A note on continual reassessment method

A widely used approach in designing the phase I clinical trial is continual reassessment method (CRM). In this paper, we prove that under simple power model and logistic model, the way CRM selects the next dose level is highly efficient from the perspective of optimal design. More specifically, for simple power model, we show that the optimal design selects the dose level such that the corresponding toxicity rate is around 0.2; as for logistic model, we show that CRM is indeed optimal, which will justify the efficiency of the algorithm in theory.