Multiple Testing in Group Sequential Trials Using Graphical Approaches

Abstract In 1997, Robert T. O'Neill introduced the framework of structuring the experimental questions to best reflect the clinical study's objectives. This task comprises the identification of the study's primary, secondary, and exploratory objectives and the requirements as to when the corresponding statistical tests are considered meaningful. A topic that has been considered much less in the literature until very recently is the application of group sequential trial designs to multiple endpoints. In 2007, Hung, Wang, and O'Neill showed that borrowing testing strategies naively from trial designs without interim analyses may not maintain the familywise Type I error rate at level α. The authors gave examples in the context of testing two hierarchically ordered endpoints in two-armed group sequential trials with one interim analysis. We consider the general situation of testing multiple hypotheses repeatedly in time using recently developed graphical approaches. We focus on closed testing procedures using weighted group sequential Bonferroni tests for the intersection hypotheses. Under mild monotonicity conditions on the error spending functions, this allows the use of sequentially rejective graphical procedures in group sequential trials. The methodology is illustrated with a numerical example for a three-armed trial comparing two doses against control for two hierarchically ordered endpoints. Key Words: Closed testingFamilywise error rateGatekeepingMultiple comparisons Acknowledgments We thank the guest editors for inviting us to contribute to this Festschrift for Dr. Robert T. O'Neill. We are grateful to Chris Jennison, who read an earlier version of this article and provided helpful comments. We also thank the editor and two anonymous referees for their thorough reviews that helped improving the quality of the article.