Bayesian dose finding for combined drugs with discrete and continuous doses

The trend of treating patients with combined drugs has grown in cancer clinical trials. Often, evaluating the synergism of multiple drugs is the pri- mary motivation for such drug-combination studies. To enhance patient response, a new agent is often investigated together with an existing standard of care (SOC) agent. Often, a certain amount of dosage of the SOC is administered in order to maintain at least some therapeutic e®ects in patients. For clinical trials in- volving a continuous-dose SOC and a discrete-dose agent, we propose a two-stage Bayesian adaptive dose-finding design. The first stage takes a continual reassess- ment method to locate the appropriate dose for the discrete-dose agent while fixing the continuous-dose SOC at the minimal therapeutic dose. In the second stage, we make a fine dose adjustment by calibrating the continuous dose to achieve the target toxicity rate as closely as possible. Dose escalation or de-escalation is based on the posterior estimates of the joint toxicity probabilities of combined doses. As the toxicity data accumulate during the trial, we adaptively assign each cohort of patients to the most appropriate dose combination. We conduct extensive simu- lation studies to examine the operating characteristics of the proposed two-stage design and demonstrate the design's good performance with practical scenarios.