  The Globaltest is a powerful test for the global null hypothesis that there
is no association between a group of features and a response of interest, which
is popular in pathway testing in metabolomics. Evaluating multiple pathways,
however, requires multiple testing correction. In this paper, we propose a
multiple testing method, based on closed testing, specifically designed for the
Globaltest. The proposed method controls the family-wise error rate
simultaneously over all possible feature sets, and therefore allows post hoc
inference, i.e. the researcher may choose the pathway database after seeing the
data without jeopardizing error control. To circumvent the exponential
computation time of closed testing, we derive a novel shortcut that allows
exact closed testing to be performed on the scale of metabolomics data. An R
package ctgt is available on CRAN. We illustrate the shortcut on several
metabolomics data examples.
