  Multi-arm multi-stage trial designs can bring notable gains in efficiency to
the drug development process. However, for normally distributed endpoints, the
determination of a design typically depends on the assumption that the patient
variance in response is known. In practice, this will not usually be the case.
To allow for unknown variance, previous research explored the performance of
t-test statistics, coupled with a quantile substitution procedure for modifying
the stopping boundaries, at controlling the familywise error-rate to the
nominal level. Here, we discuss an alternative method based on Monte Carlo
simulation that allows the group size and stopping boundaries of a multi-arm
multi-stage t-test to be optimised according to some nominated optimality
criteria. We consider several examples, provide R code for general
implementation, and show that our designs confer a familywise error-rate and
power close to the desired level. Consequently, this methodology will provide
utility in future multi-arm multi-stage trials.
