Matrix sketching framework for linear mixed models in association studies

Linear mixed models (LMMs) have been widely used in genome-wide association studies to control for population stratification and cryptic relatedness. However, estimating LMM parameters is computationally expensive, necessitating large-scale matrix operations to build the genetic relationship matrix (GRM). Over the past 25 years, Randomized Linear Algebra has provided alternative approaches to such matrix operations by leveraging matrix sketching, which often results in provably accurate fast and efficient approximations. We leverage matrix sketching to develop a fast and efficient LMM method called Matrix-Sketching LMM (MaSk-LMM) by sketching the genotype matrix to reduce its dimensions and speed up computations. Our framework comes with both theoretical guarantees and a strong empirical performance compared to the current state-of-the-art for simulated traits and complex diseases.