Constrained Bayesian Optimal Designs for Phase I Clinical Trials: Continuous Dose Space

We derive constrained Bayesian D-optimal designs for efficient estimation in phase I clinical trials with binary responses on a continuous dose space. The constraint is based on ethical considerations that patients cannot be assigned to highly toxic doses. We find that a naive restriction on the dose space, requiring patients to be assigned below the mean of a quantile, is about as effective as the more computationally intensive constrained designs.