  In oncology dose-finding trials, due to staggered enrollment, it might be
desirable to make dose-assignment decisions in real-time in the presence of
pending toxicity outcomes, for example, when the dose-limiting toxicity is
late-onset. Patients' time-to-event information may be utilized to facilitate
such decisions. We review statistical frameworks for time-to-event modeling in
dose-finding trials and summarize existing designs into two classes: TITE
designs and POD designs. TITE designs are based on inference on toxicity
probabilities, while POD designs are based on inference on dose-finding
decisions. These two classes of designs contain existing individual designs as
special cases and also give rise to new designs. We discuss and study the
theoretical properties of these designs, including large-sample convergence
properties, coherence principles, and the underlying decision rules. To
facilitate the use of these designs in practice, we introduce efficient
computational algorithms and review common practical considerations, such as
safety rules and suspension rules. Finally, the operating characteristics of
several designs are evaluated and compared through computer simulations.
