Determination of the required sample size with assurance for Three Arm Non-Inferiority trials

The concept of assurance in the two-arm non-inferiority trials has been explored, expressing the non-inferiority margin as a clinically meaningful treatment difference. This short paper focuses on developing an assurance formula in the three-arm non-inferiority trial, based on the ratio of means. The discussion starts with the simple case of known variances and then extends to the case of unknown but equal variances. To avoid complicated integration, assurance for the latter case was studied using Bayesian Clinical Trial Simulation (BCTS). The findings indicate that assurance allows the experimenter to formally take into account the uncertainty surrounding the parameter estimates by using the prior distributions. Furthermore, BCTS can be easily implemented to find the required sample size without having to resort to complex integration.