Competition-based control of the false discovery proportion

Recently, Barber and Cand\`es laid the theoretical foundation for a general framework for false discovery rate (FDR) control based on the notion of "knockoffs." A closely related FDR control methodology has long been employed in the analysis of mass spectrometry data, referred to there as "target-decoy competition" (TDC). However, any approach that aims to control the FDR, which is defined as the expected value of the false discovery proportion (FDP), suffers from a problem. Specifically, even when successfully controlling the FDR at level {\alpha}, the FDP in the list of discoveries can significantly exceed {\alpha}. We offer two new procedures to address this problem, both of which are compatible with the knockoff framework or TDC. FDP-SD rigorously controls the FDP in the competition setup by guaranteeing that the FDP is bounded by {\alpha} at any desired confidence level. The complementary TDC-UB is designed to bound the FDP for any list of top-scoring target discoveries. Compared with the just-published general framework of Katsevich and Ramdas, our proposed procedures generally offer more power (FDP-SD) and tighter bounds (TDC-UB) and often substantially so in simulated as well as real data.