Testing the Significance of Interactions in Genetic Studies Using Interaction Information and Resampling Technique

Interaction information is a model-free, non-parametric measure used for detection of interaction among variables. It frequently finds interactions which remain undetected by standard model-based methods. However in the previous studies application of interaction information was limited by lack of appropriate statistical tests. We study a challenging problem of testing the positiveness of interaction information which allows to confirm the statistical significance of the investigated interactions. It turns out that commonly used chi-squared test detects too many spurious interactions when the dependence between the variables (e.g. between two genetic markers) is strong. To overcome this problem we consider permutation test and also propose a novel HYBRID method that combines permutation and chi-squared tests and takes into account dependence between studied variables. We show in numerical experiments that, in contrast to chi-squared based test, the proposed method controls well the actual significance level and in many situations detects interactions which are undetected by standard methods. Moreover HYBRID method outperforms permutation test with respect to power and computational efficiency. The method is applied to find interactions among Single Nucleotide Polymorphisms as well as among gene expression levels of human immune cells.