An extension of the continual reassessment method using decision theory

The primary goal of a phase I trial is to find the maximally tolerated dose (MTD) of a treatment. The MTD is usually defined in terms of a tolerable probability, q(*), of toxicity. Our objective is to find the highest dose with toxicity risk that does not exceed q(*), a criterion that is often desired in designing phase I trials. This criterion differs from that of finding the dose with toxicity risk closest to q(*), that is used in methods such as the continual reassessment method. We use the theory of decision processes to find optimal sequential designs that maximize the expected number of patients within the trial allocated to the highest dose with toxicity not exceeding q(*), among the doses under consideration. The proposed method is very general in the sense that criteria other than the one considered here can be optimized and that optimal dose assignment can be defined in terms of patients within or outside the trial. It includes as an important special case the continual reassessment method. Numerical study indicates the strategy compares favourably with other phase I designs.