Graphical Approaches for Multiple Comparison Procedures

Abstract

Graphical approaches allow one to map the relative importance of different objectives as well as their relation onto an appropriately tailored multiple comparison procedure. They provide flexibility and transparency when applied to common multiplicity problems, such as comparing several treatments with a control, assessing the benefit of a new drug for more than one endpoint, and combined non-inferiority and superiority testing. Using graphical approaches, one can easily construct and explore different test strategies, thus tailoring the test procedure to the given study objectives. The resulting multiple comparison procedures are represented by directed, weighted graphs, where each node corresponds to an elementary hypothesis, together with a simple algorithm to generate and update such graphs. The class of procedures covered in this chapter includes weighted Bonferroni tests, weighted parametric tests accounting for the correlation between the test statistics, and weighted Simes’ tests. The approach is illustrated with the visualization of many commonly used multiple comparison procedures, such as Bonferroni, Holm, fixed-sequence, fallback, Hochberg, Hommel and gatekeeping procedures. Extensions to group sequential designs and families of hypotheses are also discussed. We also present several case studies to illustrate how the approach can be used in clinical practice.