A Multi-Stage Drop-the-Loser Design With Superiority Boundaries

Multi-arm multi-stage (MAMS) trials have gained popularity, due to their improved efficiency in evaluating multiple treatments. A traditional MAMS trial often decreases the expected sample size of the trial compared with just running a multi-arm approach, but with the drawback of an increase in maximum sample size. For academic led trials, this poses a particular challenge, as funding is typically based on the maximum required sample size. To address this, drop-the-loser designs were introduced, where a fixed number of treatments are dropped at each interim stage, thereby reducing the maximum sample size. In this work, we propose an enhanced multi-stage drop-the-loser design that also allows for early stopping of the entire trial for superiority. This approach aims to retain the benefits of a reduced maximum sample size while also lowering the expected sample size. The proposed design is motivated by a trial in atrial fibrillation. We derive analytical expressions for the type I error rate, power, and expected sample size, and compare the proposed design's performance to alternative methods. We outline the key requirements for implementing the proposed design and discuss the contexts in which it should be considered. For the motivating example, the results show that the proposed design substantially reduces the expected sample size compared to a standard drop-the-loser design, while lowering the maximum sample size relative to running a traditional MAMS trial or multiple separate trials.