On Benjamini–Hochberg procedure applied to midp-values

Abstract

Multiple testing with discrete p-values routinely arises in various scientific endeavors. However, procedures, including the false discovery rate (FDR) controlling Benjamini-Hochberg (BH) procedure, often used in such settings, being developed originally for p-values with continuous distributions, are too conservative, and so may not be as powerful as one would hope for. Therefore, improving the BH procedure by suitably adapting it to discrete p-values without losing its FDR control is currently an important path of research. This paper studies the FDR control of the BH procedure when it is applied to mid p-values and derive conditions under which it is conservative. Our simulation study reveals that the BH procedure applied to mid p-values may be conservative under much more general settings than characterized in this work, and that an adaptive version of the BH procedure applied to mid p-values is as powerful as an existing adaptive procedure based on randomized p-values.

Multiple Comparison Procedures for Discrete Uniform and Homogeneous Tests

“…Their method can be considered as a discrete version of the classical method of Benjamini and Liu (1999) which controls the FDR for continuous p ‐values under independence or positive dependence. Recently, Chen and Sarkar (2020) investigated the BH procedure when applied to mid p ‐values, providing in this way a correction of the BH method for discrete p ‐values. More precisely, they proved the FDR control of the BH procedure applied to two‐sided mid p ‐values of Binomial tests and Fisher's exact tests.…”