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Primarily motivated by the drug development process, several publicationshave now presented methodology for the design of multi-arm multi-stageexperiments with normally distributed outcome variables of known variance.Here, we extend these past considerations to allow the design of what we referto as an abcd multi-arm multi-stage experiment. We provide a proof of howstrong control of the a-generalised type-I familywise error-rate can beensured. We then describe how to attain the power to reject at least b out of cfalse hypotheses, which is related to controlling the b-generalised type-IIfamilywise error-rate. Following this, we detail how a design can be optimisedfor a scenario in which rejection of any d null hypotheses brings abouttermination of the experiment. We achieve this by proposing a highlycomputationally efficient approach for evaluating the performance of acandidate design. Finally, using a real clinical trial as a motivating example,we explore the effect of the design's control parameters on the statisticaloperating characteristics.

Efficient determination of optimised multi-arm multi-stage experimental designs with control of generalised error-rates