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.

中文翻译：

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离散和异构零分布下的加权 FDR 程序

具有错误发现率 (FDR) 控制的多重测试 (MT) 已在“离散范式”中广泛进行，其中 p 值具有离散和异构的零分布。然而，在这种情况下，现有的 FDR 程序通常会失去一些能力，并可能产生不可靠的推理，并且对于这种情况，似乎没有将假设分成组、采用数据自适应权重且非渐近保守的 FDR 程序。我们提出了一种基于加权 p 值的 FDR 程序，简称“加权 FDR (wFDR) 程序”，用于离散范式中的 MT，它有效地适应 p 值分布的异质性和离散性。我们在理论上证明了 wFDR 程序在独立性下的非渐近保守性，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 p 值的 MT，它比其他六个程序更强大。wFDR 程序应用于基于离散数据的两个示例、药物安全性研究和差异甲基化研究，在这些示例中，它比两种现有方法有更多的发现。