Conditional calibration for false discovery rate control under dependence

Abstract: We introduce a new class of methods for finite-sample false discovery rate (FDR) control in multiple testing problems with dependent test statistics where the dependence is fully or partially known. Our approach separately calibrates a data-dependent p-value rejection threshold for each hypothesis, relaxing or tightening the threshold as appropriate to target exact FDR control. In addition to our general framework we propose a concrete algorithm, the dependence-adjusted Benjamini-Hochberg (dBH) procedure, which adaptively thresholds the q-value for each hypothesis. Under positive regression dependence the dBH procedure uniformly dominates the standard BH procedure, and in general it uniformly dominates the Benjamini-Yekutieli (BY) procedure (also known as BH with log correction). Simulations and real data examples illustrate power gains over competing approaches to FDR control under dependence.