Optimal adaptive two-stage designs for single-arm trial with binary   endpoint
  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. 
Kevin Kunzmann and Meinhard Kieser
stat.AP