Statistical considerations of phase 3 umbrella trials allowing adding one treatment arm mid-trial

Master protocols, in particular umbrella trials and platform trials, when evaluating multiple experimental treatments with a common control, could save patient resource, increase trial efficiency, and reduce drug development cost. Compared to the phase 3 platform trials that allow unlimited number of experimental arms to be added, it is more practical for individual companies to evaluate two experimental arms with a common control in an umbrella trial and allow the second experimental arm to be added at a later time. There have been limited research done in this type of trials in terms of statistical properties and guidance. In this article, we present statistical considerations of a phase 3 three-arm umbrella design including Type I error control and power, as well as the optimal allocation ratio. We intend to not only complement the existing literature, but more importantly to provide practical guidance to pave the way for its implementation by individual companies.