EQUIVALENCE TEST AND CONFIDENCE INTERVAL FOR THE DIFFERENCE IN PROPORTIONS FOR THE PAIRED-SAMPLE DESIGN

SUMMARY This paper considers a model for the di⁄erence of two proportions in a paired or matched design of 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 eƒcient score. Equivalence is defined here as not more than 100* per cent inferior. McNemar’s test for significance is shown to be a special case of the proposed test. Further, a score-based confidence interval for the di⁄erence of two proportions is derived. One of the features of these methods is applicability to the 2]2 table with o⁄-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 a-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.