A Curve‐Free Method for Phase I Clinical Trials

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Abstract
Summary. Consider the problem of finding the dose that is as high as possible subject to having a controlled rate of toxicity. The problem is commonplace in oncology Phase I clinical trials. Such a dose is often called the maximum tolerated dose (MTD) since it represents a necessary trade‐off between efficacy and toxicity. The continual reassessment method (CRM) is an improvement over traditional up‐and‐down schemes for estimating the MTD. It is based on a Bayesian approach and on the assumption that the dose‐toxicity relationship follows a specific response curve, e.g., the logistic or power curve. The purpose of this paper is to illustrate how the assumption of a specific curve used in the CRM is not necessary and can actually hinder the efficient use of prior inputs. An alternative curve‐free method in which the probabilities of toxicity are modeled directly as an unknown multidimensional parameter is presented. To that purpose, a product‐of‐beta prior (PBP) is introduced and shown to bring about logical improvements. Practical improvements are illustrated by simulation results.

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