Closed testing with Globaltest with applications on metabolomics data
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We derive a shortcut for closed testing with Globaltest, which is powerful for pathway analysis, especially in the presence of many weak features. The shortcut strongly controls the family-wise error rate over all possible feature sets. We present our shortcut in two ways: the single-step shortcut and the iterative shortcut by embedding the single-step shortcut in branch and bound algorithm. The iterative shortcut is asymptotically equivalent to the full closed testing procedure but can be stopped at any point without sacrificing family-wise error rate control. The shortcut improves the scale of the full closed testing from 20 around features before to hundreds. It is post hoc, i.e. allowing feature sets to be chosen after seeing the data, without compromising error rate control. The procedure is illustrated on metabolomics data.
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