An application of reinforced urn processes to determining maximum tolerated dose

Based on reinforced urn process introduced by Muliere et al. [2000. Urn schemes and reinforced random walks. Stochastic Process. Appl. 88(1), 59-78] we propose a Bayesian nonparametric approach to analyse a design determining the maximum tolerated dose (MTD) in Phase I clinical trials for new drug development when intrapatient dose escalation is allowed. A predictive distribution of MTD is obtained and its point estimation may consist in the corresponding expected value.