  The genetic basis of multiple phenotypes such as gene expression, metabolite
levels, or imaging features is often investigated by testing a large collection
of hypotheses, probing the existence of association between each of the traits
and hundreds of thousands of genotyped variants. Appropriate multiplicity
adjustment is crucial to guarantee replicability of findings, and False
Discovery Rate (FDR) is frequently adopted as a measure of global error. In the
interest of interpretability, results are often summarized so that reporting
focuses on variants discovered to be associated to some phenotypes.
  We show that applying FDR-controlling procedures on the entire collection of
hypotheses fails to control the rate of false discovery of associated variants
as well as the average rate of false discovery of phenotypes influenced by such
variants. We propose a simple hierarchical testing procedure which allows
control of both these error rates and provides a more reliable basis for the
identification of variants with functional effects. We demonstrate the utility
of this approach through simulation studies comparing various error rates and
measures of power for genetic association studies of multiple traits. Finally,
we apply the proposed method to identify genetic variants which impact
flowering phenotypes in Arabdopsis thaliana, expanding the set of discoveries.
