  Competition-based FDR control has been commonly used for over a decade in the
computational mass spectrometry community (Elias and Gygi, 2007). Recently, the
approach has gained significant popularity in other fields after Barber and
Candes (2015) laid its theoretical foundation in a more general setting that
included the feature selection problem. In both cases, the competition is based
on a head-to-head comparison between an observed score and a corresponding
decoy / knockoff. Keich and Noble (2017b) recently demonstrated some advantages
of using multiple rather than a single decoy when addressing the problem of
assigning peptide sequences to observed mass spectra. In this work, we consider
a related problem -- detecting peptides based on a collection of mass spectra
-- and we develop a new framework for competition-based FDR control using
multiple null scores. Within this framework, we offer several methods, all of
which are based on a novel procedure that rigorously controls the FDR in the
finite sample setting. Using real data to study the peptide detection problem
we show that, relative to existing single-decoy methods, our approach can
increase the number of discovered peptides by up to 50% at small FDR
thresholds.
