A Bayesian approach to dose-finding studies for cancer therapies: incorporating later cycles of therapy

We consider phase I dose-finding studies for cytotoxic drugs in cancer, where the objective is identification of a target dose (TD100δ ) associated with the probability δ of a dose-limiting toxicity (DLT). Previous authors have presented a design utilising a Bayesian decision procedure based on a logistic regression model to describe the relationship between dose and the risk of a DLT (LRDP). A cautious prior, chosen to ensure that the first cohort of patients are given the lowest dose, is combined with binary observations of DLTs to update model parameters and choose a safe dose for the next cohort. This process continues with each new cohort of patients. Typically, only DLTs occurring in the first treatment cycle are included. To incorporate data from later cycles, a new Bayesian decision procedure based on an interval-censored survival model (ICSDP) has been developed. This models the probability that the first DLT occurs in each specific cycle via the probability of a DLT during a specific cycle, conditional on having no DLT in any previous cycle. The second cohort of patients start after responses have been obtained from the first cycle of the first cohort, and subsequently, dose selection for each new cohort is based on DLTs observed across all completed cycles for all patients. A simulation study comparing the ICSDP and LRDP showed that the ICSDP induces faster updating of the current estimate of the target dose, leading to shorter trials and fewer patients, whilst keeping the same level of accuracy.