Two useful strategies to speed up drug development are to increase the patient accrual rate and use novel adaptive designs. Unfortunately, these two strategies often conflict when the evaluation of the outcome cannot keep pace with the patient accrual rate and thus the interim data cannot be observed in time to make adaptive decisions. A similar logistic difficulty arises when the outcome is late-onset. Based on a novel formulation and approximation of the likelihood of the observed data, we propose a general methodology for model-assisted designs to handle toxicity data that are pending due to fast accrual or late-onset toxicity and facilitate seamless decision making in phase I dose-finding trials. The proposed time-to-event model-assisted designs consider each dose separately and the dose-escalation/de-escalation rules can be tabulated before the trial begins, which greatly simplifies trial conduct in practice compared to that under existing methods. We show that the proposed designs have desirable finite and large-sample properties and yield performance that is comparable to that of more complicated model-based designs. We provide user-friendly software for implementing the designs.

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