Randomized phase II selection design with order constrained strata

The exploratory nature of phase II trials makes it quite common to include heterogeneous patient subgroups with different prognoses in the same trial. Incorporating such patient heterogeneity or stratification into statistical calculation for sample size can improve efficiency and reduce sample sizes in single-arm phase II trials with binary outcomes. However, such consideration is lacking in randomized phase II trials. In this paper, we propose methods that can utilize some natural order constraints that may exist in stratified population to gain statistical efficiency for randomized phase II designs. For thoroughness and simplicity, we focus on the randomized phase II selection designs in this paper, although our method can be easily generalized to the randomized phase II screening designs. We consider both binary and time-to-event outcomes in our development. Compared with methods that do not use order constraints, our method is shown to improve the probabilities of correct selection or reduce sample size in our simulation and real examples.