Methods of designing two-stage winner trials with survival outcomes

In drug development, especially for oncology studies, a recent proposal is to combine a costly phase II dose selection study with a subsequent phase III study into a single trial that compares the selected (winning) dose from the first stage with the control group. This design may also be used in phase III trials, in which the winning active treatment regimen, selected at the first stage, is compared with the control group at the second stage. This design is known as a two-stage winner design, as proposed by Shun et al. (2008) for continuous outcomes. Time-to-event data are often analyzed in oncology trials. In order to derive the critical value and power of this design, per Shun et al. (2008), it is essential to calculate the asymptotic covariance and correlation of the log-rank statistics for survival outcomes between the two stages. In this paper, we derive the asymptotic covariance and correlation, and provide additional approximate design parameters. Examples are given to illustrate the method, and simulations are performed to evaluate the veracity of these approximate design parameters.