Testing multiple biological mediators simultaneously

MOTIVATION Modern biomedical and epidemiological studies often measure hundreds or thousands of biomarkers, such as gene expression or metabolite levels. Although there is an extensive statistical literature on adjusting for 'multiple comparisons' when testing whether these biomarkers are directly associated with a disease, testing whether they are biological mediators between a known risk factor and a disease requires a more complex null hypothesis, thus offering additional methodological challenges. RESULTS We propose a permutation approach that tests multiple putative mediators and controls the family wise error rate. We demonstrate that, unlike when testing direct associations, replacing the Bonferroni correction with a permutation approach that focuses on the maximum of the test statistics can significantly improve the power to detect mediators even when all biomarkers are independent. Through simulations, we show the power of our method is 2-5× larger than the power achieved by Bonferroni correction. Finally, we apply our permutation test to a case-control study of dietary risk factors and colorectal adenoma to show that, of 149 test metabolites, docosahexaenoate is a possible mediator between fish consumption and decreased colorectal adenoma risk. AVAILABILITY AND IMPLEMENTATION R-package included in online Supplementary Material.