An Assessment of Up-and-Down Designs and Associated Estimators in Phase I Trials

In this article, we consider some up-and-down designs that are discussed in Ivanova et al. (2003) for estimating the maximum tolerated dose (MTD) in phase I trials: the biased coin design, k-in-a-row rule, Narayana rule, and continual reassessment method (CRM). A large-scale Monte Carlo simulation study, which is substantially more extensive than Ivanova et al. (2003), is conducted to examine the performance of these five designs for different sample sizes and underlying dose-response curves. For the estimation of MTD, we propose a modified maximum likelihood estimator (MMLE) in addition to those in Ivanova et al. (2003). The selection of different dose-response curves and their parameters allows us to evaluate the robustness features of the designs as well as the performance of the estimators. The results obtained, in addition to revealing that the new estimator performs better than others in many situations, enable us to make recommendations on designs.