A Permutation Approach to Testing Interactions for Binary Response by Comparing Correlations Between Classes

Abstract

To date testing interactions in high dimensions is a challenging task. Existing methods often have issues with sensitivity to modeling assumptions and heavily asymptotic nominal p-values. To help alleviate these issues, we propose a permutation-based method for testing marginal interactions with a binary response. Our method searches for pairwise correlations that differ between classes. In this article, we compare our method on real and simulated data to the standard approach of running many pairwise logistic models. On simulated data our method finds more significant interactions at a lower false discovery rate (especially in the presence of main effects). On real genomic data, although there is no gold standard, our method finds apparent signal and tells a believable story, while logistic regression does not. We also give asymptotic consistency results under not too restrictive assumptions. Supplementary materials for this article are available online.

• Correlation
• False discovery rate
• High dimensional
• Logistic regression

Additional information

Notes on contributors

Noah Simon

Noah Simon is Assistant Professor, Department of Biostatistics, University of Washington, Seattle, WA 98195; and Stanford University, Stanford, CA 94305 (E-mail: [email protected]). Robert Tibshirani is Professor, Department of Statistics, Department of Health Research and Policy, Stanford University, Stanford, CA, 94305 (E-mail: [email protected]).

Robert Tibshirani

Noah Simon is Assistant Professor, Department of Biostatistics, University of Washington, Seattle, WA 98195; and Stanford University, Stanford, CA 94305 (E-mail: [email protected]). Robert Tibshirani is Professor, Department of Statistics, Department of Health Research and Policy, Stanford University, Stanford, CA, 94305 (E-mail: [email protected]).