Multivariate Log-Contrast Regression with Sub-Compositional Predictors: Testing the Association Between Preterm Infants' Gut Microbiome and Neurobehavioral Outcomes

TL;DR

This paper introduces a novel constrained multi-view regression model with low-rank assumptions to analyze the association between gut microbiome sub-compositions and neurobehavioral outcomes in preterm infants, providing insights into the gut-brain axis.

Contribution

It develops a scaled composite nuclear norm penalization method for joint feature selection and inference in compositional microbiome data with linear constraints, advancing microbiome-outcome association analysis.

Findings

Identified key gut microbes linked to neurobehavioral outcomes.

Results align with existing biological knowledge.

Supports the role of gut microbiome in early life stress effects.

Abstract

The so-called gut-brain axis has stimulated extensive research on microbiomes. One focus is to assess the association between certain clinical outcomes and the relative abundances of gut microbes, which can be presented as sub-compositional data in conformity with the taxonomic hierarchy of bacteria. Motivated by a study for identifying the microbes in the gut microbiome of preterm infants that impact their later neurobehavioral outcomes, we formulate a constrained integrative multi-view regression, where the neurobehavioral scores form multivariate response, the sub-compositional microbiome data form multi-view feature matrices, and a set of linear constraints on their corresponding sub-coefficient matrices ensures the conformity to the simplex geometry. To enable joint selection and inference of sub-compositions/views, we assume all the sub-coefficient matrices are possibly of low-rank, i.e., the outcomes are associated with the microbiome through different sets of latent sub-compositional factors from different taxa. We propose a scaled composite nuclear norm penalization approach for model estimation and develop a hypothesis testing procedure through de-biasing to assess the significance of different views. Simulation studies confirm the effectiveness of the proposed procedure. In the preterm infant study, the identified microbes are mostly consistent with existing studies and biological understandings. Our approach supports that stressful early life experiences imprint gut microbiome through the regulation of the gut-brain axis.