Throughout recent years, there has been a rapidly increasing interest regarding the evaluation of so-called targeted therapies. These therapies are assumed to show a greater benefit in a pre-specified subgroup of patientscommonly identified by a predictive biomarkeras compared to the total patient population of interest. This situation has led to the necessity to develop biostatistical methods allowing an efficient evaluation of such treatments. Among others, adaptive enrichment designs have been proposed as a solution. These designs allow the selection of the most promising patient population based on an efficacy analysis at interim and restricting recruitment to these patients afterwards. As has recently been shown, the performance of the applied interim decision rule in such a design plays a crucial role in ensuring a successful trial. In this work, we investigate the situation when the primary outcome of the trial is a binary variable. Optimal decision rules are derived which incorporate the uncertainty about the treatment effects. These optimal decision rules are evaluated with respect to their performance in an adaptive enrichment design in terms of correct selection probability and power, and are compared to proposed ad hoc decision rules. Our methods are illustrated by means of a clinical trial example.