Toxicity-dependent feasibility bounds for the escalation with overdose control approach in phase I cancer trials

Phase I trials of anti-cancer therapies aim to identify a maximum tolerated dose (MTD), defined as the dose that causes unacceptable toxicity in a target proportion of patients. Both rule-based and model-based methods have been proposed for MTD recommendation. The escalation with overdose control (EWOC) approach is a model-based design where the dose assigned to the next patient is one that, given all available data, has a posterior probability of exceeding the MTD equal to a pre-specified value known as the feasibility bound. The aim is to conservatively dose-escalate and approach the MTD, avoiding severe overdosing early on in a trial. The EWOC approach has been applied in practice with the feasibility bound either fixed or varying throughout a trial, yet some of the methods may recommend incoherent dose-escalation, that is, an increase in dose after observing severe toxicity at the current dose. We present examples where varying feasibility bounds have been used in practice, and propose a toxicity-dependent feasibility bound approach that guarantees coherent dose-escalation and incorporates the desirable features of other EWOC approaches. We show via detailed simulation studies that the toxicity-dependent feasibility bound approach provides improved MTD recommendation properties to the original EWOC approach for both discrete and continuous doses across most dose-toxicity scenarios, with comparable performance to other approaches without recommending incoherent dose escalation.