Small-scale inference: Empirical Bayes and confidence methods for as few as a single comparison

By constraining the possible values of the proportion of null hypotheses that are true, the local false discovery rate (LFDR) can be estimated using as few as one comparison. The proportion of proteins with equivalent abundance was estimated to be about 20% for patient group I and about 90% for group II. The simultaneously-estimated LFDRs give approximately the same inferences as individual-protein confidence levels for group I but are much closer to individual-protein LFDR estimates for group II. Simulations confirm that confidence-based inference or LFDR-based inference performs markedly better for low or high proportions of true null hypotheses, respectively.