Estimating SNP heritability in presence of population substructure in biobank-scale datasets

SNP heritability of a trait is measured by the proportion of total variance explained by the additive effects of genome-wide single nucleotide polymorphisms (SNPs). Linear mixed models are routinely used to estimate SNP heritability for many complex traits. The basic concept behind this approach is to model genetic contribution as a random effect, where the variance of this genetic contribution attributes to the heritability of the trait. This linear mixed model approach requires estimation of ‘relatedness’ among individuals in the sample, which is usually captured by estimating a genetic relationship matrix (GRM). Heritability is estimated by the restricted maximum likelihood (REML) or method of moments (MOM) approaches, and this estimation relies heavily on the GRM computed from the genetic data on individuals. Presence of population substructure in the data could significantly impact the GRM estimation and may introduce bias in heritability estimation. The common practice of accounting for such population substructure is to adjust for the top few principal components of the GRM as covariates in the linear mixed model. Here we propose an alternative way of estimating heritability in multi-ethnic studies. Our proposed approach is a MOM estimator derived from the Haseman-Elston regression and gives an asymptotically unbiased estimate of heritability in presence of population stratification. It introduces adjustments for the population stratification in a second-order estimating equation and allows for the total phenotypic variance vary by ethnicity. We study the performance of different MOM and REML approaches in presence of population stratification through extensive simulation studies. We estimate the heritability of height, weight and other anthropometric traits in the UK Biobank cohort to investigate the impact of subtle population substructure on SNP heritability estimation.