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Minimizing the number of patients exposed to potentially harmful drugs inearly onco logical trials is a major concern during planning. Adaptive designsaccount for the inherent uncertainty about the true effect size by determiningthe final sample size within an ongoing trial after an interim look at thedata. We formulate the problem of finding adaptive designs which minimizeexpected sample size under the null hypothesis for single-arm trials withbinary outcome as an integer linear program. This representation can be used toidentify optimal adaptive designs which improve previous designs in two ways:Firstly, designs can be found exhibiting lower expected sample size under thenull hypothesis than those provided by previous algorithms. Secondly, weexplain how integer programming techniques can be exploited to removepathologies of the optimal and previous solutions arising from the discretenature of the underlying statistics. The resulting designs are both efficientin terms of expected sample size under the null hypothesis and wellinterpretable.

Optimal adaptive two-stage designs for single-arm trial with binary endpoint