A Bayesian adaptive dose selection procedure with an overdispersed count endpoint

Adaptive trial designs can considerably improve upon traditional designs, by modifying design aspects of the ongoing trial, like early stopping, adding, or dropping doses, or changing the sample size. In the present work, we propose a two-stage Bayesian adaptive design for a Phase IIb study aimed at selecting the lowest effective dose for Phase III. In this setting, efficacy has been proved for a high dose in a Phase IIa proof-of-concept study, but the existence of a lower but still effective dose is investigated before the scheduled Phase III starts. In the first stage, we randomize patients to placebo, maximal tolerated dose, and one or more additional doses within the dose range. Based on an interim analysis, we either stop the study for futility or success or continue the study to the second stage, where newly recruited patients are allocated to placebo, some fairly high dose, and one additional dose chosen based on interim data. At the interim analysis, we use the criteria based on the predictive probability of success to decide on whether to stop or to continue the trial and, in the latter case, which dose to select for the second stage. Finally, we will select a dose as lowest effective dose for Phase III either at the end of the first stage or at the end of the second stage. We evaluate the operating characteristics of the procedure via simulations and present the results for several scenarios, comparing the performance of the proposed procedure to those of the non-adaptive design.