Approximating the distribution of maximally selected McNemar's statistics

Daniel Rabinowitz, Rebecca A. Betensky

Research output: Contribution to journalArticlepeer-review


It is common in epidemiologic analyses to summarize continuous outcomes as falling above or below a threshold. With paired data and with a threshold chosen without reference to the outcomes, McNemar's test of marginal homogeneity may be applied to the resulting dichotomous pairs when testing for equality of the marginal distributions of the underlying continuous outcomes. If the threshold is chosen to maximize the test statistic, however, referring the resulting test statistic to the nominal χ2 distribution is incorrect; Instead, the p-value must be adjusted for the multiple comparisons. Here the distribution of a maximally selected McNemar's statistic is derived, and it is shown that an approximation due to Durbin (1985, Journal of Applied Probability 22, 99-122) may be used to estimate approximate p-values. The methodology is illustrated by an application to measurements of insulin-like growth factor-I (IGF-I)in matched prostate cancer cases and controls from the Physicians' Health Study. The results of Simulation experiments that assess the accuracy of the approximation in moderate sample sizes are reported.

Original languageEnglish (US)
Pages (from-to)897-902
Number of pages6
Issue number3
StatePublished - 2000


  • Boundary crossing
  • Durbin's approximation
  • Matched pairs
  • Maximally selected χ statistic

ASJC Scopus subject areas

  • Statistics and Probability
  • General Biochemistry, Genetics and Molecular Biology
  • General Immunology and Microbiology
  • General Agricultural and Biological Sciences
  • Applied Mathematics


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