A surface-free design for phase I dual-agent combination trials

In oncology, there is a growing number of therapies given in combination. Recently, several dose-finding designs for Phase I dose-escalation trials for combinations were proposed. The majority of novel designs use a pre-specified parametric model restricting the search of the target combination to a surface of a particular form. In this work, we propose a novel model-free design for combination studies, which is based on the assumption of monotonicity within each agent only. Specifically, we parametrise the ratios between each neighbouring combination by independent Beta distributions. As a result, the design does not require the specification of any particular parametric model or knowledge about increasing orderings of toxicity. We compare the performance of the proposed design to the model-based continual reassessment method for partial ordering and to another model-free alternative, the product of independent beta design. In an extensive simulation study, we show that the proposed design leads to comparable or better proportions of correct selections of the target combination while leading to the same or fewer average number of toxic responses in a trial.