Abstract: 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.
Key words and phrases: Markov chain Monte Carlo, penalty, stopping rule, stochastic moves, toxicity.