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Phase I dose-escalation trials must be guided by a safety model in order toavoid exposing patients to unacceptably high risk of toxicities. Traditionally,these trials are based on one type of schedule. In more recent practice,however, there is often a need to consider more than one schedule, which meansthat in addition to the dose itself, the schedule needs to be varied in thetrial. Hence, the aim is finding an acceptable dose-schedule combination.However, most established methods for dose-escalation trials are designed toescalate the dose only and ad-hoc choices must be made to adapt these to themore complicated setting of finding an acceptable dose-schedule combination. Inthis paper, we introduce a Bayesian time-to-event model which takes explicitlythe dose amount and schedule into account through the use of pharmacokineticprinciples. The model uses a time-varying exposure measure to account for therisk of a dose-limiting toxicity over time. The dose-schedule decisions areinformed by an escalation with overdose control criterion. The model isformulated using interpretable parameters which facilitates the specificationof priors. In a simulation study, we compared the proposed method with anexisting method. The simulation study demonstrates that the proposed methodyields similar or better results compared to an existing method in terms ofrecommending acceptable dose-schedule combinations, yet reduces the number ofpatients enrolled in most of scenarios. The \texttt{R} and \texttt{Stan} codeto implement the proposed method is publicly available from Github(\url{https://github.com/gunhanb/TITEPK_code}).

A Bayesian time‐to‐event pharmacokinetic model for phase I dose‐escalation trials with multiple schedules