Consistency of continual reassessment method under model misspecification

This paper studies large sample behaviour of the continual reassessment method used to determine the target dose levels in phase I clinical trials. A sequential maximum likelihood procedure is investigated for local estimation of a given targeted toxicity level. Consistency and asymptotic normality for the maximum likelihood estimates are established under model misspecification and it is shown that, in general, the recommended dose level will converge to the target level. There are, however, situations in which the recommended dose may converge to a level close to the target level, but not necessarily the closest. This contrasts with the conclusions of O'Quigley, Pepe & Fisher (1990) and we describe this situation as well as providing the conditions under which convergence is assured.