  Alcohol consumption has been shown to influence cardiovascular mechanisms in
humans, leading to observable alterations in the plasma metabolomic profile.
Regression models are commonly employed to investigate these effects, treating
metabolomics features as the outcomes and alcohol intake as the exposure. Given
the latent dependence structure among the numerous metabolomic features (e.g.,
co-expression networks with interconnected modules), modeling this structure is
crucial for accurately identifying metabolomic features associated with alcohol
intake. However, integrating dependence structures into regression models
remains difficult in both estimation and inference procedures due to their
large or high dimensionality. To bridge this gap, we propose an innovative
multivariate regression model that accounts for correlations among outcome
features by incorporating an interconnected community structure. Furthermore,
we derive closed-form and likelihood-based estimators, accompanied by explicit
exact and explicit asymptotic covariance matrix estimators, respectively.
Simulation analysis demonstrates that our approach provides accurate estimation
of both dependence and regression coefficients, and enhances sensitivity while
maintaining a well-controlled discovery rate, as evidenced through benchmarking
against existing regression models. Finally, we apply our approach to assess
the impact of alcohol intake on $249$ metabolomic biomarkers measured using
nuclear magnetic resonance spectroscopy. The results indicate that alcohol
intake can elevate high-density lipoprotein levels by enhancing the transport
rate of Apolipoproteins A1.
