The Bayesian Continual Reassessment Method Using a Mixture of Uniforms Prior

• Activity Number: 1
• Type: Invited
• Date/Time: Sunday, July 29, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Thomas M Braun*+
• Companies: University of Michigan
• Keywords: dose-finding ; Phase I trial ; adaptive clinical trial ; Bayesian methods ; indifference intervals

Abstract

Traditionally, 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). This model is used to determine the maximum tolerated dose, the dose with a probability of DLT closest to a desired target. To enforce the monotonicity of the probability of DLT with dose, a prior distribution with known variance and support on the positive real line is assumed for the parameter in the model. Investigators are then asked to supply the a priori probability of DLT for each dose, known as the "skeleton". The values in the skeleton implicitly lead to a set of indifference intervals, with one interval for each dose, that contain parameter values that support each dose being the MTD. We propose placing a uniform distribution over each of these 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 uniform prior in a variety of settings.