On tests of equivalence via non-unity relative risk for matched-pair design

Matched-pair design is often used in clinical trials to increase the efficiency of treatment comparison. We consider the problem of equivalence test with a relative risk endpoint in matched-pair studies with binary outcomes, and develop several score and Wald-type statistics for testing a hypothesis of non-unity relative risk. Examples from an assessment of HIV screening test and a cross-over clinical trial of soft contact lenses are used to illustrate the proposed methods. Through simulations we compare the empirical performance of these tests with the test proposed by Lachenbruch and Lynch. We show that a score test based on a reparameterized multinomial model by Tango performs best in the sense that the test satisfactorily controls the type I error rate and its empirical type I error rates are generally much closer to the prespecified nominal significance level than those of the other tests.