Testing non-inferiority for three-arm trials under the PH model

The objective of non-inferiority (NI) trials is to show that a new treatment is not worse than a reference treatment by more than a pre-specified margin. For ethical reasons, NI trials usually do not include a placebo arm such that neither the assay sensitivity nor the constancy can be validated. On the other hand, three-arm NI trials consisting of the new treatment, reference treatment, and placebo, can simultaneously test the superiority of the new treatment over placebo and the NI of the new treatment compared with the reference treatment. In this article, we consider assessing NI of a new treatment in three-arm trials with time to event outcomes subject to right censoring. Under the proportional hazards model, we develop a testing procedure for assessing NI based on the infimum of ratio of survival difference between the new treatment and the placebo to that between the reference treatment and the placebo within a specific time period. The proposed test statistics involves the estimates of treatment parameters and survival function evaluated at a specific time point and their corresponding standard error estimates. Simulation study indicates that the proposed test controls the type I error well and has decent power to detect the NI under moderate to large sample settings.