Comparing Bayesian early stopping boundaries for phase II clinical trials

When designing phase II clinical trials, it is important to construct interim monitoring rules that achieve a balance between reliable early stopping for futility or safety and maintaining a high true positive probability (TPP), which is the probability of not stopping if the new treatment is truly safe and effective. We define and compare several methods for specifying early stopping boundaries as functions of interim sample size, rather than as fixed cut-offs, using Bayesian posterior probabilities as decision criteria. We consider boundaries with constant, linear, or exponential shapes. For design optimization criteria, we use the TPP and mean number of patients enrolled in the trial. Simulations to evaluate and compare the designs' operating characteristics under a range of scenarios show that, while there is no uniformly optimal boundary, an appropriately calibrated exponential shape maintains high TPP while limiting the number of patients assigned to a treatment with an inferior response rate or an excessive toxicity rate.