Test for rare variants by environment interactions in sequencing association studies

type="main" xml:lang="en"> We consider in this article testing rare variants by environment interactions in sequencing association studies. Current methods for studying the association of rare variants with traits cannot be readily applied for testing for rare variants by environment interactions, as these methods do not effectively control for the main effects of rare variants, leading to unstable results and/or inflated Type 1 error rates. We will first analytically study the bias of the use of conventional burden-based tests for rare variants by environment interactions, and show the tests can often be invalid and result in inflated Type 1 error rates. To overcome these difficulties, we develop the interaction sequence kernel association test (iSKAT) for assessing rare variants by environment interactions. The proposed test iSKAT is optimal in a class of variance component tests and is powerful and robust to the proportion of variants in a gene that interact with environment and the signs of the effects. This test properly controls for the main effects of the rare variants using weighted ridge regression while adjusting for covariates. We demonstrate the performance of iSKAT using simulation studies and illustrate its application by analysis of a candidate gene sequencing study of plasma adiponectin levels.