False discovery proportion estimation by permutations: confidence for significance analysis of microarrays

Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2018 · Volume 80 · Issue 1

Abstract

Significance analysis of microarrays (SAM) is a highly popular permutation-based multiple-testing method that estimates the false discovery proportion (FDP): the fraction of false positive results among all rejected hypotheses. Perhaps surprisingly, until now this method had no known properties. This paper extends SAM by providing 1−αupper confidence bounds for the FDP, so that exact confidence statements can be made. As a special case, an estimate of the FDP is obtained that underestimates the FDP with probability at most 0.5. Moreover, using a closed testing procedure, this paper decreases the upper bounds and estimates in such a way that the confidence level is maintained. We base our methods on a general result on exact testing with random permutations.

Keywords

Confidence, False discovery proportion, Multiple testing, Permutation

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