  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. More
recently, however, multiple schedules are more frequently investigated in the
same trial. Here, we consider 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 adapted the time-to-event pharmacokinetics (TITE-PK) model, which were
originally developed for simultaneous investigation of multiple schedules.
TITE-PK integrates information from multiple schedules using a pharmacokinetics
(PK) model. In a simulation study, the developed appraoch is compared to the
bridging continual reassessment method and the Bayesian logistic regression
model using a meta-analytic-prior. TITE-PK results in better performance than
comparators in terms of recommending acceptable dose and avoiding overly toxic
doses for sequential phase I trials in most of the scenarios considered.
Furthermore, better performance of TITE-PK is achieved while requiring similar
number of patients in the simulated trials. For the scenarios involving one
schedule, TITE-PK displays similar performance with alternatives in terms of
acceptable dose recommendations. The \texttt{R} and \texttt{Stan} code for the
implementation of an illustrative sequential phase I trial example is publicly
available at https://github.com/gunhanb/TITEPK_sequential.
