ABSTRACT
Another boundary that is often used in clinical trials is the Pocock boundary. The Pocock boundary rejects the null hypothesis at each analysis using the same critical value on the Z scale. Table 11.1 presents the operating characteristics for a Pocock rejection boundary. Whereas the O’BrienFleming boundary starts out with a ratio of power to type error that is much greater than 32, we can see in Table 11.1 that the Pocock boundary starts out with a ratio of power to type 1 error at the first analysis that is less than 32 and gradually increases to 32 from the first analysis to the last analysis. In Figure 11.1, we see that the ratio of the change in power to the change in type
1 error is always greater than 32 for some treatment effect size. The Pocock boundary differs in this regard from the O’Brien-Fleming boundary we evaluated in Table 10.3 where the ratio of the change in power to the change in type 1 error was less than 32 at the final analysis for all treatment effect sizes. So, while one should be concerned about a study that rejects at the last analysis of an O’Brien-Fleming stopping boundary, one should also be concerned about a study that stops at the first analysis of a Pocock boundary. In this situation, there are clinically meaningful alternatives that have a low ratio of power to type 1 error and hence rejecting the null hypothesis by the Pocock boundary at an early analysis may lead to the regulator and society assuming more risk than desired.
