Department of Mathematics and Statistics, Washington State University, Pullman, WA, USA.
Department of Statistics and Data Science, Carnegie Mellon University, Pittsburgh, PA, USA.
Biom J. 2020 Oct;62(6):1544-1563. doi: 10.1002/bimj.201900216. Epub 2020 May 4.
Multiple testing (MT) with false discovery rate (FDR) control has been widely conducted in the "discrete paradigm" where p-values have discrete and heterogeneous null distributions. However, in this scenario existing FDR procedures often lose some power and may yield unreliable inference, and for this scenario there does not seem to be an FDR procedure that partitions hypotheses into groups, employs data-adaptive weights and is nonasymptotically conservative. We propose a weighted p-value-based FDR procedure, "weighted FDR (wFDR) procedure" for short, for MT in the discrete paradigm that efficiently adapts to both heterogeneity and discreteness of p-value distributions. We theoretically justify the nonasymptotic conservativeness of the wFDR procedure under independence, and show via simulation studies that, for MT based on p-values of binomial test or Fisher's exact test, it is more powerful than six other procedures. The wFDR procedure is applied to two examples based on discrete data, a drug safety study, and a differential methylation study, where it makes more discoveries than two existing methods.
多假设检验（Multiple Testing，MT）结合错误发现率(False Discovery Rate，FDR)控制在“离散范式”中被广泛应用，其中 p 值具有离散且异质的零分布。然而，在这种情况下，现有的 FDR 程序往往会失去一些功效，并且可能导致不可靠的推断。对于这种情况，似乎没有一种 FDR 程序可以将假设分成组，采用数据自适应权重并且是非渐近保守的。我们提出了一种基于加权 p 值的 FDR 程序，简称加权 FDR（weighted FDR，wFDR）程序，用于离散范式中的 MT，该程序可以有效地适应 p 值分布的异质性和离散性。我们从理论上证明了在独立性下 wFDR 程序的非渐近保守性，并通过模拟研究表明，对于基于二项式检验或 Fisher 精确检验的 MT，它比其他六种程序更有效。wFDR 程序应用于两个基于离散数据的示例，一个是药物安全性研究，另一个是差异甲基化研究，其中它比两种现有的方法做出了更多的发现。
