When can whole-genome SNP heritability be reliably estimated from summary statistics?

LD Score Regression (LDSC) is a prominent method, which estimates whole-genome SNP heritability from summary statistics via the slope of a linear regression of GWAS test statistics corresponding to a trait of interest against LD scores. It was claimed by the LDSC authors that the free intercept in the regression accounts for confounding bias such as population stratification. In this study, we argue that the intercept in LDSC must be fixed to 1 for accurate SNP heritability estimation. We show both theoretically and with simulations that the estimated intercept does not accurately capture population stratification effects, and that it adversely affects the accuracy of the heritability estimate introducing bias and increasing variance. Fixing the intercept to 1 eliminates bias and reduces variance when no population stratification is present. On the other hand, under population stratification, LDSC is biased with both the free and the fixed intercept. Additionally, we show that estimated standard errors in LDSC are underestimated, potentially leading to false-positives in downstream GWAS analyses.