In this talk, I present a Bayesian adaptive design for drug combination early phase cancer clinical trials when a fraction of dose limiting toxicities is attributable to one or both drugs. Copula regression models are used to describe the dose toxicity relationship. The dose escalation algorithm uses cohorts of two patients, following the continual reassessment method scheme, where at each stage of the trial, we search for the dose of one agent given the current dose of the other agent. At the end of the trial, the maximum tolerated dose (MTD) curve is estimated as a function of model parameters in the setting of continuous dose levels. An outcome adaptive design is then carried out in a phase II trial with the goal of determining dose combinations along the MTD curve that achieve maximal treatment efficacy. The methodology is illustrated by extensive simulations and application to a real trial. We show that the design is safe under a large number of practical scenarios and the optimal dose estimated with high precision.