Optimal designs for phase II clinical trials with heterogeneous patient populations

We consider single-arm phase II cancer clinical trials with tumor response as the primary outcome. Oftentimes, the patient population of a phase II clinical trial consists of subpopulations with different expected response rates. A well-accepted design in this case is to specify the response rate and the prevalence of each subpopulation, to compute the response rate of the whole population using the weighted (by prevalence) average of the response rates across subpopulations, and to find a standard phase II design, such as Simon's minimax or optimal design, for testing on the response rate of the whole population based on the unstratified binomial test. In such trials, while the response rate is the primary parameter and the prevalence of each subpopulation is a nuisance parameter, the validity of an unstratified statistical test for deciding acceptance or rejection of the experimental treatment is influenced by observed prevalence. In order to avoid bias due to the discrepancy between observed and specified values of the nuisance parameter, we have to use stratified test for such trials. In this paper, we propose optimal and minimax designs for stratified binomial test. We also develop a user-friendly interactive software to visualize the optimal designs and help users make correct statistical decisions.