Simons optimal two-stage design has been widely used in early phase clinical trials for Oncology and AIDS studies with binary endpoints.With this approach,the second stage sample size is fixed when the trial passes the first stage with sufficient activity.Adaptive designs,such as those due to Banerjee and Tsiatis(2006)and Englert and Kieser(2013),are flexible in the sense that the second stage sample size depends on the response from the first stage,and these designs are often seen to reduce the expected sample size under the null hypothesis as compared to Simons approach.An unappealing trait of the existing designs is that they are not associated with a second stage sample size which is a non-increasing function of the first stage response rate.