Underestimation of heritability using a mixed model with a polygenic covariance structure in a genome-wide association study for complex traits

Recently, the use of a mixed model methodology in genome-wide association studies (GWAS) has been considered effective for controlling population stratification and explaining the polygenic effects of complex traits. However, estimating polygenic variance components and heritability was biased when the mixed model was used. This bias results from a diluted genetic relationship covariance structure, particularly with a limited number of underlying causal variants. We simulated disease and quantitative phenotypes with a variety of heritabilities (0.1, 0.2, 0.3, 0.4, and 0.5), prevalence rates (0.1, 0.2, 0.3, and 0.5), and causal variant numbers (10, 30, 50, and 100). Heritabilities from the simulated data using restricted maximum likelihood were underestimated in many populations (P<0.05). The underestimation increased with a large heritability, a small prevalence, and a small number of causal variants. The underestimation was larger in analyzing disease traits compared with quantitative traits. This study suggests an underestimated heritability in GWAS upon using the mixed model methodology with an excessively larger number of variants versus causal variants.