Variance Component Selection With Applications to Microbiome Taxonomic Data

Tree-aggregated predictive modeling of microbiome data

Modern high-throughput sequencing technologies provide low-cost microbiome survey data across all habitats of life at unprecedented scale. At the most granular level, the primary data consist of sparse counts of amplicon sequence variants or operational taxonomic units that are associated with taxonomic and phylogenetic group information. In this contribution, we leverage the hierarchical structure of amplicon data and propose a data-driven and scalable tree-guided aggregation framework to associate microbial subcompositions with response variables of interest. The excess number of zero or low count measurements at the read level forces traditional microbiome data analysis workflows to remove rare sequencing variants or group them by a fixed taxonomic rank, such as genus or phylum, or by phylogenetic similarity. By contrast, our framework, which we call trac (tree-aggregation of compositional data), learns data-adaptive taxon aggregation levels for predictive modeling, greatly reducing the need for user-defined aggregation in preprocessing while simultaneously integrating seamlessly into the compositional data analysis framework. We illustrate the versatility of our framework in the context of large-scale regression problems in human gut, soil, and marine microbial ecosystems. We posit that the inferred aggregation levels provide highly interpretable taxon groupings that can help microbiome researchers gain insights into the structure and functioning of the underlying ecosystem of interest.

Penalized variance components for association of multiple genes with traits

Variance component models have gained popularity for genetic analyses, driven by their flexibility to simultaneously analyze multiple genetic variants in a gene by kernel statistics, and their ability to account for population stratification via genomic relationship matrices. For exploratory analyses with modest sample sizes and a potentially large number of variance components, it can be challenging to use standard maximum-likelihood or restricted maximum-likelihood methods to estimate variance components, because these iterative methods often fail to converge when likelihood surfaces are fairly flat, and standard-likelihood ratio statistical tests are not adequate. To overcome these limitations, we developed a penalized-likelihood model, whereby the penalty function follows the popular elastic-net approach, applying both L1 and L2 penalties to the variance components. By simulations, we demonstrate the potential gain in power by using both L1 and L2 penalties, and results from our simulations suggest that assigning 80% of the penalty parameter to the L1 penalty and 20% to the L2 penalty provides a reasonable balance between false-positive and false-negative results. Larger sample size improves the properties of our methods, at the cost of longer computation time. Application of our methods to a study of the influence of DNA methylation on levels of cortisol in reaction to stress testing shows how our method can be used to prioritize findings for further functional studies.

Correlation and association analyses in microbiome study integrating multiomics in health and disease

Correlation and association analyses are one of the most widely used statistical methods in research fields, including microbiome and integrative multiomics studies. Correlation and association have two implications: dependence and co-occurrence. Microbiome data are structured as phylogenetic tree and have several unique characteristics, including high dimensionality, compositionality, sparsity with excess zeros, and heterogeneity. These unique characteristics cause several statistical issues when analyzing microbiome data and integrating multiomics data, such as large p and small n, dependency, overdispersion, and zero-inflation. In microbiome research, on the one hand, classic correlation and association methods are still applied in real studies and used for the development of new methods; on the other hand, new methods have been developed to target statistical issues arising from unique characteristics of microbiome data. Here, we first provide a comprehensive view of classic and newly developed univariate correlation and association-based methods. We discuss the appropriateness and limitations of using classic methods and demonstrate how the newly developed methods mitigate the issues of microbiome data. Second, we emphasize that concepts of correlation and association analyses have been shifted by introducing network analysis, microbe-metabolite interactions, functional analysis, etc. Third, we introduce multivariate correlation and association-based methods, which are organized by the categories of exploratory, interpretive, and discriminatory analyses and classification methods. Fourth, we focus on the hypothesis testing of univariate and multivariate regression-based association methods, including alpha and beta diversities-based, count-based, and relative abundance (or compositional)-based association analyses. We demonstrate the characteristics and limitations of each approaches. Fifth, we introduce two specific microbiome-based methods: phylogenetic tree-based association analysis and testing for survival outcomes. Sixth, we provide an overall view of longitudinal methods in analysis of microbiome and omics data, which cover standard, static, regression-based time series methods, principal trend analysis, and newly developed univariate overdispersed and zero-inflated as well as multivariate distance/kernel-based longitudinal models. Finally, we comment on current association analysis and future direction of association analysis in microbiome and multiomics studies.

Switching control strategy for the HIV dynamic system with some unknown parameters

In human immunodeficiency virus (HIV) infection, many factors may influence the counts of healthy cells, immune cells and viruses. Drug treatment design for the HIV dynamic system is a valuable subject to be studied. This study considers an HIV dynamic system model with some unknown parameters and unmeasurable CD8 + T cell count and proposes a switching control strategy to force all states of the system to achieve a healthy status. It is a switching form with two different drug therapies and is designed based on the Lyapunov function theory such that the states of the HIV system approach the health equilibrium asymptotically without the influence of unknown parameters and unmeasurable cell counts. The values of all states and drug concentrations are assured to be positive in the control process so that the control strategy can satisfy the actual treatment requirements. Finally, a numerical example is illustrated to show the effectiveness of the proposed control strategy.

pldist: ecological dissimilarities for paired and longitudinal microbiome association analysis

MOTIVATION

The human microbiome is notoriously variable across individuals, with a wide range of 'healthy' microbiomes. Paired and longitudinal studies of the microbiome have become increasingly popular as a way to reduce unmeasured confounding and to increase statistical power by reducing large inter-subject variability. Statistical methods for analyzing such datasets are scarce.

RESULTS

We introduce a paired UniFrac dissimilarity that summarizes within-individual (or within-pair) shifts in microbiome composition and then compares these compositional shifts across individuals (or pairs). This dissimilarity depends on a novel transformation of relative abundances, which we then extend to more than two time points and incorporate into several phylogenetic and non-phylogenetic dissimilarities. The data transformation and resulting dissimilarities may be used in a wide variety of downstream analyses, including ordination analysis and distance-based hypothesis testing. Simulations demonstrate that tests based on these dissimilarities retain appropriate type 1 error and high power. We apply the method in two real datasets.

AVAILABILITY AND IMPLEMENTATION

The R package pldist is available on GitHub at https://github.com/aplantin/pldist.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Why targeting the microbiome is not so successful: can randomness overcome the adaptation that occurs following gut manipulation?

The microbiome is explored as a potential target for therapy of bowel and systemic diseases. Fecal microbiota transplantation (FMT) has demonstrated efficacy in Clostridium difficile infection. However, clinical results regarding other diseases are modest, despite the abundant research on the microbiome over the last decade. Both high rate variability of the microbiome and adaptation to gut manipulations may underlie the lack of ultimate effects of FMT, probiotics, prebiotics, synbiotics, and antibiotics, which are aimed at restoring a healthier microbiome. The present review discusses the inherent variability of the microbiome and multiple factors that affect its diversity, as possible causes of the adaptation of the gut microbiome to chronic manipulation. The potential use of randomness is proposed, as a means of overcoming the adaptation and of restoring some of the inherent variability, with the goal of improving the long-term efficacy of these therapies.