Continuous Bayesian adaptive randomization based on event times with covariates

In comparative clinical trials, the randomization probabilities may be unbalanced adaptively by utilizing the interim data available at each patient's entry time to favour the treatment or treatments having comparatively superior outcomes. This is ethically appealing because, on average, more patients are assigned to the more successful treatments. Consequently, physicians are more likely to enroll patients onto trials where the randomization is outcome-adaptive rather than balanced in the conventional manner. Outcome-adaptive methods based on a binary variable may be applied by reducing an event time to the indicator of the event's occurrence within a predetermined time interval. This results in a loss of information, however, since it ignores the censoring times of patients who have not experienced the event but whose evaluation interval is not complete. This paper proposes and compares exact and approximate Bayesian outcome-adaptive randomization procedures based on time-to-event outcomes. The procedures account for baseline prognostic covariates, and they may be applied continuously over the course of the trial. We illustrate these methods by application to a phase II selection trial in acute leukaemia. A simulation study in the context of this trial is presented.