Optimal adaptive promising zone designs

We develop optimal decision rules for sample size re-estimation in two-stage adaptive group sequential clinical trials. It is usual for the initial sample size specification of such trials to be adequate to detect a realistic treatment effect delta a with good power, but not sufficient to detect the smallest clinically meaningful treatment effect delta min. Moreover it is difficult for the sponsors of such trials to make the up-front commitment needed to adequately power a study to detect delta min. It is easier to justify increasing the sample size if the interim data enter a so-called "promising zone" that ensures with high probability that the trial will succeed. We have considered promising zone designs that optimize unconditional power and promising zone designs that optimize conditional power and have discussed the tension that exists between these two objectives. Where there is reluctance to base the sample size re-estimation rule on the parameter delta min we propose a Bayesian option whereby a prior distribution is assigned to the unknown treatment effect delta, which is then integrated out of the objective function with respect to its posterior distribution at the interim analysis.