Phase I clinical trials aim to find the maximum tolerated dose of an experimental drug. We consider dose escalation, de-escalation or staying at the current dose as three different stochastic moves over the lattice of a sequence of prespecified dose levels. Each move is chosen by minimizing an expected penalty that determines the dose level for treating the next cohort of patients. We develop a stopping rule under which the termination of the trial ensures that the posterior probability that the current dose is the maximum tolerated dose is larger than a prespecified value. Under a new class of priors, posterior estimates for the dose toxicity probabilities are obtained using the Markov chain Monte Carlo method. We demonstrate the new designs using a real phase I clinical trial.
Ji, Yuan; Li, Yisheng; and Yin, Guosheng, "Bayesian Dose-Finding Designs Based on a New Statistical Framework for Phase I Clinical Trials" (December 2005). UT MD Anderson Cancer Center Department of Biostatistics Working Paper Series. Working Paper 19.