  Primarily motivated by the drug development process, several publications
have now presented methodology for the design of multi-arm multi-stage
experiments with normally distributed outcome variables of known variance.
Here, we extend these past considerations to allow the design of what we refer
to as an abcd multi-arm multi-stage experiment. We provide a proof of how
strong control of the a-generalised type-I familywise error-rate can be
ensured. We then describe how to attain the power to reject at least b out of c
false hypotheses, which is related to controlling the b-generalised type-II
familywise error-rate. Following this, we detail how a design can be optimised
for a scenario in which rejection of any d null hypotheses brings about
termination of the experiment. We achieve this by proposing a highly
computationally efficient approach for evaluating the performance of a
candidate design. Finally, using a real clinical trial as a motivating example,
we explore the effect of the design's control parameters on the statistical
operating characteristics.
