Control procedures and estimators of the false discovery rate and their application in low-dimensional settings: an empirical investigation

Background: When many (up to millions) of statistical tests are conducted in discovery set analyses such as genome-wide association studies (GWAS), approaches controlling family-wise error rate (FWER) or false discovery rate (FDR) are required to reduce the number of false positive decisions. Some methods were specifically developed in the context of high-dimensional settings and partially rely on the estimation of the proportion of true null hypotheses. However, these approaches are also applied in low-dimensional settings such as replication set analyses that might be restricted to a small number of specific hypotheses. The aim of this study was to compare different approaches in low-dimensional settings using (a) real data from the CKDGen Consortium and (b) a simulation study. Results: In both application and simulation FWER approaches were less powerful compared to FDR control methods, whether a larger number of hypotheses were tested or not. Most powerful was the q-value method. However, the specificity of this method to maintain true null hypotheses was especially decreased when the number of tested hypotheses was small. In this low-dimensional situation, estimation of the proportion of true null hypotheses was biased. Conclusions: The results highlight the importance of a sizeable data set for a reliable estimation of the proportion of true null hypotheses. Consequently, methods relying on this estimation should only be applied in high-dimensional settings. Furthermore, if the focus lies on testing of a small number of hypotheses such as in replication settings, FWER methods rather than FDR methods should be preferred to maintain high specificity.