Traditionally, the Bayesian formulation of the Continual Reassessment Method (CRM) is implemented with a one-parameter model describing the association of dose with the probability of dose-limiting toxicity (DLT). Determination of the appropriate value of the prior variance is often done via simulation over a grid search of possible values until suitable operating characteristics are found. However, it is under-appreciated that the operating characteristics for a given value of the prior variance vary by the “skeleton,” which is the vector of a priori probabilities of DLT for each dose. The skeleton implicitly leads to a set of indifference intervals, with one interval for each dose, that contain values of the model parameter that support each dose being the MTD. To remove the need of selecting a value for the prior variance, we propose placing a uniform distribution over each of the indifference intervals, making the prior distribution for the model parameter a mixture of uniform distributions. Via simulation, we compare the operating characteristics of the CRM using a traditional continuous prior to using the mixture-of-uniforms prior in a variety of settings and show that the mixture-of-uniforms prior leads to operating characteristics that are less sensitive to the chosen skeleton.
Braun, Thomas M., "The Bayesian Continual Reassessment Method Using a Mixture-of-Uniforms Prior" (January 2012). The University of Michigan Department of Biostatistics Working Paper Series. Working Paper 92.