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False discovery proportion estimation by permutations: confidence for significance analysis of microarrays
Author(s) -
Hemerik Jesse,
Goeman Jelle J.
Publication year - 2018
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/rssb.12238
Subject(s) - permutation (music) , confidence interval , multiple comparisons problem , statistics , fraction (chemistry) , mathematics , false discovery rate , computer science , biology , genetics , physics , chemistry , organic chemistry , acoustics , gene
Summary 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− α upper 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.