SC07: Graphical Multiple Comparison Procedures: Combining Flexibility with Optimality

Addressing multiplicity is essential in confirmatory clinical trials to ensure valid statistical inference. Various multiple comparison procedures (MCPs) have been developed that allow one to map the relative importance of different study objectives, as well as their relation onto an appropriately tailored multiple test procedure, including fixed-sequence, fallback, and gatekeeping procedures. This course focuses on graphical approaches that address a wide range of multiplicity problems, such as comparing multiple treatments against a control and multiple endpoint analyses. Graphical approaches enable the construction and exploration of tailored MCPs to meet specific study objectives. The resulting MCPs are represented by directed, weighted graphs, where each node corresponds to an elementary hypothesis. A simple algorithm facilitates the sequential testing of hypotheses. Optimizing MCPs to maximize the probability of success is often a key concern for clinical trial teams. We will discuss clinically relevant objective functions for optimization and introduce an efficient algorithm based on constrained nonlinear optimization to identify optimal graphs. Case studies will demonstrate the flexibility and practicality of these approaches in clinical trial settings. Applications in clinical trials will highlight the utility and adaptability of this approach. Moreover, we will introduce the graphicalMCP R package, which implements weighted Bonferroni tests, weighted parametric tests (accounting for correlations between test statistics), and weighted Simes' tests. We also briefly consider power and sample size calculation. Example code for optimizing graphs will be demonstrated and shared, providing participants with practical tools to implement these methods effectively.