Sequential designs for ordinal phase I clinical trials.

Sequential designs for phase I clinical trials which incorporate maximum likelihood estimates (MLE) as data accrue are inherently problematic because of limited data for estimation early on. We address this problem for small phase I clinical trials with ordinal responses. In particular, we explore the problem of the nonexistence of the MLE of the logistic parameters under a proportional odds model with one predictor. We incorporate the probability of an undetermined MLE as a restriction, as well as ethical considerations, into a proposed sequential optimal approach, which consists of a start-up design, a follow-on design and a sequential dose-finding design. Comparisons with nonparametric sequential designs are also performed based on simulation studies with parameters drawn from a real data set.