Dynamic ordering design for dose finding in drug-combination trials

Drug-combination studies have become increasingly popular in oncology. One of the critical concerns in phase I drug-combination trials is the uncertainty in toxicity evaluation. Most of the existing phase I designs aim to identify the maximum tolerated dose (MTD) by reducing the two-dimensional searching space to one dimension via a prespecified model or splitting the two-dimensional space into multiple one-dimensional subspaces based on the partially known toxicity order. Nevertheless, both strategies often lead to complicated trials which may either be sensitive to model assumptions or induce longer trial durations due to subtrial split. We develop two versions of dynamic ordering design (DOD) for dose finding in drug-combination trials, where the dose-finding problem is cast in the Bayesian model selection framework. The toxicity order of dose combinations is continuously updated via a two-dimensional pool-adjacent-violators algorithm, and then the dose assignment for each incoming cohort is selected based on the optimal model under the dynamic toxicity order. We conduct extensive simulation studies to evaluate the performance of DOD in comparison with four other commonly used designs under various scenarios. Simulation results show that the two versions of DOD possess competitive performances in terms of correct MTD selection as well as safety, and we apply both versions of DOD to two real oncology trials for illustration.