  We propose a new integrated phase I/II trial design to identify the most
efficacious dose combination that also satisfies certain safety requirements
for drug-combination trials. We first take a Bayesian copula-type model for
dose finding in phase I. After identifying a set of admissible doses, we
immediately move the entire set forward to phase II. We propose a novel
adaptive randomization scheme to favor assigning patients to more efficacious
dose-combination arms. Our adaptive randomization scheme takes into account
both the point estimate and variability of efficacy. By using a moving
reference to compare the relative efficacy among treatment arms, our method
achieves a high resolution to distinguish different arms. We also consider
groupwise adaptive randomization when efficacy is late-onset. We conduct
extensive simulation studies to examine the operating characteristics of the
proposed design, and illustrate our method using a phase I/II melanoma clinical
trial.
