Relationship between LD Score and Haseman-Elston Regression

Estimating SNP-heritability from summary statistics using LD Score regression provides a convenient alternative to standard variance component models, because LD Score regression is computationally very fast and does not require individual genotype data. However, the mathematical relationship between variance component methods and LD Score regression is not clear; in particular, it is not known in general how much of an increase in standard error one incurs by working with summary data instead of individual genotypes. In this paper, I show that in samples of unrelated individuals, LD Score regression with constrained intercept is essentially the same as Haseman-Elston (HE) regression, which is currently the state-of-the-art method for estimating SNP-heritability from ascertained case/control samples. Similar results hold for SNP-genetic correlation.