Over-ruling a group sequential boundary--a stopping rule versus a guideline.

We evaluate the properties of group sequential procedures where the trial is continued even though the boundary for statistical significance (stopping) to demonstrate effectiveness has been crossed. In this case, one may buy-back the previously spent alpha probability to be re-spent or re-distributed at future looks. We show that such plans using an O'Brien-Fleming-like spending function have a negligible effect on the final type I error probability and on the ultimate power of the study. With a Pocock-like bound, however, there is a small additional loss in power. We also show that this approach can be simplified by using a fixed-sample size Z critical value for future looks after buying-back previously spent alpha, such as using a critical Z value of 1.96 for alpha=0.025. We show that this procedure preserves the type I error probability while incurring a minimal loss in power. In this sense, one still has a stopping boundary rather than simply a guideline. This concept is discussed relative to monitoring procedures for inferiority or futility, and cases where both an upper and lower boundary are employed.