Designs for single- or multiple-agent phase I trials

Phase I trials of cytotoxic agents in oncology are usually dose-finding studies that involve a single cytotoxic agent. Many statistical methods have been proposed for these trials, all of which are based on the assumption of a monotonic dose-toxicity curve. For single-agent trials, this is a valid assumption. In many trials, however, investigators are interested in finding the maximally tolerated dose based on escalating multiple cytotoxic agents. When there are multiple agents, monotonicity of the dose-toxicity curve is not clearly defined. In this article we present a design for phase I trials in which the toxicity probabilities follow a partial order, meaning that there are pairs of treatments for which the ordering of the toxicity probabilities is not known at the start of the trial. We compare the new design to existing methods for simple orders and investigate the properties of the design for two partial orders.