  Minimizing the number of patients exposed to potentially harmful drugs in
early onco logical trials is a major concern during planning. Adaptive designs
account for the inherent uncertainty about the true effect size by determining
the final sample size within an ongoing trial after an interim look at the
data. We formulate the problem of finding adaptive designs which minimize
expected sample size under the null hypothesis for single-arm trials with
binary outcome as an integer linear program. This representation can be used to
identify optimal adaptive designs which improve previous designs in two ways:
Firstly, designs can be found exhibiting lower expected sample size under the
null hypothesis than those provided by previous algorithms. Secondly, we
explain how integer programming techniques can be exploited to remove
pathologies of the optimal and previous solutions arising from the discrete
nature of the underlying statistics. The resulting designs are both efficient
in terms of expected sample size under the null hypothesis and well
interpretable.
