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Closed testing with Globaltest, with application in metabolomics

Author

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  • Ningning Xu
  • Aldo Solari
  • Jelle J. Goeman

Abstract

The Globaltest is a powerful test for the global null hypothesis that there is no association between a group of features and a response of interest, which is popular in pathway testing in metabolomics. Evaluating multiple feature sets, however, requires multiple testing correction. In this paper, we propose a multiple testing method, based on closed testing, specifically designed for the Globaltest. The proposed method controls the familywise error rate simultaneously over all possible feature sets, and therefore allows post hoc inference, that is, the researcher may choose feature sets of interest after seeing the data without jeopardizing error control. To circumvent the exponential computation time of closed testing, we derive a novel shortcut that allows exact closed testing to be performed on the scale of metabolomics data. An R package ctgt is available on comprehensive R archive network for the implementation of the shortcut procedure, with applications on several real metabolomics data examples.

Suggested Citation

  • Ningning Xu & Aldo Solari & Jelle J. Goeman, 2023. "Closed testing with Globaltest, with application in metabolomics," Biometrics, The International Biometric Society, vol. 79(2), pages 1103-1113, June.
    • Handle: RePEc:bla:biomet:v:79:y:2023:i:2:p:1103-1113
    DOI: 10.1111/biom.13693
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    References listed on IDEAS

    as
    1. Jelle J. Goeman & Sara A. Van De Geer & Hans C. Van Houwelingen, 2006. "Testing against a high dimensional alternative," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 477-493, June.
    2. Brannath, Werner & Bretz, Frank, 2010. "Shortcuts for Locally Consonant Closed Test Procedures," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 660-669.
    3. Jelle J. Goeman & Hans C. van Houwelingen & Livio Finos, 2011. "Testing against a high-dimensional alternative in the generalized linear model: asymptotic type I error control," Biometrika, Biometrika Trust, vol. 98(2), pages 381-390.
    4. Jelle J Goeman & Rosa J Meijer & Thijmen J P Krebs & Aldo Solari, 2019. "Simultaneous control of all false discovery proportions in large-scale multiple hypothesis testing," Biometrika, Biometrika Trust, vol. 106(4), pages 841-856.
    5. Jiangtao Gou & Ajit C. Tamhane & Dong Xi & Dror Rom, 2014. "A class of improved hybrid Hochberg–Hommel type step-up multiple test procedures," Biometrika, Biometrika Trust, vol. 101(4), pages 899-911.
    6. Westfall, Peter H. & Tobias, Randall D., 2007. "Multiple Testing of General Contrasts: Truncated Closure and the Extended ShafferRoyen Method," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 487-494, June.
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