Sequential Implementation of Stepwise Procedures for Identifying the Maximum Tolerated Dose

Abstract

This article considers the problem of finding the maximum tolerated dose (MTD) of a drug in human trials. The MTD is defined as the maximum test dose with toxicity probability less than or equal to a target toxicity rate. We adopt the multiple test framework, with step-down tests used in an escalation stage and step-up tests used in a deescalation stage, to allow sequential dose assignments for ethical purposes. By formulating the estimation problem as a testing problem, the proposed procedures formally control the error probability of selecting an unsafe dose. In addition, we can control the probability of correctly selecting the MTD under a parameter subspace where no toxicity probability lies in an interval bracketed by the target toxicity rate and an unacceptably high toxicity rate, the so-called “indifference zone.” This frequentist property, which is currently lacking in the conduct of dose-finding trials in humans, is appealing from a regulatory standpoint. We give the general expressions of the selection probabilities and apply some common statistical tests to the stepwise procedure. The design parameters are calibrated so that the average number of patients receiving an overdose is kept low. From a practical viewpoint, stepwise tests are simple and easy to understand, and the sequential implementation operates in a manner similar to the traditional algorithm familiar to clinicians. Extensive simulations illustrate that our methods yield good, competitive operating characteristics under a wide range of scenarios with realistic sample size and performs well even in situations in which other existing methods may fail, namely when the dose–toxicity curve is flat up to the targeted MTD.