A sequential Bayesian phase II/III design is proposed for comparative clinical trials. The design is based on both survival time and discrete early events that may be related to survival and assumes a parametric mixture model. Phase II involves a small number of centers. Patients are randomized between treatments throughout, and sequential decisions are based on predictive probabilities of concluding superiority of the experimental treatment. Whether to stop early, continue, or shift into phase III is assessed repeatedly in phase II. Phase III begins when additional institutions are incorporated into the ongoing phase II trial. Simulation studies in the context of a non-small-cell lung cancer trial indicate that the proposed method maintains overall size and power while usually requiring substantially smaller sample size and shorter trial duration when compared with conventional group-sequential phase III designs.