(2)E[z1jz2j]=N1N2ρgMℓj+ρNsN1N2, where zij denotes the z-score for study i and SNPj, Ni is the sample size for study i, ρg is genetic covariance, ℓj is LD Score [19], Ns is the number of individuals included in both studies, and ρ is the phenotypic correlation among the Ns overlapping samples. We derive this equation in the Supplementary Note. We estimate genetic covariance by regressing z1jz2j against ℓjN1jN2j, (where Nij is the sample size for SNP j in study i) then multiplying the resulting slope by M, the number of SNPs in the reference panel with MAF between 5% and 50% (technically, this is an estimate of the genetic covariance among SNPs with 5–50% MAF; Supplementary Note).
