  Dose-finding clinical trials in oncology aim to determine the maximum
tolerated dose (MTD) of a new drug, generally defined by the proportion of
patients with short-term dose-limiting toxicities (DLTs). Model-based
approaches for such phase I oncology trials have been widely designed and are
mostly restricted to the DLTs occurring during the first cycle of treatment,
although patients continue to receive treatment for multiple cycles. We aim to
estimate the probability of DLTs over sequences of treatment cycles via a
Bayesian cumulative modeling approach, where the probability of DLT is modeled
taking into account the cumulative effect of the administered drug and the DLT
cycle of occurrence. We propose a design, called DICE (Dose-fInding
CumulativE), for dose escalation and de-escalation according to previously
observed toxicities, which aims at finding the MTD sequence (MTS). We performed
an extensive simulation study comparing this approach to the time-to-event
continual reassessment method (TITE-CRM) and to a benchmark. In general, our
approach achieved a better or comparable percentage of correct MTS selection.
Moreover, we investigated the DICE prediction ability.
