Estimation of permutation-based metabolome-wide significance thresholds: Supplementary material

Abstract

A key issue in the omics literature is the search for statistically significant relationships between molecular markers and phenotype. The aim is to detect disease-related discriminatory features while controlling for false positive associations at adequate power. Metabolome-wide association studies have revealed significant relationships of metabolic phenotypes with disease risk by analysing hundreds to tens of thousands of molecular variables leading to multivariate data which are highly noisy and collinear. In this context, conventional Bonferroni or Sidak multiple testing corrections are rather useful as these are valid for independent tests, while permutation procedures allow for the estimation of significance levels from the null distribution without assuming independence among features. Nevertheless, under the permutation approach the distribution of p-values may present systematic deviations from the theoretical null distribution which leads to overly conservative adjusted threshold estimates i.e. smaller than a Bonferroni or Sidak correction. We make use of parametric approximation methods based on a multivariate Normal distribution to derive stable estimates of the metabolome-wide significance level. A univariate approach is applied based on a permutation procedure which effectively controls the overall type I error rate at the α level. We illustrate the approach for different model parametrizations and distributional features of the outcome measure, using both simulated and real data. We also investigate different levels of correlation within the features and between the features and the outcome. MWSL is an open-source R software package for the empirical estimation of the metabolome-wide significance level available at https://github.com/AlinaPeluso/MWSL.