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  • Title: A note on monotonicity assumptions for exact unconditional tests in binary matched-pairs designs.
    Author: Li X, Liu M, Goldberg JD.
    Journal: Biometrics; 2011 Dec; 67(4):1666-8. PubMed ID: 21466507.
    Abstract:
    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, Biometrics 64, 716-723) proposed an E + M p-value, that showed better performance than the existing M p-value and C p-value. However, the analytical calculation of the E + M p-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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