The adjusted sample sizes N1˜ and N2˜ reflect differences in power between the studies due to measurement scale and relative heritability that is not captured by sample size. The calculation of Z2˜ reduces the contribution of the continuous phenotype’s GWAS to the meta-analysis based on imperfect genetic correlation with the dichotomous phenotype of interest (i.e. ADHD). The adjustments are computed based on the sample prevalence (P) and population prevalence (K) of the dichotomous phenotype, the estimated liability scale SNP heritability of the two phenotypes (h12 and h22), and the genetic correlation (rg) between the two phenotypes, as well as the average SNP LD score (lj) and the number of SNPs (M). Heritability and genetic correlation values to compute these weights are computed using LD score regression. This meta-analysis weighting scheme is consistent with weights alternatively derived based on modelling the joint distribution of marginal GWAS beta across traits131.
