A Note on Monotonicity Assumptions for Exact Unconditional Tests in Binary Matched-Pairs Designs

Authors

  • Xiaochun Li,

    Corresponding author
    1. Division of Biostatistics, Department of Environmental Medicine, New York University School of Medicine, New York, New York 10016, U.S.A.
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  • Mengling Liu,

    1. Division of Biostatistics, Department of Environmental Medicine, New York University School of Medicine, New York, New York 10016, U.S.A.
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  • Judith D. Goldberg

    1. Division of Biostatistics, Department of Environmental Medicine, New York University School of Medicine, New York, New York 10016, U.S.A.
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email: xiaochun.li@nyu.edu

Abstract

Summary Exact unconditional tests have been widely applied to test the difference between two probabilities for 2 × 2 matched-pairs binary data with small sample size. In this context, Lloyd (2008, Biometrics64, 716–723) proposed an E + Mp-value, that showed better performance than the existing Mp-value and Cp-value. However, the analytical calculation of the E + Mp-value requires that the Barnard convexity condition be satisfied; this can be challenging to prove theoretically. In this article, by a simple reformulation, we show that a weaker condition, conditional monotonicity, is sufficient to calculate all three p-values (M, C, and E + M) and their corresponding exact sizes. Moreover, this conditional monotonicity condition is applicable to noninferiority tests.

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