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Discussion on “Optimal test procedures for multiple hypotheses controlling the familywise expected loss” by Willi Maurer, Frank Bretz, and Xiaolei Xun

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  • Yoav Benjamini
  • Ruth Heller
  • Abba Krieger
  • Saharon Rosset

Abstract

We discuss three issues. In the first part, we discuss the criteria emphasized by Maurer, Bretz, and Xun, warning that it modifies the per comparison error rate that does not address the concerns raised by multiple testing. In the second part, we strengthen the optimality results developed in the paper, based on our recent results. In the third part, we highlight the potentially important role that the use of weights may have in practice and discuss the difficulties in assigning weights that convey the importance in the gain and loss functions, especially as it pertains to multiple endpoints.

Suggested Citation

  • Yoav Benjamini & Ruth Heller & Abba Krieger & Saharon Rosset, 2023. "Discussion on “Optimal test procedures for multiple hypotheses controlling the familywise expected loss” by Willi Maurer, Frank Bretz, and Xiaolei Xun," Biometrics, The International Biometric Society, vol. 79(4), pages 2794-2797, December.
    • Handle: RePEc:bla:biomet:v:79:y:2023:i:4:p:2794-2797
    DOI: 10.1111/biom.13906
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    References listed on IDEAS

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    1. Christopher R. Genovese & Kathryn Roeder & Larry Wasserman, 2006. "False discovery control with p-value weighting," Biometrika, Biometrika Trust, vol. 93(3), pages 509-524, September.
    2. Saharon Rosset & Ruth Heller & Amichai Painsky & Ehud Aharoni, 2022. "Optimal and maximin procedures for multiple testing problems," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(4), pages 1105-1128, September.
    3. Michael Rosenblum & Han Liu & En-Hsu Yen, 2014. "Optimal Tests of Treatment Effects for the Overall Population and Two Subpopulations in Randomized Trials, Using Sparse Linear Programming," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1216-1228, September.
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