Interval designs have recently attracted enormous attention due to their simplicity and desirable properties. We develop a Bayesian optimal interval design for dose finding in drug-combination trials. To determine the next dose combination based on the cumulative data, we propose an allocation rule by maximizing the posterior probability that the toxicity rate of the next dose falls inside a prespecified probability interval. The entire dose-finding procedure is nonparametric (model-free), which is thus robust and also does not require the typical "nonparametric" prephase used in model-based designs for drug-combination trials. The proposed two-dimensional interval design enjoys convergence properties for large samples. We conduct simulation studies to demonstrate the finite-sample performance of the proposed method under various scenarios and further make a modication to estimate toxicity contours by parallel dose-finding paths. Simulation results show that on average the performance of the proposed design is comparable with model-based designs, but it is much easier to implement.
Keywords: Dose finding; drug combination; interval design; maximum tolerated dose; nonparametric method; toxicity contour.