A Bayesian dose finding design for clinical trials combining a cytotoxic agent with a molecularly targeted agent

Novel molecularly targeted agents (MTAs) have emerged as valuable alternatives or complements to traditional cytotoxic agents in the treatment of cancer. Clinicians are combining cytotoxic agents with MTAs in a single trial to achieve treatment synergism and better outcomes for patients. An important feature of such combinational trials is that, unlike the efficacy of the cytotoxic agent, that of the MTA may initially increase at low dose levels and then approximately plateau at higher dose levels as MTA saturation levels are reached. Therefore, the goal of the trial is to find the optimal dose combination that yields the highest efficacy with the lowest toxicity and meanwhile satisfies a certain safety requirement. We propose a Bayesian phase I-II design to find the optimal dose combination. We model toxicity by using a logistic regression and propose a novel proportional hazard model for efficacy, which accounts for the plateau in the MTA dose-efficacy curve. We evaluate the operating characteristics of the proposed design through simulation studies under various practical scenarios. The results show that the design proposed performs well and selects the optimal dose combination with high probability.