A weighted FDR procedure under discrete and heterogeneous null distributions

Multiple testing with false discovery rate (FDR) control has been widely conducted in the "discrete paradigm" where p-values have discrete and heterogeneous null distributions with finitely many discontinuities. However, existing FDR procedures may lose some power when applied to such p-values. We propose a weighted FDR procedure for multiple testing in the discrete paradigm that efficiently adapts to both the heterogeneity and discreteness of p-value distributions. We prove the conservativeness of the weighted FDR procedure and demonstrate that it is more powerful than several other procedures for multiple testing based on p-values of binomial test or Fisher's exact test. The weighted FDR procedure is applied to a drug safety study and a differential methylation study based on discrete data, where it makes more discoveries than the Benjamini-Hochberg procedure at the same FDR level.