Summary Much of the statistical methodology underlying the experimental design of phase 1 trials in oncology is intended for studies involving a single cytotoxic agent. The goal of these studies is to estimate the maximally tolerated dose, the highest dose
that can be administered with an acceptable level of toxicity. A fundamental assumption of these methods is monotonicity of the dose–toxicity curve. This is a reasonable assumption for single‐agent trials in which the administration of greater doses of the agent can be expected
to produce dose‐limiting toxicities in increasing proportions of patients. When studying multiple agents, the assumption may not hold because the ordering of the toxicity probabilities could possibly be unknown for several of the available drug combinations. At the same time, some of
the orderings are known and so we describe the whole situation as that of a partial ordering. In this article, we propose a new two‐dimensional dose‐finding method for multiple‐agent trials that simplifies to the continual reassessment method (CRM), introduced by O'Quigley, Pepe, and Fisher (1990, Biometrics46, 33–48), when the ordering is fully known. This design enables us to relax the assumption of a monotonic dose–toxicity curve. We compare our approach and some simulation results to a CRM design
in which the ordering is known as well as to other suggestions for partial orders.
Department of Mathematics and Computer Science, Hampden-Sydney College, Hampden-Sydney, Virginia 23943, U.S.A. 2:
Division of Biostatistics and Epidemiology, Department of Public Health Sciences, University of Virginia, Charlottesville, Virginia 22908, U.S.A. 3:
Inserm, Université Paris VI, Place Jussieu, 75005 Paris, France