A Non-parametric Approach to the Design and Analysis of Two-dimensional Dose-finding Trials

This paper investigates the design and analysis of dose-finding trials with two agents. The set of doses for each agent is fixed in advance. The goal of the trial is to find the set of dose combinations with probability of toxicity closest to a pre-specified value. For each of the two agents we assume that the probability of toxicity of an agent is non-decreasing with dose when the dose of the other agent is fixed. Using this assumption we construct a new non-parametric design that operates on a two-dimensional grid of all possible dose combinations. A bivariate isotonic regression estimator of the maximum tolerated combinations is described. We conclude that the new design and the bivariate isotonic estimator are superior to the procedure where several independent dose-finding trials are run.