A note on monotonicity assumptions for exact unconditional tests in binary matched-pairs designs

Biometrics. 2011 Dec;67(4):1666-8. doi: 10.1111/j.1541-0420.2011.01593.x. Epub 2011 Apr 5.

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.

Publication types

  • Research Support, N.I.H., Extramural

MeSH terms

  • Data Interpretation, Statistical*
  • Humans
  • Matched-Pair Analysis*
  • Models, Statistical
  • Placebos
  • Randomized Controlled Trials as Topic / statistics & numerical data*
  • Research Design*
  • Treatment Outcome

Substances

  • Placebos