Conditional Inference Following Group Sequential Testing

The work of Fisher1 and Buehler2 discuss the importance of con-ditioning on recognizable subsets of the sample space. The stopping time is an easily identifiable divider of the sample space when con-sidering group sequential testing. We present confidence intervals which are correct when conditioning on the subset of data such that a trial stopped at a particular analysis. Although these intervals may not be practical, they do have very desirable properties for ob-servations which are highly unusual (given any value of the mean). In addition, they provide insight into how information about the mean is distributed between the two sufficient statistics. Condi-tional coverage probabilities are used as a way to compare the sam-ple mean, stagewise, and repeated confidence intervals. However, none of these intervals outperforms the others when conditioning on stopping time