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Approximating probabilities of correlated events

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Abstract

Efron (1997) considered several approximations of p-values for simultaneous hypothesis testing. An extension of his approaches is considered here to approximate various probabilities of correlated events. Compared with multiple-integrations, our proposed method, the parallelogram formulas, based on a one-dimensional integral, not only substantially reduces the computational complexity but also maintains good accuracy. Applications of the proposed method to genetic association studies and group sequential analysis are investigated in detail. Numerical results including real data analysis and simulation studies demonstrate that the proposed method performs well.

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Authors and Affiliations

  1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    QiZhai Li

  2. Biostatistics Branch, Division of Cancer Epidemiology and Genetics, National Cancer Institute, Bethesda, MD, 20892, USA

    QiZhai Li, ZhaoHai Li & Kai Yu

  3. Office of Biostatistics Research, National Heart, Lung and Blood Institute, Bethesda, MD, 20892, USA

    Gang Zheng

  4. Biostatistics and Bioinformatics Branch, National Institute of Child Health and Human Development, Bethesda, MD, 20892, USA

    AiYi Liu

  5. Department of Statistics, George Washington University, Washington, DC, 20052, USA

    ZhaoHai Li

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  1. QiZhai Li
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  2. Gang Zheng
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  3. AiYi Liu
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  4. ZhaoHai Li
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  5. Kai Yu
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Correspondence to QiZhai Li.

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Li, Q., Zheng, G., Liu, A. et al. Approximating probabilities of correlated events. Sci. China Math. 53, 2937–2948 (2010). https://doi.org/10.1007/s11425-010-4053-0

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  • DOI: https://doi.org/10.1007/s11425-010-4053-0

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