Graphical Approaches to Multiple Test Procedures

• Activity Number: 277
• Type: Invited
• Date/Time: Tuesday, August 2, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Biopharmaceutical Section
• Author(s): Frank Bretz*+
• Companies: Novartis Pharma AG
• Keywords: gatekeeping ; fallback ; Bonferroni ; truncated ; Simes ; parametric

Abstract

A variety of sequentially rejective, weighted Bonferroni tests have been proposed for clinical trials with multiple treatment arms or endpoints, such as gatekeeping procedures, fixed sequence tests and fallback procedures. These approaches allow one to reflect the difference in importance as well as the relationship between the various research questions by choosing suitable weights. In this presentation we propose a simple iterative graphical approach to construct and perform such Bonferroni-type tests. The resulting multiple test procedures are expressed as directed, weighted graphs, where each node corresponds to an elementary null hypothesis, together with a simple algorithm to generate such graphs while sequentially testing the individual hypotheses. A case study is used to demonstrate how this approach can be used to tailor a multiple test procedure to given study objectives. The approach is also illustrated with the visualization of several common gatekeeping strategies. Extensions of the basic graphical approach are discussed briefly, including parametric methods accounting for the correlation between the test statistics, weighted Simes tests and truncated test procedures.