Bayesian adaptive linearization method for phase I drug combination trials with dimension reduction.

Many phase I drug combination designs have been proposed to find the maximum tolerated combination (MTC). Due to the two-dimension nature of drug combination trials, these designs typically require complicated statistical modeling and estimation, which limit their use in practice. In this article, we propose an easy-to-implement Bayesian phase I combination design, called Bayesian adaptive linearization method (BALM), to simplify the dose finding for drug combination trials. BALM takes the dimension reduction approach. It selects a subset of combinations, through a procedure called linearization, to convert the two-dimensional dose matrix into a string of combinations that are fully ordered in toxicity. As a result, existing single-agent dose-finding methods can be directly used to find the MTC. In case that the selected linear path does not contain the MTC, a dose-insertion procedure is performed to add new doses whose expected toxicity rate is equal to the target toxicity rate. Our simulation studies show that the proposed BALM design performs better than competing, more complicated combination designs.