This paper addresses the dose-finding problem in cancer trials in which we are concerned with the gradation of severe toxicities that are considered dose limiting. In order to differentiate the tolerance for different toxicity types and grades, we propose a novel extension of the continual reassessment method that explicitly accounts for multiple toxicity constraints. We apply the proposed methods to redesign a bortezomib trial in lymphoma patients and compare their performance with that of the existing methods. Based on simulations, our proposed methods achieve comparable accuracy in identifying the maximum tolerated dose but have better control of the erroneous allocation and recommendation of an overdose.
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