Testing non-inferiority for three-arm trials under the class of log transformation model

Non-inferiority (NI) trials are used to determine if new treatments are not worse than a reference treatment by more than a pre-specified margin. If the use of a placebo is ethically justifiable, it is advised that an additional placebo group is included in trials for validation of assay sensitivity and constancy. This constitutes a three-arm clinical trial with a placebo. In this article, we consider assessing the NI of a new treatment in three-arm trials with time to event data subject to right censoring. Under the class of log transformation models, we propose a testing procedure for determining NI based on the infimum of ratio of the difference between the survival functions of new treatment and the placebo to that of the reference treatment and the placebo. The proposed test statistics relies on the estimated treatment parameters and survival function evaluated at the end of follow-up and their estimated standard errors. Simulation studies demonstrate that the proposed test can control type I errors well and detect the NI effectively with moderate and large samples.