The accuracy of LD Score regression as an estimator of confounding and genetic correlations in genome-wide association studies

In order to infer that a single-nucleotide polymorphism (SNP) either affects a phenotype or is linkage disequilibrium with a causal site, we must have some assurance that any SNP-phenotype correlation is not the result of confounding with some environmental variable that also affects the trait. In this work we study the properties of LD Score regression, a recently developed method for using summary statistics from genome-wide association studies (GWAS) to ensure that confounding does not inflate the number of false positives. We do not treat the effects of genetic variation as a random variable and thus are able to obtain results about the unbiasedness of this method. We demonstrate that LD Score regression can produce estimates of confounding at null SNPs that are nearly unbiased under fairly general conditions. This robustness holds in the case of the parent genotype affecting the offspring phenotype through some environmental mechanism, despite the resulting correlation over SNPs between LD Scores and the degree of confounding. LD Score regression is thus an even stronger technique for causal inference than foreseen by its developers. Additionally, we demonstrate that LD Score regression can produce reasonably robust estimates of the genetic correlation, even when its estimates of the genetic covariance and the two univariate heritabilities are substantially biased.