A Fast, Accurate Two-Step Linear Mixed Model for Genetic Analysis Applied to Repeat MRI Measurements

Large-scale biobanks are being collected around the world in efforts to better understand human health and risk factors for disease. They often survey hundreds of thousands of individuals, combining questionnaires with clinical, genetic, demographic, and imaging assessments; some of this data may be collected longitudinally. Genetic associations analysis of such datasets requires methods to properly handle relatedness, population structure and other types of biases introduced by confounders. Most popular and accurate approaches rely on linear mixed model (LMM) algorithms, which are iterative and computational complexity of each iteration scales by the square of the sample size, slowing the pace of discoveries (up to several days for single trait analysis), and, furthermore, limiting the use of repeat phenotypic measurements. Here, we describe our new, non-iterative, much faster and accurate Two-Step Linear Mixed Model (2sLMM) approach, that has a computational complexity that scales linearly with sample size. We show that the first step retains accurate estimates of the heritability (the proportion of the trait variance explained by additive genetic factors), even when increasingly complex genetic relationships between individuals are modeled. Second step provides a faster framework to obtain the effect sizes of covariates in regression model. We applied Two-Step LMM to real data from the UK Biobank, which recently released genotyping information and processed MRI data from 9,725 individuals. We used the left and right hippocampus volume (HV) as repeated measures, and observed increased and more accurate heritability estimation, consistent with simulations.