Rotation-based multiple testing in the multivariate linear model

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.