Adaptive Phase I clinical trial design using Markov models for conditional probability of toxicity.

Many Phase I trials in oncology involve multiple-dose administrations on the same patient over multiple cycles, with a typical cycle lasting 3 weeks and having about six cycles per patient with a goal to find the maximum tolerated dose (MTD) and study the dose-toxicity relationship. A patient's dose is unchanged over the cycles and the data are reduced to a binary endpoint and the occurrence of a toxicity and analyzed by considering the toxicity either from the first dose or from any cycle on the study. In this article, an alternative approach allowing an assessment of toxicity from each cycle and dose variations for patient over cycles is presented. A Markov model for the conditional probability of toxicity on any cycle given no toxicity in previous cycles is formulated as a function of the current and previous doses. The extra information from each cycle provides more precise estimation of the dose-toxicity relationship. Simulation results demonstrating gains in using the Markov model as compared to analyses of a single binary outcome are presented. Methods for utilizing the Markov model to conduct a Phase I study, including choices for selecting doses for the next cycle for each patient, are developed and presented via simulation.