An optimal stratified Simon two-stage design

In Phase II oncology trials, therapies are increasingly being evaluated for their effectiveness in specific populations of interest. Such targeted trials require designs that allow for stratification based on the participants' molecular characterisation. A targeted design proposed by Jones and Holmgren (JH) Jones CL, Holmgren E: 'An adaptive Simon two-stage design for phase 2 studies of targeted therapies', Contemporary Clinical Trials 28 (2007) 654-661.determines whether a drug only has activity in a disease sub-population or in the wider disease population. Their adaptive design uses results from a single interim analysis to decide whether to enrich the study population with a subgroup or not; it is based on two parallel Simon two-stage designs. We study the JH design in detail and extend it by providing a few alternative ways to control the familywise error rate, in the weak sense as well as the strong sense. We also introduce a novel optimal design by minimising the expected sample size. Our extended design contributes to the much needed framework for conducting Phase II trials in stratified medicine.