Conditional power calculations for early acceptance of H0 embedded in sequential tests

For ethical and efficiency concerns one often wishes to design a clinical trial to stop early if there is a strong treatment effect or if there is strong evidence of no treatment effect. There is a large literature to address the design of sequential trials for detecting treatment differences. There has been less attention paid to the design of trials for detecting lack of a treatment difference and most of the designs proposed have been ad hoc modifications of the traditional designs. In the context of fixed sample tests, various authors have proposed basing the decision to stop in favour of the null hypothesis, H0, on conditional power calculations for the end of the trial given the current data. Here I extend this procedure to the popular sequential designs: the O'Brien-Fleming test and the repeated significance test. I derive explicit boundaries for monitoring the test statistic useful for visualizing the impact of the parameters on the operating characteristics of the tests and thus for the design of the tests. Also, they facilitate the use of boundary crossing methods for approximations of power. I derive appropriate boundaries retrospectively for two clinical trials: one that concluded with no treatment difference (AIDS Clinical Trials Group protocol 118) and one that stopped early for positive effect (Beta-Blocker Heart Attack Trial). Finally, I compare the procedures based on the different upper boundaries and assess the impact of allowing for early stopping in favour of H0 in numerical examples.