A variational approach to optimal two-stage designs

Recalculating the sample size in adaptive two-stage designs is a well-established method to gain flexibility in a clinical trial. Jennison and Turnbull (2015) proposed an "optimal" adaptive two-stage design based on the inverse normal combination test, which minimizes a mixed criterion of expected sample size under the alternative and conditional power. We demonstrate that the use of a combination test is not necessary to control the type one error rate and use variational techniques to develop a general adaptive design that is globally optimal under predefined optimality criteria. This approach yields to more efficient designs and furthermore allows to investigate the efficiency of the inverse normal method and the relation between local (interim-based) recalculation rules and global (unconditional) optimality of adaptive two-stage designs.