Extending the two-stage single arm phase II clinical trial design to the delayed response scenario

Two-stage single arm designs are widely used in phase II clinical trials with binary endpoints. The trial may be stopped early due to insufficient positive responses in the first stage. There may be some enrolled subjects who have yet to respond by the end of the first stage, and their data are ignored if the first stage results in rejection of the trial. It is possible that the result after the first stage is rejection by a slim margin, while the results of pipeline subjects are quite positive. In this case, combining the data from the two sources may provide a valuable opportunity to rescue a promising treatment that was mistakenly rejected. We propose a novel double-check design to take advantage of the pipeline subjects' data to establish a rescue criterion based on two-stage design. When the rescue criterion is met, the decision to reject the trial at the end of the first stage can be reversed, allowing the trial to continue. A derivation based on a binomial distribution shows that the double-check strategy can strictly preserve the type I error rate. Further examination shows that the strategy can provide a slight increase in overall power and a substantial increase in conditional power when the proportion of positive response at the end of the first stage is at the margin. The extra rescue opportunity's cost is pretty low, only a slight increasing in the expected sample size.