On the coherence of model-based dose-finding designs for drug combination trials

The concept of coherence was proposed for single-agent phase I clinical trials to describe the property that a design never escalates the dose when the most recently treated patient has toxicity and never de-escalates the dose when the most recently treated patient has no toxicity. It provides a useful theoretical tool for investigating the properties of phase I trial designs. In this paper, we generalize the concept of coherence to drug combination trials, which are substantially different and more challenging than single-agent trials. For example, in the dose-combination matrix, each dose has up to 8 neighboring doses as candidates for dose escalation and de-escalation, and the toxicity orders of these doses are only partially known. We derive sufficient conditions for a model-based drug combination trial design to be coherent. Our results are more general and relaxed than the existing results and are applicable to both single-agent and drug combination trials. We illustrate the application of our theoretical results with a number of drug combination dose-finding designs in the literature.