Permutation-based multiple testing when fitting many generalized linear models

Electronic Journal of Statistics, vol. 19

Abstract

In many applied sciences a popular analysis strategy for high-dimensional data is to fit many multivariate generalized linear models in parallel. This paper presents a novel approach to address the resulting multiple testing problem by combining a recently developed sign-flip test with permutation-based multiple-testing procedures. Our method builds upon the univariate Flipscores test which offers robustness against misspecified variances in generalized linear models, a crucial feature in high-dimensional settings where comprehensive model validation is particularly challenging. We extend this approach to the multivariate setting, enabling adaptation to unknown response correlation structures. This approach yields relevant power improvements over conventional multiple testing methods when correlation is present.

Authors 5

1. Riccardo De Santis

   University of Padua

   Affiliation as printed

   University of Padova, Italy

2. Jelle J. Goeman Aachen

   Leiden University Medical Center

   Affiliation as printed

   Leiden University Medical Center, The Netherlands

3. Samuel Davenport

   University of California San Diego

   Affiliation as printed

   University of California San Diego, United States

4. Jesse Hemerik

   Erasmus University Rotterdam

   Affiliation as printed

   Erasmus University Rotterdam, The Netherlands

5. Livio Finos

   University of Padua

   Affiliation as printed

   University of Padova, Italy