SUPPLEMENT: DisCo P-ad: Distance Correlation-Based p-Value Adjustment Enhances Multiple-Testing Corrections for Metabolomics

Correcting for multiple-testing is critical for high-dimensional omics studies, such as genomics and metabolomics, where there are numerous measurements per sample. One strategy is to estimate the number of statistically independent tests, called the effective number of tests, based on the eigen-analysis of the correlation matrix between the features. This effective number is then used for a subsequent single-step adjustment to obtain the pointwise significance level. Such practice is commonplace in Genome-Wide Association Studies (GWAS) but is also becoming increasingly relevant to Metabolome-Wide Association Studies (MWAS). However, many procedures for estimating the effective number of tests may be too conservative or too lenient, only assume a linear association between features, or have not been evaluated on metabolomics data. Therefore, we propose a modification to the p-value adjustment based on a more general measure of association between two predictors, the Distance Correlation, with specific focus on MWAS. We assessed common GWAS \textit{p}-value adjustment procedures and one tailored for MWAS, which rely on eigen-analysis of the Pearson's correlation matrix. Our study, including varying sample size-to-feature ratios, response types, and metabolite groupings, highlights the superior performance of the Distance Correlation. We introduce the Distance Correlation-based p-value adjustment (DisCo P-ad) as a novel modification that can enhance existing eigen-analysis based procedures by increasing power or reducing false positives. While our focus is on metabolomics, DisCo P-ad can readily be applied to other high-dimensional omics studies.

Keywords: Multiple-testing; Effective number of tests; Correlated tests; Eigen-analysis; Pointwise error rate; Metabolome-wide association study