Adjustment for multiple testing is applied to control false positives. When many hypotheses are tested simultaneously, the probability that at least one type I error is committed is large. One common approach for accounting for multiple testing is to control the false discovery rate (FDR) [23]. The FDR is the expected proportion of falsely rejected hypotheses out of the rejected hypotheses. One can also control the family wise error rate (FWER), which is the probability of making one or more type I errors among the family of hypothesis tests. When the number of tests is large and some of the test hypotheses are in fact false, FWER is too conservative. Since multiple pathways might be involved in a complex trait, FDR, which controls the expected proportion of false discoveries, is more suited to identifying pathways relevant to a trait. To account for multiple testing in our pathway analyses, we used a robust method to estimate the false discovery rate proposed by Pounds and Cheng [24]. The q-value is the minimum FDR at which the test is called significant. For a given significant level α, the point estimate of q-value (α) is defined as
