Adaptive tests for detecting gene-gene and gene-environment interactions.

There has been an increasing interest in detecting gene-gene and gene-environment interactions in genetic association studies. A major statistical challenge is how to deal with a large number of parameters measuring possible interaction effects, which leads to reduced power of any statistical test due to a large number of degrees of freedom or high cost of adjustment for multiple testing. Hence, a popular idea is to first apply some dimension reduction techniques before testing, while another is to apply only statistical tests that are developed for and robust to high-dimensional data. To combine both ideas, we propose applying an adaptive sum of squared score (SSU) test and several other adaptive tests. These adaptive tests are extensions of the adaptive Neyman test [Fan, 1996], which was originally proposed for high-dimensional data, providing a simple and effective way for dimension reduction. On the other hand, the original SSU test coincides with a version of a test specifically developed for high-dimensional data. We apply these adaptive tests and their original nonadaptive versions to simulated data to detect interactions between two groups of SNPs (e.g. multiple SNPs in two candidate regions). We found that for sparse models (i.e. with only few non-zero interaction parameters), the adaptive SSU test and its close variant, an adaptive version of the weighted sum of squared score (SSUw) test, improved the power over their non-adaptive versions, and performed consistently well across various scenarios. The proposed adaptive tests are built in the general framework of regression analysis, and can thus be applied to various types of traits in the presence of covariates.