Microbial correlation: a semi-parametric model for investigating microbial co-metabolism

The gut microbiome plays a crucial role in human health, yet the mechanisms underlying host-microbiome interactions remain unclear, limiting its translational potential. Recent microbiome multiomics studies, particularly paired microbiome-metabolome studies (PM2S), provide valuable insights into gut metabolism as a key mediator of these interactions. Our preliminary data reveal strong correlations among certain gut metabolites, suggesting shared metabolic pathways and microbial co-metabolism. However, these findings are confounded by various factors, underscoring the need for a more rigorous statistical approach. Thus, we introduce microbial correlation, a novel metric that quantifies how two metabolites are co-regulated by the same gut microbes while accounting for confounders. Statistically, it is based on a partially linear model that isolates microbial-driven associations, and a consistent estimator is established based on semi-parametric theory. To improve efficiency, we develop a calibrated estimator with a parametric rate, maximizing the use of large external metagenomic datasets without paired metabolomic profiles. This calibrated estimator also enables efficient p-value calculation for identifying significant microbial co-metabolism signals. Through extensive numerical analysis, our method identifies important microbial co-metabolism patterns for healthy individuals, serving as a benchmark for future studies in diseased populations.