Optimal futility stopping boundaries for binary endpoints.

The choice of the futility boundary and the time point of the interim analysis have a major impact on the properties of the study design. Therefore, they should be thoroughly investigated at the planning stage. The introduced method of selecting optimal futility boundaries provides a more flexible alternative to Simon's designs with non-binding stopping rules. The probability of wrongly stopping for futility is minimized and the optimized futility boundaries don't exhibit the unfavorable properties of an undesirably high probability of falsely declaring futility or a high proportion of the planned sample evaluated at the interim time point.