Competition-based control of the false discovery proportion

TL;DR

This paper introduces FDP-SD, a new method that provides rigorous, confidence-level control over the false discovery proportion in competition-based FDR procedures, improving power over existing methods.

Contribution

FDP-SD is a novel procedure that guarantees FDP bounds at any confidence level, enhancing control and power in competition-based FDR analysis.

Findings

FDP-SD controls FDP with high confidence in simulations and real data.

FDP-SD often outperforms existing methods in power.

FDP-SD provides rigorous FDP bounds in knockoff and TDC setups.

Abstract

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 FDP-SD, a new procedure that rigorously controls the FDP in the competition (knockoff / TDC) setup by guaranteeing that the FDP is bounded by $\alpha$ at any desired confidence level. Compared with the just-published general framework of Katsevich and Ramdas, FDP-SD generally delivers more power and often substantially so in simulated as well as real data.