Phase I trial design for drug combinations with Bayesian model averaging.

Various statistical models have been proposed for two-dimensional dose finding in drug-combination trials. However, it is often a dilemma to decide which model to use when conducting a particular drug-combination trial. We make a comprehensive comparison of four dose-finding methods, and for fairness, we apply the same dose-finding algorithm under the four model structures. Through extensive simulation studies, we compare the operating characteristics of these methods in various practical scenarios. The results show that different models may lead to different design properties and that no single model performs uniformly better in all scenarios. As a result, we propose using Bayesian model averaging to overcome the arbitrariness of the model specification and enhance the robustness of the design. We assign a discrete probability mass to each model as the prior model probability and then estimate the toxicity probabilities of combined doses in the Bayesian model averaging framework. During the trial, we adaptively allocated each new cohort of patients to the most appropriate dose combination by comparing the posterior estimates of the toxicity probabilities with the prespecified toxicity target. The simulation results demonstrate that the Bayesian model averaging approach is robust under various scenarios.