  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 of 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 dose escalation/de-escalation rules of the
proposed time-to-event model-assisted designs 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 superior to that of
more complicated model-based designs. We provide user-friendly software for
implementing the designs.
