Correcting false discovery rates for their bias toward false positives

Abstract

Conventional methods of adjusting p values for multiple comparisons seek to control a family-wise error rate (FWER) such as a genome-wise error rate. The recognition that they lead to excessive false negative rates in genomics applications has led to widespread use of false discovery rates (FDRs) in place of the conventional adjustments. While this is an improvement, the way FDRs are used in the analysis of genomics data leads to the opposite problem, excessive false positive rates. In this sense, the FDR overcorrects for the excessive conservatism (bias toward false negatives) of the FWER-controlling methods of adjusting p values.

Estimators of the local FDR (LFDR) are much less biased but have not been widely adopted because they have high variance compared to estimated FDRs. To reduce that variance, we propose estimating the LFDR by correcting an estimated FDR or the level at which an FDR is controlled.