Pareto-Optimal Designs for Two-Stage Phase II Trials

Music City Center 

Phase II single-arm trials with binary endpoints often use Simon's two-stage minimax and optimal designs. These designs are derived by first identifying feasible solutions constrained by type I and II error rates. The minimax design minimizes total sample size, while the optimal design minimizes expected sample size under the null response rate. However, because they do not explicitly optimize error rates, their estimated values often deviate from the targets. To address this limitation, we propose the Pareto optimal design, which applies multi-objective optimization (MOO) to generate a Pareto frontier, improving alignment between estimated and desired error rates. This approach also enhances the probability of early termination when the null response rate holds. Furthermore, we demonstrate the use of a genetic algorithm (GA)-based MOO framework to efficiently identify Pareto-optimal designs.

Phase II

Simon's two-stage design

Pareto frontier

Multi-objective optimization 

Biopharmaceutical Section