A simulation-free approach to assessing the performance of the continual reassessment method

The continual reassessment method (CRM) is an adaptive design for Phase I trials whose operating characteristics, including appropriate sample size, probability of correctly identifying the maximum tolerated dose, and the expected proportion of participants assigned to each dose, can only be determined via simulation. The actual time to determine a final "best" design can take several hours or days, depending on the number of scenarios that are examined. The computational cost increases as the kernel of the one-parameter CRM design is expanded to other settings, including additional parameters, monitoring of both toxicity and efficacy, and studies of combinations of two agents. For a given vector of true DLT probabilities, we have developed an approach that replaces a simulation study of thousands of hypothetical trials with a single simulation. Our approach, which is founded on the consistency of the CRM, very accurately reflects the results produced by the simulation study, but does so in a fraction of time required by the simulation study. Relative to traditional simulations, we extensively examine how our method is able to assess the operating characteristics of a CRM design for a hypothetical trial whose characteristics are based upon a previously published Phase I trial. We also provide a metric of nonconsistency and demonstrate that although nonconsistency can impact the operating characteristics of our method, the degree of over- or under-estimation is unpredictable. As a solution, we provide an algorithm for maintaining the consistency of a chosen CRM design so that our method is applicable for any trial.