• three-arm design;
  • non-inferiority trial;
  • prespecified non-inferiority margin;
  • assay sensitivity;
  • optimal allocation;
  • bivariate normal distribution


Three-arm trials including the experimental treatment, an active reference treatment and a placebo are recommended in the guidelines of the ICH and EMEA/CPMP as a useful approach to the assessment of assay sensitivity. Generally, the acceptable non-inferiority margin Δ has been defined as the maximum clinically irrelevant difference between treatments in many two-arm non-inferiority trials. However, many recent articles discussing three-arm trials have considered a design with unknown Δ which is the prespecified fraction f of unknown effect size of the reference drug, where the prespecified fraction f is treated as if it were a revised margin. Therefore, these methods cannot be applied to the case where the acceptable non-inferiority margin must be a prespecified difference between treatments.

In this paper, we propose a statistical test procedure for three-arm non-inferiority trials with the margin Δ defined as a prespecified difference between treatments under the situation that the primary endpoints are normally distributed with a common, but unknown, variance. In addition, we derive the optimal allocation that minimizes the total sample size. The proposed method is illustrated with data on a randomized controlled trial on major depressive disorder. Copyright © 2010 John Wiley & Sons, Ltd.