Linkage disequilibrium (LD) score regression is an increasingly popular method used to quantify the level of confounding in genome-wide association studies (GWAS) or to estimate heritability and genetic correlation between traits. When applied to a pair of GWAS, the LD score regression (LDSC) methodology produces a statistic, referred to as the bivariate LDSC intercept, which deviation from 0 is classically interpreted as an indication of sample overlap between the two GWAS. Here we propose an extension of the theory underlying the bivariate LDSC methodology, which accounts for population stratification within and between GWAS. Our extended theory predicts an inflation of the bivariate LDSC intercept when sample sizes and heritability are large, even in the absence of sample overlap. We illustrate our theoretical results with simulations based on actual SNP genotypes and we propose a re-interpretation of previously published results in the light of our extended theory.

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