Optimal continuous-monitoring design of single-arm phase II trial based on the simulated annealing method

Simon's two-stage design is commonly used in phase II single-arm clinical trials because of its simplicity and smaller sample size under the null hypothesis compared to the one-stage design. Some studies extend this design to accommodate more interim analyses (i.e., three-stage or four-stage designs). However, most of these studies, together with the original Simon's two-stage design, are based on the exhaustive search method, which is difficult to extend to high-dimensional, general multi-stage designs. In this study, we propose a simulated annealing (SA)-based design to optimize the early stopping boundaries and minimize the expected sample size for multi-stage or continuous monitoring single-arm trials. We compare the results of the SA method, the decision-theoretic method, the predictive probability method, and the posterior probability method. The SA method can reach the smallest expected sample sizes in all scenarios under the constraints of the same type I and type II errors. The expected sample sizes from the SA method are generally 10-20% smaller than those from the posterior probability method or the predictive probability method, and are slightly smaller than those from the decision-theoretic method in almost all scenarios. The SA method offers an excellent alternative in designing phase II trials with continuous monitoring.