Probabilistic Over-Representation Analysis for Metabolite Set Enrichment Analysis Considering Undetected Metabolites

Abstract

Over-representation analysis (ORA) is widely used to identify significant pathways in metabolomic data. However, traditional ORA approaches, such as those implemented in MetaboAnalyst, do not account for undetected metabolites, potentially resulting in significant biases since undetected metabolites are automatically classified as non-significant. In this study, we used fasting mouse metabolomic data and developed a novel ORA method that leverages information from detected significant metabolites to estimate the possible range of p-values by considering all possible significance combinations among undetected metabolites. Furthermore, we introduced two probabilistic models—a binomial distribution to estimate the number of significant undetected metabolites and a beta distribution to model their proportion—resulting in narrower p-value ranges. Finally, a hierarchical Bayesian model utilizing shared information across all pathways was applied, with resampling from the specified distributions to calculate ORA p-values and achieve the narrowest p-value confidence intervals. This approach highlights the importance of accounting for undetected metabolites in pathway enrichment analysis to enhance the reliability of ORA results.