Coherence principles in dose-finding studies

This paper studies the coherence conditions of dose-finding methods in the context of phase I clinical trials, where the objective is to estimate a targeted quantile of the unknown dose-toxicity curve. Most phase I methods are outcome-adaptive, and thus escalate or de-escalate doses for future patients based on the previous observations. An escalation for a new patient is said to be coherent only when the previous patient does not show sign of toxicity. Likewise, a de-escalation is coherent only when a toxic outcome has just been seen. The coherence conditions, motivated by ethical concerns in trial conduct, are satisfied by many statistical designs in the literature, but not by some commonly used modifications of the methods. This paper shows examples in which coherence is violated, and discusses how the coherence principles may be applied to calibrate a two-stage design and to deal with situations with delayed toxicity.