Abstract
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. Here we provide a mathematical analysis 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 unbiased estimates of confounding at null SNPs under very general conditions. This robustness holds even in cases now thought to be unfavorable, such as a 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 produces unbiased estimates of the genetic correlation, even when its estimates of the genetic covariance and the two univariate heritabilities are substantially biased.
Footnotes
The authors declare no conict of interest.