For a meta-analysis of a large number of cohorts, such as the GIANT Consortium meta-analysis3,4, we are usually unable to obtain pooled individual-level genotype data of the whole discovery set; hence, we do not have the X′X matrix. X′X is essentially a variance-covariance matrix of SNP genotypes, which can be estimated from the allele frequencies in the meta-analysis sample along with LD correlations between SNPs from a reference sample, such as one of the meta-analysis cohorts for which individual-level genotype data are available. We let W = {wij} denote the genotype matrix of the reference sample with sample size of m, where wij = –2fj, 1 – 2fj or 2 – 2fj for the three genotypes, with fj being the allele frequency of a SNP j in the reference sample, and we let DW denote the diagonal matrix of W′W with DW(j)=∑imwij2. If the reference sample is from the same population as the meta-analysis sample, the LD correlation between a pair of SNPs j and k should be similar in the two samples32,33, with (9)∑inxijxik∑inxij2∑inxik2≈∑imwijwik∑imwij2∑imwik2 so that X′X is approximately equal to B, with the jkth element of B being (10)Bjk≈DjDkDW(j)DW(k)∑imwijwik
