Two-dimensional calibration-free odds design for phase I drug-combination trials

In oncology, it is commonplace to treat patients with a combination of drugs that deliver different effects from different disease-curing or cancer-elimination perspectives. Such drug combinations can often achieve higher efficacy in comparison with single-drug treatment due to synergy or non-overlapping toxicity. Due to the small sample size, there is a growing need for efficient designs for phase I clinical trials, especially for drug-combination trials. In the existing experimental design for phase I drug-combination trials, most of the proposed methods are parametric and model-based, either requiring tuning parameters or prior knowledge of the drug toxicity probabilities. We propose a two-dimensional calibration-free odds (2dCFO) design for drug-combination trials, which utilizes not only the current dose information but also that from all the neighborhood doses (i.e., along the left, right, up and down directions). In contrast to interval-based designs which only use the current dose information, the 2dCFO is more efficient and makes more accurate decisions because of its additional leverage over richer resources of neighborhood data. Because our design makes decisions completely based on odds ratios, it does not rely upon any dose-toxicity curve assumption. The simulations show that the 2dCFO delivers satisfactory performances in terms of accuracy and efficiency as well as demonstrating great robustness due to its non-parametric or model-free nature. More importantly, the 2dCFO only requires the minimal specification of the target toxicity probability, which greatly eases the design process from the clinicians' aspects.