A multi-arm multi-stage design for trials with all pairwise testing

Abstract: Multi-arm multi-stage (MAMS) trials have gained popularity to enhance the efficiency of clinical trials, potentially reducing both duration and costs. This paper focuses on designing MAMS trials where no control treatment exists. This can arise when multiple standard treatments are already established or no treatment is available for a severe disease, making it unethical to withhold a potentially helpful option. The proposed design incorporates interim analyses to allow early termination of notably worst treatments and stops the trial entirely if all remaining treatments are performing similarly. The proposed design controls the familywise error rate (FWER) for all pairwise comparisons and provides the conditions guaranteeing FWER control in the strong sense. The FWER and power are used to calculate both the stopping boundaries and the sample size required. Analytic solutions to compute the expected sample size are also derived. A trial motivated by a study conducted in sepsis, where there was no control treatment, is shown. The multi-arm multi-stage all pairwise (MAMSAP) design proposed here is compared to multiple different approaches. For the trial studied, the proposed method yields the lowest required maximum and expected sample size when controlling the FWER and power at the desired levels.