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Choosing between methods of combining $p$-values

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  • N A Heard
  • P Rubin-Delanchy

Abstract

Summary Combining $p$-values from independent statistical tests is a popular approach to meta-analysis, particularly when the data underlying the tests are either no longer available or are difficult to combine. Numerous $p$-value combination methods appear in the literature, each with different statistical properties, yet often the final choice used in a meta-analysis can seem arbitrary, as if all effort has been expended in building the models that gave rise to the $p$-values. Birnbaum (1954) showed that any reasonable $p$-value combiner must be optimal against some alternative hypothesis. Starting from this perspective and recasting each method of combining $p$-values as a likelihood ratio test, we present theoretical results for some standard combiners that provide guidance on how a powerful combiner might be chosen in practice.

Suggested Citation

  • N A Heard & P Rubin-Delanchy, 2018. "Choosing between methods of combining $p$-values," Biometrika, Biometrika Trust, vol. 105(1), pages 239-246.
    • Handle: RePEc:oup:biomet:v:105:y:2018:i:1:p:239-246.
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    File URL: http://hdl.handle.net/10.1093/biomet/asx076
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    Cited by:

    1. Xiong, Peihan & Hu, Taizhong, 2022. "On Samuel’s p-value model and the Simes test under dependence," Statistics & Probability Letters, Elsevier, vol. 187(C).
    2. Song, Zhi & Mukherjee, Amitava & Zhang, Jiujun, 2021. "Some robust approaches based on copula for monitoring bivariate processes and component-wise assessment," European Journal of Operational Research, Elsevier, vol. 289(1), pages 177-196.
    3. Leonhard Held, 2020. "The harmonic mean χ2‐test to substantiate scientific findings," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(3), pages 697-708, June.
    4. Paulo C. Rodrigues & Vanda M. Lourenço, 2020. "Comments on: Hierarchical Inference for genome-wide association studies: a view on methodology with software by Paulo C. Rodrigues and Vanda M. Lourenço," Computational Statistics, Springer, vol. 35(1), pages 57-58, March.
    5. Yu, Xiufan & Yao, Jiawei & Xue, Lingzhou, 2024. "Power enhancement for testing multi-factor asset pricing models via Fisher’s method," Journal of Econometrics, Elsevier, vol. 239(2).
    6. Juan Antonio Villatoro-García & Jordi Martorell-Marugán & Daniel Toro-Domínguez & Yolanda Román-Montoya & Pedro Femia & Pedro Carmona-Sáez, 2022. "DExMA: An R Package for Performing Gene Expression Meta-Analysis with Missing Genes," Mathematics, MDPI, vol. 10(18), pages 1-15, September.
    7. Wimmer, Thomas & Geyer-Klingeberg, Jerome & Hütter, Marie & Schmid, Florian & Rathgeber, Andreas, 2021. "The impact of speculation on commodity prices: A Meta-Granger analysis," Journal of Commodity Markets, Elsevier, vol. 22(C).
    8. Jai Won Choi & Balgobin Nandram & Boseung Choi, 2022. "Combining Correlated P-values From Primary Data Analyses," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 11(6), pages 1-12, November.
    9. Patrick B. Langthaler & Riccardo Ceccato & Luigi Salmaso & Rosa Arboretti & Arne C. Bathke, 2023. "Permutation testing for thick data when the number of variables is much greater than the sample size: recent developments and some recommendations," Computational Statistics, Springer, vol. 38(1), pages 101-132, March.
    10. Xin Yuan & Yanran Ma & Ruitian Gao & Shuya Cui & Yifan Wang & Botao Fa & Shiyang Ma & Ting Wei & Shuangge Ma & Zhangsheng Yu, 2024. "HEARTSVG: a fast and accurate method for identifying spatially variable genes in large-scale spatial transcriptomics," Nature Communications, Nature, vol. 15(1), pages 1-14, December.
    11. Zimmermann, Paul, 2021. "The role of the leverage effect in the price discovery process of credit markets," Journal of Economic Dynamics and Control, Elsevier, vol. 122(C).

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