Multivariate Regression With Dependence Structures: Evaluating Associations Between Plasma Metabolomics and Alcohol Intake in Older Adults.

High-dimensional omics data often exhibit complex yet organized dependencies, characterized by intelligent network properties like high modularity, small-worldness characteristics, and scale-free topology. However, integrating these structured interdependencies between omics variables into multivariate regression models presents challenges. The primary difficulty lies in accurately specifying and estimating dependency parameters that capture these network patterns within regression frameworks. Common covariance estimation methods may not preserve these network properties and can also be computationally intensive. To address these challenges, we propose a novel multivariate regression model that incorporates an interconnected community structure, reflecting the organized relationships among omics outcome variables. Our approach includes efficient estimation algorithms, featuring closed-form regression estimators and likelihood-based dependence estimators. We also establish the asymptotic properties of estimators to ensure theoretical robustness and hypothesis testing. Extensive simulations demonstrate the enhanced accuracy and sensitivity of our method, as evidenced through benchmarking against existing regression models. We applied our approach to a dataset to assess the associations between 249 metabolomic biomarkers, measured using nuclear magnetic resonance spectroscopy, and alcohol intake among 3984 participants. Results indicate that light alcohol consumption is positively associated with high-density lipoprotein cholesterol (HDL, i.e., the good cholesterol), high-density lipoprotein particles, and Apolipoproteins A1, indicators linked to cardiovascular health.