A Comparative study of the Estimation of the Maximum Tolerated Dose

Dose-response analysis (DRA) has been a very popular topic within statistical estimation especially in biomedical areas. In addition to estimating the entire dose-response relationship, assessing the risk itself at a certain dose level has been of much interest in some applications, such as in estimating the maximum tolerated dose (MTD) in Phase I clinical trials. Although a variety of parametric dose-response models have been proposed and successfully used in practice, many of the exiting models may not be appropriate in terms of capturing the underlying shape of the dose-response curve. As the estimation of the MTD depends crucially on the assumed dose-response curve, we explore both parametric and nonparametric methods. In addition, we compare both frequentist and Bayesian MTD estimation methods and propose new approaches that are based on Bernstein polynomials to model a dose-response function, which is ∗Seung Jun Shin is a graduate student and Sujit K. Ghosh is a Professor, both in the Department of Statistics at North Carolina State University, Raleigh, NC 27695-8203. Emails: [email protected] and [email protected]