On sample size determination in multi-armed confirmatory adaptive designs

An important application of confirmatory adaptive designs is the data-driven selection of treatment arms in multi-armed trials. A general methodology for adaptive designs is based on the combination testing principle. Using this principle, selection of treatment arms in multi-armed designs, recalculation of sample size, and more general data-driven changes to the design are possible without undermining type I error control. In this paper we consider aspects related to the sample size determination for multi-armed designs. We assess sample size calculations that are based on ad hoc formulas such as the Bonferroni correction. An important aspect will be the choice of the control group sample size. We further consider the weighting scheme in the combination testing approach. Our assessment is restricted to two-stage designs. In general, simulation tools will be necessary to assess the statistical properties of these designs.