Modern Statistical and Computational Advances in Microbiome-multiomics Integration

Microbe-derived metabolites are key mediators in the interactions between a host and their microbiome. Understanding the causal links between the gut microbiome, its metabolites, and a clinical outcome provides new potential for understanding, preventing and treating microbiome-associated diseases. While many studies have focused on the mediating role of the microbiome, few have specifically explored the role of bacterial metabolites as mediators, with the microbiome itself acting as the exposure. This shift in perspective introduces unique methodological challenges, particularly due to the high dimensionality and compositional structure of microbiome data. To address these challenges, we propose a latent variable mediation framework that captures variation in microbial composition through a microbial balance, defined as the log-ratio between two unknown subsets of taxa. This balance serves as a latent scalar exposure and simplifies the estimation of the overall indirect effect at the community level, while simultaneously identifying specific taxa that contribute to the overall direct and indirect effects. This article covers the model's estimation and inference, and illustrates its real-world application using data from a randomized controlled crossover feeding trial. 

Mediation analysis has emerged as a versatile tool for answering mechanistic questions in microbiome research because it provides a statistical framework for attributing treatment effects to alternative causal pathways. Using a series of linked regressions, this analysis quantifies how complementary data relate to one another and respond to treatments. Despite these advances, existing software's rigid assumptions often result in users viewing mediation analysis as a black box. We designed the multimedia R package to make advanced mediation analysis techniques accessible, ensuring that statistical components are interpretable and adaptable. The package provides a uniform interface to direct and indirect effect estimation, synthetic null hypothesis testing, bootstrap confidence interval construction, and sensitivity analysis, enabling experimentation with various mediator and outcome models while maintaining a simple overall workflow. The software includes modules for regularized linear, compositional, random forest, hierarchical, and hurdle modeling, making it well-suited to microbiome data. Our case study revisits a study of the microbiome and metabolome of Inflammatory Bowel Disease patients, uncovering potential mechanistic interactions between the microbiome and disease-associated metabolites, not found in the original study. In addition to summarizing the package, we will explain the software design patterns that we drew inspiration from and how they could inform reproducible multi-omics integration more generally. A gallery of examples and reference page can be found at https://go.wisc.edu/830110. 

There is growing interest in understanding how interactions among features in complex systems evolve across experimental conditions. In many scientific studies, experimental groups are naturally ordered, such as disease stages, exposure levels, or time points. In such settings, it is scientifically meaningful to assess whether associations between pairs of variables evolve systematically across the ordering. To address this problem, we develop a class of ordered correlation procedures for second-order inference across multiple ordered environments. The proposed framework enables formal testing of whether correlations or partial correlations between pairs of features change systematically across ordered groups, as well as identification of features that drive coordinated changes in correlation networks. The methods accommodate high-dimensional settings, missing data, and both marginal and conditional measures of dependence. We evaluate finite-sample performance through simulations and illustrate practical utility using multi-omics data from the Multi-Center AIDS Cohort Study (MACS), providing a principled framework for analyzing evolving association networks in ordered multi-environment studies. 

We propose a counterfactual Bayesian causal mediation model designed for multiple correlated mediators and outcomes. Built upon a rigorous counterfactual framework that addresses assumption violations caused by exposure-induced confounding, our approach first models the mediators and outcomes jointly using a multivariate Gaussian distribution. Crucially, we parameterize both the joint mean and the covariance matrix as functions of the exposure and confounders. By simultaneously modeling the full network of mediating mechanisms in this manner, the method successfully controls for inter-mediator confounding while accommodating exposure-by-mediator and exposure-by-confounder interaction effects. To alleviate the severe parameterization challenges and computational burdens inherent in this complex multivariate structure, we then adopt a Bayesian paradigm. This framework integrates a latent factorization method with a covariance regression technique to perform low-rank estimation, efficiently extracting signals from noisy, high-dimensional data. Combined with Markov chain Monte Carlo (MCMC) sampling, these two approaches yield a highly efficient pipeline capable of simultaneously handling tens to hundreds of correlated mediating features. This significantly expands the utility of causal mediation analysis in biomedical and clinical studies where sample sizes are typically small-to-moderate (e.g., fewer than a few hundred observations). Ultimately, our method decomposes the total effect into the direct effect, the joint indirect effect, and individual marginal indirect effects. Its capability to quantify the collective impact of all mediation candidates while evaluating their individual contributions offers a statistically robust and biologically realistic framework for identifying molecular targets and revealing underlying mechanisms. We rigorously validated the accuracy and robustness of our statistical inferences through extensive simulation studies, and to demonstrate its practical utility, we applied the method to real-world datasets, utilizing high-dimensional omics data as mediators to successfully uncover underlying biological mechanisms.