Tests for equivalence based on odds ratio for matched-pair design

Currently, methods for evaluation of equivalence under a matched-pair design use either difference in proportions or relative risk as measures of risk association. However, these measures of association are only for cross-sectional studies or prospective investigations, such as clinical trials and they cannot be applied to retrospective research such as case-control studies. As a result, under a matched-pair design, we propose the use of the conditional odds ratio for assessment of equivalence in both prospective and retrospective research. We suggest the use of the asymptotic confidence interval of the conditional odds ratio for evaluation of equivalence. In addition, a score test based on the restricted maximum likelihood estimator (RMLE) is derived to test the hypothesis of equivalence under a matched-pair design. On the other hand, a sample size formula is also provided. A simulation study was conducted to empirically investigate the size and power of the proposed procedures. Simulation results show that the score test not only adequately controls the Type I error but it can also provide sufficient power. A numerical example illustrates the proposed methods.