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  "Title": "Global test for groups of variables via model comparisons",
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  "Date": "2021-01-27",
  "Author": "U. Mansmann, R. Meister, M. Hummel, R. Scheufele, with\ncontributions from S. Knueppel",
  "Description": "The association between a variable of interest (e.g. two\ngroups) and the global pattern of a group of variables (e.g. a\ngene set) is tested via a global F-test. We give the following\narguments in support of the GlobalAncova approach: After\nappropriate normalisation, gene-expression-data appear rather\nsymmetrical and outliers are no real problem, so least squares\nshould be rather robust. ANCOVA with interaction yields\nsaturated data modelling e.g. different means per group and\ngene. Covariate adjustment can help to correct for possible\nselection bias. Variance homogeneity and uncorrelated residuals\ncannot be expected. Application of ordinary least squares gives\nunbiased, but no longer optimal estimates\n(Gauss-Markov-Aitken). Therefore, using the classical F-test is\ninappropriate, due to correlation. The test statistic however\nmirrors deviations from the null hypothesis. In combination\nwith a permutation approach, empirical significance levels can\nbe approximated. Alternatively, an approximation yields\nasymptotic p-values. The framework is generalized to groups of\ncategorical variables or even mixed data by a likelihood ratio\napproach. Closed and hierarchical testing procedures are\nsupported. This work was supported by the NGFN grant 01 GR\n0459, BMBF, Germany and BMBF grant 01ZX1309B, Germany.",
  "Maintainer": "Manuela Hummel <manuela.hummel@web.de>",
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