Finally, we meta-analyzed the ADHD GWAS with the results from each replication cohort. For deCODE and 23andMe inverse variance-weighted meta-analyses were performed. For meta-analysis with the EAGLE/QIMR GWAS of ADHD-related behaviors in childhood population samples we used a modified sample size-based weighting method. Modified sample size-based weights were derived to accounts for the respective heritabilities, genetic correlation, and measurement scale of the GWASs (Supplementary Information). To summarize, given z-scores Z1j and Z2j resulting from GWAS of SNP j in a dichotomous phenotype (e.g. ADHD) with sample size NI and a continuous phenotype (e.g. ADHD-related traits) with sample size N2, respectively, we calculate Zj,meta=N˜1jZ1j+N˜2jZ˜2jN˜1j+N˜2j where Z˜2j=sign(rg) Z2j1+(1−rg2)N2jh22lj/M N˜1j=N1jP(1−P)ϕ(Φ−1[K])2[K(1−K)]2 N˜2j=N2jrg2h22/h121+(1−rg2)N2jh22lj/M
