
In genetic association studies, one analyzes associations between a (potentially very large) set of genetic markers and a phenotype of interest. This is a particular multiple test problem which has several challenging aspects, for instance the high dimensionality of the statistical parameter and the discreteness of the statistical model. In this chapter, we discuss how to fine-tune multiple tests that we have described theoretically in Part I in order to address these challenges. In particular, we propose the usage of realized randomized \(p\)-values in data-adaptive multiple tests and show how linkage disequilibrium among genetic markers can be employed to construct simultaneous test procedures and to establish probability bounds which lead to effective numbers of tests. Finally, we analyze (positive) dependency properties among test statistics and the applicability of standard margin-based multiple tests. The methods are applied to two real-life datasets.
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