(1)E[χj2]=N∑CτCℓ(j,C)+Na+1 where N is sample size, C indexes categories, ℓ(j, C) is the LD score of SNP j with respect to category C (defined as ℓ(j,C)=∑k∈Crjk2), a is a term that measures the contribution of confounding biases [16], and if the categories are disjoint, τC is the per-SNP heritability in category C; if the categories overlap, then the per-SNP heritability of SNP j is ΣC:j∈C τC Equation (1) allows us to estimate τC via a (computationally simple) multiple regression of χ2 against ℓ(j, C), for either a quantitative or case-control study. We define the enrichment of a category to be the proportion of SNP-heritability in the category divided by the proportion of SNPs. We estimate standard errors with a block jackknife [16], and use these standard errors to calculate z-scores, P-values, and FDRs. We have released open-source software implementing the method (URLs); for further details see the Online Methods and Supplementary Note.
