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Optimal multiple testing under a Gaussian prior on the effect sizes

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  • Edgar Dobriban
  • Kristen Fortney
  • Stuart K. Kim
  • Art B. Owen

Abstract

We develop a new method for large-scale frequentist multiple testing with Bayesian prior information. We find optimal $p$-value weights that maximize the average power of the weighted Bonferroni method. Due to the nonconvexity of the optimization problem, previous methods that account for uncertain prior information are suitable for only a small number of tests. For a Gaussian prior on the effect sizes, we give an efficient algorithm that is guaranteed to find the optimal weights nearly exactly. Our method can discover new loci in genome-wide association studies and compares favourably to competitors. An open-source implementation is available.

Suggested Citation

  • Edgar Dobriban & Kristen Fortney & Stuart K. Kim & Art B. Owen, 2015. "Optimal multiple testing under a Gaussian prior on the effect sizes," Biometrika, Biometrika Trust, vol. 102(4), pages 753-766.
    • Handle: RePEc:oup:biomet:v:102:y:2015:i:4:p:753-766.
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    File URL: http://hdl.handle.net/10.1093/biomet/asv050
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    References listed on IDEAS

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    1. Rubin Daniel & Dudoit Sandrine & van der Laan Mark, 2006. "A Method to Increase the Power of Multiple Testing Procedures Through Sample Splitting," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 5(1), pages 1-20, August.
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    Cited by:

    1. Ruth Heller & Abba Krieger & Saharon Rosset, 2023. "Optimal multiple testing and design in clinical trials," Biometrics, The International Biometric Society, vol. 79(3), pages 1908-1919, September.
    2. Nikolaos Ignatiadis & Wolfgang Huber, 2021. "Covariate powered cross‐weighted multiple testing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(4), pages 720-751, September.
    3. 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.

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