Non-inferiority testing for the odds ratio in two independent binomial proportions using the method of variance estimates recovery

This study introduces a non-inferiority test, which is based on the method of variance estimates recovery (MOVER), for the odds ratio in two independent binomial populations. In order to address the limitations of existing methods for single binomial proportions, we propose modified asymptotic confidence intervals within the MOVER framework, incorporating asymmetric parameters. We systematically evaluate the type I error control and statistical power of seven MOVER variants (M1–M7) and the Gart adjusted logit test (GAL) in non-inferiority settings. Comprehensive evaluations demonstrate that the M6 achieves optimal performance, maintaining the highest proportion of type I error rates below the significance level α, while retaining competitive power. When stricter type I error control is prioritized, M5 or M4 provides viable alternatives. Although M7 yields the highest power, its type I error is significantly inflated. The M1–M3 exhibit adequate error control but critically low power, while GAL shows moderate performance. The MOVER-based approach offers enhanced flexibility to accommodate diverse research requirements, with empirical results supporting its practical utility in non-inferiority testing. The proposed tests were illustrated with a real-world example.