title: Rotation-based multiple testing in the multivariate linear model.
abstract: In observational microarray studies, issues of confounding invariably arise. One approach to account for measured confounders is to include them as covariates in a multivariate linear model. For this model, however, the application of permutation-based multiple testing procedures is problematic because exchangeability of responses, in general, does not hold. Nevertheless, it is possible to achieve rotatability of transformed responses at the cost of a distributional assumption. We argue that rotation-based multiple testing, by allowing for adjustments for confounding, represents an important extension of permutation-based multiple testing procedures. The proposed methodology is illustrated with a microarray observational study on breast cancer tumors. Software to perform the procedure described in this article is available in the flip R package.
authors.affiliation: Department of Economics, Management and Statistics, University of Milano-Bicocca, Milan, Italy.
authors.forename: Aldo
authors.initials: A
authors.lastname: Solari
authors.forename: Livio
authors.initials: L
authors.lastname: Finos
authors.forename: Jelle J
authors.initials: JJ
authors.lastname: Goeman
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D020869:Gene Expression Profiling / Q000379:methods*; D016014:Linear Models; D015999:Multivariate Analysis; D020411:Oligonucleotide Array Sequence Analysis / Q000379:methods*; D015203:Reproducibility of Results; D012399:Rotation; D012680:Sensitivity and Specificity
keywords: Exchangeability; Familywise error rate; Microarray; Multiple testing; Permutation test; Rotation test