Graphical approaches using a Bonferroni mixture of weighted Simes tests

Graphical approaches to multiple testing procedures are very flexible and easy to communicate with non-statisticians. The availability of the R package gMCP further propelled the application of graphical approaches in randomized clinical trials. Bretz et al. (Biometrical Journal 2011; 53:894-913) introduced a class of nonparametric testing procedures based on a Bonferroni mixture of weighted Simes tests for intersection hypotheses. Such approaches are extremely useful when the conditions for the Simes test are known to hold for hypotheses within certain subsets but may not hold for hypotheses across subsets. We describe the calculation of adjusted p-values for such approaches, which is currently not available in the gMCP package. We also optimize the generation of the weights for each intersection hypothesis in the closure of a graph-based multiple testing procedure, which can dramatically reduce the computing time for simulation-based power calculations. We show the validity of the Simes test for comparing several treatments with a control, performing noninferiority and superiority tests, or testing the treatment effect in an overall and a subpopulation for the normal, binary, count, and time-to-event data. The proposed method is illustrated using an example for designing a confirmatory clinical trial. Copyright © 2016 John Wiley & Sons, Ltd.