Sample size determination for time-to-event endpoints in randomized selection trials with generalized exponential distribution

Randomized selection trials are frequently used to compare experimental treatments that have the potential to be beneficial, but they often do not include a control group. While time-toevent endpoints are commonly applied in clinical investigations, methodologies for determining the required sample size for such endpoints, except exponential distribution, are lacking. In recent times, there has been a shift in clinical trials, with a growing emphasis on progressionfree survival as a primary endpoint. However, the utilization of this measure has typically been restricted to specific time points for both sample size determination and analysis. This alteration in approach could wield a substantial influence on the clinical trial process, potentially diminishing the capacity to discern variances between treatment groups. In the calculation of sample sizes for randomized trials, this investigation operates under the assumption that the time-to-event endpoint conforms to either an exponential, Weibull, or generalized exponential distribution.