Abstract Late-onset toxicity is common for novel molecularly targeted agents and immunotherapy. It causes major logistic difficulty for existing adaptive phase I trial designs, which require the observance of toxicity early enough to apply dose-escalation rules for new patients. The same logistic difficulty arises when the accrual is rapid. We propose the time-to-event Bayesian optimal interval (TITE-BOIN) design to accelerate phase I trials by allowing for real-time dose assignment decisions for new patients whil…