Sequential phase I dose-escalation trials with multiple schedules.

Phase I dose-escalation trials constitute the first step in investigating the safety of potentially promising drugs in humans. Conventional methods for phase I dose-escalation trials are based on a single treatment schedule only. In medical practice, however, multiple schedules are more frequently investigated in the same trial. Investigation of the acceptable dose and schedule combination in a phase I trial can be done simultaneously or sequentially. Here, we consider the latter, sequential phase I trials, where the trial proceeds with a new schedule (e.g. daily or weekly dosing) once the dose escalation with another schedule has been completed. The aim is to utilize the information from both the completed and the ongoing dose-escalation trial to inform decisions on the dose level for the next dose cohort. For this purpose, we propose to use the time-to-event pharmacokinetics (TITE-PK) model which can integrate information from multiple schedules using pharmacokinetics (PK) principles. In a simulation study, we used the Bayesian Logistic Regression Model (BLRM) as the comparator, which only considers the number of DLT occurred, not the time-to-first DLT, and uses an ad-hoc approach to analyze multiple schedules. TITE-PK results in better performance compared to the BLRM in terms of recommending acceptable dose for sequential phase I trials in most of the scenarios considered. The \texttt{R} and \texttt{Stan} code for the implementation of an illustrative sequential phase I trial example is publicly available (\url{https://github.com/gunhanb/TITEPK_sequential}).