Bayesian dose finding by jointly modelling toxicity and efficacy as time‐to‐event outcomes

Summary. In traditional phase I and II clinical trial designs, toxicity and efficacy are often modelled as binary outcomes. Such methods ignore information on when the outcome event occurs, such as experiencing toxicity or achieving cure or remission. They also have difficulty accommodating a high accrual rate under which toxicity and efficacy outcomes cannot be observed in a timely manner, and thus delay treatment assignment. To address these issues, we propose a Bayesian adaptive phase I–II design that jointly models toxicity and efficacy as time‐to‐event outcomes. At each decision‐making time, patients who have not experienced toxicity or efficacy are naturally censored. We apply the marginal cure rate model to account explicitly for those patients who are insusceptible to efficacy owing to drug resistance. The correlation between the bivariate time‐to‐toxicity and time‐to‐efficacy outcomes is properly adjusted through the Clayton model. After screening out the excessively toxic or futile doses, we adaptively assign each new patient to the most appropriate dose on the basis of the ratio of the areas under the predicted survival curves corresponding to toxicity and efficacy. We conducted extensive simulation studies to examine the operating characteristics of the method proposed, and we illustrate the application of the method in a clinical trial in prostate cancer. Our design selects the target dose with a high probability, treats most patients at the desirable dose and potentially shortens the duration of a trial.