Sample size calculation for randomized selection trials with a time-to-event endpoint and a margin of practical equivalence

Selection trials are used to compare potentially active experimental treatments without a control arm. While sample size calculation methods exist for binary endpoints, no such methods are available for time-to-event endpoints, even though these are ubiquitous in clinical trials. Recent selection trials have begun using progression-free survival as their primary endpoint, but have dichotomized it at a specific time point for sample size calculation and analysis. This changes the clinical question and may reduce power to detect a difference between the arms. In this article, we develop the theory for sample size calculation in selection trials where the time-to-event endpoint is assumed to follow an exponential or Weilbull distribution. We provide a free web application for sample size calculation, as well as an R package, that researchers can use in the design of their studies.