SEAGLE: A Scalable Exact Algorithm for Large-Scale Set-Based GxE Tests in Biobank Data.

The explosion of biobank data offers immediate opportunities for gene-environment (GxE) interaction studies of complex diseases because of the large sample sizes and the rich collection in genetic and non-genetic information. However, the extremely large sample size also introduces new computational challenges in GxE assessment, especially for set-based GxE variance component (VC) tests, which are a widely used strategy to boost overall GxE signals and to evaluate the joint GxE effect of multiple variants from a biologically meaningful unit (e.g., gene). In this work, we focus on continuous traits and present SEAGLE, a Scalable Exact AlGorithm for Large-scale set-based GxE tests, to permit GxE VC tests for biobank-scale data. SEAGLE employs modern matrix computations to achieve the same "exact" results as the original GxE VC tests without imposing additional assumptions or relying on approximations. SEAGLE can easily accommodate sample sizes in the order of $10^5$, is implementable on standard laptops, and does not require specialized computing equipment. We demonstrate SEAGLE's performance through extensive simulations. We illustrate its utility by conducting genome-wide gene-based GxE analysis on the Taiwan Biobank data to explore the interaction of gene and physical activity status on body mass index.