A Direct Approach to False Discovery Rates

TLDR

Multiple‑hypothesis testing requires controlling compound error rates, and traditional FDR control relies on intricate sequential p‑value rejection methods. The authors propose an alternative strategy that fixes the rejection region first and then estimates the corresponding error rate, rather than fixing the error rate and deriving the rejection region. They apply this method to both the positive false discovery rate (pFDR) and the standard FDR, including calculation of the q‑value as the pFDR analogue, and provide evidence of its benefits. The approach yields greater applicability, accuracy, and power—pFDR appears to be the more relevant metric, and numerical examples show up to an eight‑fold increase in power over the Benjamini–Hochberg FDR method.

Abstract

Summary Multiple-hypothesis testing involves guarding against much more complicated errors than single-hypothesis testing. Whereas we typically control the type I error rate for a single-hypothesis test, a compound error rate is controlled for multiple-hypothesis tests. For example, controlling the false discovery rate FDR traditionally involves intricate sequential p-value rejection methods based on the observed data. Whereas a sequential p-value method fixes the error rate and estimates its corresponding rejection region, we propose the opposite approach—we fix the rejection region and then estimate its corresponding error rate. This new approach offers increased applicability, accuracy and power. We apply the methodology to both the positive false discovery rate pFDR and FDR, and provide evidence for its benefits. It is shown that pFDR is probably the quantity of interest over FDR. Also discussed is the calculation of the q-value, the pFDR analogue of the p-value, which eliminates the need to set the error rate beforehand as is traditionally done. Some simple numerical examples are presented that show that this new approach can yield an increase of over eight times in power compared with the Benjamini–Hochberg FDR method.