Covariate-powered weighted multiple testing with false discovery rate control
Consider a multiple testing setup where we observe mutually independent pairs of p-values and covariates , such that under the null hypothesis. Our goal is to use the information potentially available in the covariates to increase power compared to conventional procedures that only use the , while controlling the false discovery rate (FDR). To this end, we recently introduced independent hypothesis weighting (IHW), a weighted Benjamini-Hochberg method, in which the weights are chosen as a function of the covariate in a data-driven manner. We showed empirically in simulations and datasets from genomics and proteomics that IHW leads to a large power increase, while controlling the FDR. The key idea was to use hypothesis splitting to learn the weight-covariate function without overfitting. In this paper, we provide a survey of IHW and related approaches by presenting them under the lens of the two-groups model, when it is valid conditionally on a covariate. Furthermore, a slightly modified variant of IHW is proposed and shown to enjoy finite sample FDR control. The same ideas can also be applied for finite-sample control of the family-wise error rate (FWER) via IHW-Bonferroni.