Performance of two-stage continual reassessment method relative to an optimal benchmark

The two-stage, likelihood-based continual reassessment method (CRM-L) entails the specification of a set of design parameters prior to the beginning of its use in a study. The impression of clinicians is that the success of model-based designs, such as CRM-L, depends upon some of the choices made with regard to these specifications, such as the choice of parametric dose-toxicity model and the initial guess of toxicity probabilities.

In studying the efficiency and comparative performance of competing dose-finding designs for finite (typically small) samples, the nonparametric optimal benchmark is a useful tool. When comparing a dose-finding design to the optimal design, we are able to assess how much room there is for potential improvement.

The optimal method, based only on an assumption of monotonicity of the dose-toxicity function, is a valuable theoretical construct serving as a benchmark in theoretical studies, similar to that of a Cramér-Rao bound. We consider the performance of CRM-L under various design specifications and how it compares to the optimal design across a range of practical situations.

Using simple recommendations for design specifications, the CRM-L will produce performances, in terms of identifying doses at and around the maximum tolerated dose (MTD), that are close to the optimal method on average over a broad group of dose-toxicity scenarios.

Although the simulation settings vary in the number of doses considered, the target toxicity rate, and the sample size, the results here are presented for a small, though widely used, set of two-stage CRM designs.

Based on simulations here, and many others not shown, CRM-L is almost as accurate, in many scenarios, as the nonparametric optimal design. On average, there appears to be very little margin for improvement. Even if a finely tuned skeleton offers some improvement over a simple skeleton, the improvement is necessarily very small.