Sequential designs for logistic phase I clinical trials.
Both parametric and nonparametric sequential designs and estimation methods are implemented in phase I clinical trials. In this article, we take a systematic approach, consisting of a start-up design, a follow-on design, a sequential dose-finding design, and an estimation method, to find an efficient estimate of the maximum tolerated dose under the assumption that the dose-response curve has a true underlying logistic distribution. In particular, for the problem of the nonexistence of the maximum likelihood estimates of the logistic parameters, a constraint on the probability of an undetermined maximum likelihood estimator (MLE) is incorporated into the parametric sequential designs. In addition, this approach can also be extended to incorporate ethical considerations, which prohibit an administered dose from exceeding the maximum acceptable dose. Comparison based on simulation studies between the systematic designs and nonparametric designs are described both for continuous dose spaces and discrete dose spaces, respectively.