Two-Dimensional Dose Finding in Discrete Dose Space

The objective of a Phase I trial with two agents is to find a set of maximum-tolerated dose combinations that yield a prespecified toxicity rate. In this article, we consider the case where several doses of one agent are fixed and the goal is to find the maximum-tolerated dose of the other agent to be used in combination with each of the doses of agent one. We propose a Bayesian design that uses a parsimonious working model for the dose-toxicity relationship. We show that the new design is more effective in identifying the maximum-tolerated combinations than one-dimensional designs applied at each dose level of one of the agents.