Although the risk difference (RD) is the most common and well explored functional form for testing efficacy with dichotomous endpoint, odds ratio (OR) is also suggested and well applied measure for non-inferiority (NI) trials. Since the construction and interpretation of these function forms are quite different, this study aims to provide detailed discussions and comprehensive comparisons on the design and testing approach for RD and OR scales for the fixed and group sequential three-arm NI trials under various of situations. The sample size determinations and testing approaches for assessing NI of a new treatment in three-arm clinical trials for RD and OR scales were reviewed comprehensively. Simulation studies are conducted for hundreds of scenarios with parameter configurations of the response rates, randomized allocations, NI margins and interim analysis. The operating characteristic (OC) of RD and OR scales based on the MLE and RMLE methods were thoroughly investigated. A trial example was designed and analyzed to demonstrate the methodologies. It is found that sample size determination on OR scale gives smaller sample size and robust procedure compared to RD scale in the majority of situations. When evaluating the behaviors of the attained power, the RMLE methods based on OR scale outperforms the MLE method and tend to have more power to reject the null hypothesis especially under the small sample size situations. Compared to the fixed design, the group sequential design has better OC, which provides a comparable power while needing smaller total average sample sizes for all cases. In addition, we suggest a lower significance level with a higher power for the sample size determination in the superiority test stage in the group sequential design, which can significantly reduce the total sample sizes while the number of subjects in the placebo group does not increase much. It can offer some recommendations for the investigators to choose the optimal endpoints and parameter configurations to design a three-arm NI trial under certain situations.
