Speaker
Description
The closed testing principle is a fundamental framework to construct multiple testing procedures controlling the familywise error rate in the strong sense. However, a major challenge in the application of the principle is the number of intersection hypothesis tests that need to be specified, which increases exponentially in the number of elementary hypotheses tested and makes it difficult to communicate the resulting multiple testing strategy. Graph-based tests are a transparent approach to specify the intersection hypothesis tests in a closed test. They have been initially proposed for Bonferroni-type tests, for which they formalise an intuitive alpha recycling mechanism. In this setting they also yield a simple sequentially rejective testing algorithm and unify well-known multiple testing procedures, such as gatekeeping, fixed sequence, and fallback procedures making the underlying testing strategy transparent. More generally, the graphical approach can be used to define weighted hypothesis tests for all intersection hypotheses of a closed test. This allows the use of graphs for the construction of closed tests that account for the correlation structure of the test statistics and thereby to improve efficiency.
In this talk, we review graph-based closed tests, the rationale of the underlying algorithm and discuss the potential loss of consonance of the resulting closed test that can occur if correlations are taken into account. Furthermore, we discuss applications to group-sequential and adaptive designs based on p-value combination and conditional error approaches.
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