The continual reassessment method (CRM) is a sequential design for phase I clinical trials. The CRM updates the model parameter of dose-toxicity relationship using the accumulated data, and selects the estimated maximum tolerated dose (MTD) as the dose used in the next cohort. In some situations, however, it is necessary to select the appropriate clinical dose considering both efficacy and toxicity. Recently, many methods for selecting the dose with the highest utility considering both toxicity and efficacy have been proposed. Although a trial is to be terminated when the response rates at all doses are very low or estimated toxicity is very high, no other formal and quantitative stopping rules have been proposed. From the ethical and economic viewpoints, it is desirable to halt the trial early if the necessary information about efficacy and toxicity is available. The design proposed by Thall and Cook (2004) is a CRM that considers toxicity and efficacy simultaneously. Adopting this design, we propose a rule to stop a trial if the Bayesian confidence interval of the predicted benefit in the next cohort lies within a given range. Computer simulations show that this proposed method allows early stopping compared to the conventional method, without greatly reducing the percentage of correct selection of the optimum dose. Even when there is misspecification of the efficacy-toxicity trade-off contours, the proposed method recommends the optimum or a safer dose.
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