Sample size calculations for noninferiority trials for time-to-event data using the concept of proportional time

Noninferiority trials intend to show that a new treatment is ‘not worse'' than a standard-of-care active control and can be used as an alternative when it is likely to cause fewer side effects compared to the active control. In the case of time-to-event endpoints, existing methods of sample size calculation are done either assuming proportional hazards between the two study arms, or assuming exponentially distributed lifetimes. In scenarios where these assumptions are not true, there are few reliable methods for calculating the sample sizes for a time-to-event noninferiority trial. Additionally, the choice of the non-inferiority margin is obtained either from a meta-analysis of prior studies, or strongly justifiable ‘expert opinion'', or from a ‘well conducted'' definitive large-sample study. Thus, when historical data do not support the traditional assumptions, it would not be appropriate to use these methods to design a noninferiority trial. For such scenarios, an alternate method of sample size calculation based on the assumption of Proportional Time is proposed. This method utilizes the generalized gamma ratio distribution to perform the sample size calculations. A practical example is discussed, followed by insights on choice of the non-inferiority margin, and the indirect testing of superiority of treatment compared to placebo.KEYWORDS: Generalized gamma, noninferiority, non-proportional hazards, proportional time, relative time, sample size