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

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  • Jesse Hemerik
  • Jelle J. Goeman

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−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.

Suggested Citation

  • Jesse Hemerik & Jelle J. Goeman, 2018. "False discovery proportion estimation by permutations: confidence for significance analysis of microarrays," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(1), pages 137-155, January.
    • Handle: RePEc:bla:jorssb:v:80:y:2018:i:1:p:137-155
    DOI: 10.1111/rssb.12238
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    Cited by:

    1. Guillermo Durand & Gilles Blanchard & Pierre Neuvial & Etienne Roquain, 2020. "Post hoc false positive control for structured hypotheses," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(4), pages 1114-1148, December.
    2. N W Koning & J Hemerik, 2024. "More efficient exact group invariance testing: using a representative subgroup," Biometrika, Biometrika Trust, vol. 111(2), pages 441-458.
    3. Jesse Hemerik & Jelle J. Goeman, 2021. "Another Look at the Lady Tasting Tea and Differences Between Permutation Tests and Randomisation Tests," International Statistical Review, International Statistical Institute, vol. 89(2), pages 367-381, August.
    4. Jesse Hemerik & Jelle J. Goeman & Livio Finos, 2020. "Robust testing in generalized linear models by sign flipping score contributions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(3), pages 841-864, July.
    5. Benjamin R. Auer, 2022. "On false discoveries of standard t-tests in investment management applications," Review of Managerial Science, Springer, vol. 16(3), pages 751-768, April.
    6. J. Liu & Xinlian Zhang & T. Chen & T. Wu & T. Lin & L. Jiang & S. Lang & L. Liu & L. Natarajan & J.X. Tu & T. Kosciolek & J. Morton & T.T. Nguyen & B. Schnabl & R. Knight & C. Feng & Y. Zhong & X.M. T, 2022. "A semiparametric model for between‐subject attributes: Applications to beta‐diversity of microbiome data," Biometrics, The International Biometric Society, vol. 78(3), pages 950-962, September.
    7. Ferraccioli, Federico & Sangalli, Laura M. & Finos, Livio, 2022. "Some first inferential tools for spatial regression with differential regularization," Journal of Multivariate Analysis, Elsevier, vol. 189(C).

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