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Division of  Theoretical Epidemiology , The Institute of Public Health,
4-6-1 Shirokanedai, Minato-ku, Tokyo 108, Japan



This paper considers a model for the difference of two proportions in a paired or matched design clinical trials, case-control studies and also sensitivity comparison studies of two laboratory tests. This model includes a parameter indicating both interpatient variability of response probabilities and their correlation. Under the proposed model, we derive a one-sided test for equivalence based upon the efficient score. Equivalence is defined here as not more than 100 per cent inferior. McNemar's test for singnificance is shown to be a special case of the proposed test. Further, a score-based confidence interval  for the difference of two proportions is derived. One of the  features of the these mothods is applicability to the Q~Q table with off-diagonal zero cells; all the McNemar type tests and confidence intervals published so far cannot apply to such data . A Monte Carlo simulation study shows that the proposed test has empirical significance levels closer to the nominal x-level than the other tests recently proposed and further that the proposed confidence interval has better empirical coverage probability than those of the four published methods. © 1998 John Wiley & Sons, Ltd.