Closed testing with Globaltest, with application in metabolomics

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 feature sets, 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 familywise error rate simultaneously over all possible feature sets, and therefore allows post hoc inference, that is, the researcher may choose feature sets of interest 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 comprehensive R archive network for the implementation of the shortcut procedure, with applications on several real metabolomics data examples.