title: A note on monotonicity assumptions for exact unconditional tests in binary matched-pairs designs.
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.
authors.affiliation: Department of Environmental Medicine, New York University School of Medicine, New York, New York 10016, USA. xiaochun.li@nyu.edu
authors.forename: Xiaochun
authors.initials: X
authors.lastname: Li
authors.forename: Mengling
authors.initials: M
authors.lastname: Liu
authors.forename: Judith D
authors.initials: JD
authors.lastname: Goldberg
mesh_terms: D003627:Data Interpretation, Statistical; D006801:Humans; D016555:Matched-Pair Analysis; D015233:Models, Statistical; D010919:Placebos; D016032:Randomized Controlled Trials as Topic / Q000706:statistics & numerical data*; D012107:Research Design; D016896:Treatment Outcome
chemical_list: D010919:Placebos