  We propose an adaptive design for early phase drug combination cancer trials
with the goal of estimating the maximum tolerated dose (MTD). A nonparametric
Bayesian model, using beta priors truncated to the set of partially ordered
dose combinations, is used to describe the probability of dose limiting
toxicity (DLT). Dose allocation between successive cohorts of patients is
estimated using a modified Continual Reassessment scheme. The updated
probabilities of DLT are calculated with a Gibbs sampler that employs a
weighting mechanism to calibrate the influence of data versus the prior. At the
end of the trial, we recommend one or more dose combinations as the MTD based
on our proposed algorithm. The design operating characteristics indicate that
our method is comparable with existing methods. As an illustration, we apply
our method to a phase I clinical trial of CB-839 and Gemcitabine.
