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The so-called gut-brain axis has stimulated extensive research onmicrobiomes. One focus is to assess the association between certain clinicaloutcomes and the relative abundances of gut microbes, which can be presented assub-compositional data in conformity with the taxonomic hierarchy of bacteria.Motivated by a study for identifying the microbes in the gut microbiome ofpreterm infants that impact their later neurobehavioral outcomes, we formulatea constrained integrative multi-view regression, where the neurobehavioralscores form multivariate response, the sub-compositional microbiome data formmulti-view feature matrices, and a set of linear constraints on theircorresponding sub-coefficient matrices ensures the conformity to the simplexgeometry. To enable joint selection and inference of sub-compositions/views, weassume all the sub-coefficient matrices are possibly of low-rank, i.e., theoutcomes are associated with the microbiome through different sets of latentsub-compositional factors from different taxa. We propose a scaled compositenuclear norm penalization approach for model estimation and develop ahypothesis testing procedure through de-biasing to assess the significance ofdifferent views. Simulation studies confirm the effectiveness of the proposedprocedure. In the preterm infant study, the identified microbes are mostlyconsistent with existing studies and biological understandings. Our approachsupports that stressful early life experiences imprint gut microbiome throughthe regulation of the gut-brain axis.

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