Group sequential design for time-to-event data using the concept of proportional time

Sequential monitoring of efficacy and safety is an important part of clinical trials. A Group Sequential design allows researchers to perform interim monitoring after groups of patients have completed the study. Statistical literature is well developed for continuous and binary outcomes and relies on asymptotic normality of the test statistic. However, in the case of time-to-event data, existing methods of sample size calculation are done either assuming proportional hazards or assuming exponentially distributed lifetimes. In scenarios where these assumptions are not true, as evidenced from historical data, these traditional methods are restrictive and cannot always be used. As interim monitoring is driven by ethical, financial, and administrative considerations, it is imperative that sample size calculations be done in an efficient manner keeping in mind the specific needs of a clinical trial with a time-to-event outcome. To address these issues, a novel group sequential design is proposed using the concept of Proportional Time. This method utilizes the generalized gamma ratio distribution to calculate the efficacy and safety boundaries and can be used for all distributions that are members of the generalized gamma family using an error spending approach. The design incorporates features specific to survival data such as loss to follow-up, administrative censoring, varying accrual times and patterns, binding or non-binding futility rules with or without skips, and flexible alpha and beta spending mechanisms. Three practical examples are discussed, followed by discussion of the important aspects of the proposed design.