Stratified LD score regression7 is a method for partitioning heritability. Given (potentially overlapping) genomic annotations C1,…, CK, one of which is the category of all SNPs, we model the causal effect of SNP j on phenotype Y as drawn from a distribution with mean 0 and variance (1)Var(βi)= ∑kτk1{i∈Ck}.(If the genomic annotations are real-valued rather than subsets of SNPs, we can replace 1{i∈Ck} with any other function of the SNP indices65.) We then model the phenotype Y as depending linearly on genotype: Y=X⋅β+ε, where X is a vector of SNP values for an individual, and each SNP has been standardized to mean 0 and variance 1 in the population. Because each SNP is standardized, and because βi has mean zero, we can call Var(βi) the per-SNP heritability of SNP i. (Note that here, because we model β as random, our definition of heritability is different from definitions of heritability in which β is fixed, and so we are estimating a fundamentally different quantity than some other methods67.)
