverage information on the phylogenetic tree structure to flexibly aggregate rare features. We demonstrate through simulation studies that TARO accurately recovers a low-rank coefficient matrix and identifies relevant features. We applied TARO to microbiome and metabolomic profiles gathered from subjects being screened for colorectal cancer to understand how gut microrganisms shape intestinal metabolite abundances.

Availability and implementation

The R package TARO implementing the proposed methods is available online at https://github.com/amishra-stats/taro-package .

Super-taxon in human microbiome are identified to be associated with colorectal cancer

Background

Microbial communities in the human body, also known as human microbiota, impact human health, such as colorectal cancer (CRC). However, the different roles that microbial communities play in healthy and disease hosts remain largely unknown. The microbial communities are typically recorded through the taxa counts of operational taxonomic units (OTUs). The sparsity and high correlations among OTUs pose major challenges for understanding the microbiota-disease relation. Furthermore, the taxa data are structured in the sense that OTUs are related evolutionarily by a hierarchical structure.

Results

In this study, we borrow the idea of super-variant from statistical genetics, and propose a new concept called super-taxon to exploit hierarchical structure of taxa for microbiome studies, which is essentially a combination of taxonomic units. Specifically, we model a genus which consists of a set of OTUs at low hierarchy and is designed to reflect both marginal and joint effects of OTUs associated with the risk of CRC to address these issues. We first demonstrate the power of super-taxon in detecting highly correlated OTUs. Then, we identify CRC-associated OTUs in two publicly available datasets via a discovery-validation procedure. Specifically, four species of two genera are found to be associated with CRC: Parvimonas micra, Parvimonas sp., Peptostreptococcus stomatis, and Peptostreptococcus anaerobius. More importantly, for the first time, we report the joint effect of Parvimonas micra and Parvimonas sp. (p = 0.0084) as well as that of Peptostrepto-coccus stomatis and Peptostreptococcus anaerobius (p = 8.21e-06) on CRC. The proposed approach provides a novel and useful tool for identifying disease-related microbes by taking the hierarchical structure of taxa into account and further sheds new lights on their potential joint effects as a community in disease development.

Conclusions

Our work shows that proposed approaches are effective to study the microbiota-disease relation taking into account for the sparsity, hierarchical and correlated structure among microbes.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12859-022-04786-9.

mbDenoise: microbiome data denoising using zero-inflated probabilistic principal components analysis

The analysis of microbiome data has several technical challenges. In particular, count matrices contain a large proportion of zeros, some of which are biological, whereas others are technical. Furthermore, the measurements suffer from unequal sequencing depth, overdispersion, and data redundancy. These nuisance factors introduce substantial noise. We propose an accurate and robust method, mbDenoise, for denoising microbiome data. Assuming a zero-inflated probabilistic PCA (ZIPPCA) model, mbDenoise uses variational approximation to learn the latent structure and recovers the true abundance levels using the posterior, borrowing information across samples and taxa. mbDenoise outperforms state-of-the-art methods to extract the signal for downstream analyses.