In addition to testing concordance for the direction of effect, we also evaluate replication for the magnitude of the effect sizes. Specifically, for each of deCODE and 23andMe we regressed the effect size in the replication cohort (i.e. the log odds ratio) on the estimated effect size from the ADHD GWAS after adjustment for winner’s curse for loci with P < 1e-6. Winner’s curse correction is perfomed by computing posterior mean estimates of marginal SNP effects βj after fitting a spike-and-alab distribution βj~{0N(0,τ2)with probabilityπotherwise by maximum likelihood as described by Okbay et al.78 (Supplementary Information). For the regression of effect sizes we oriented all variants in the direction of the risk increasing allele estimated from the ADHD GWAS, constrained the intercept to zero, and weighted the variants proportional to the inverse of their squared standard error from the ADHD GWAS. A regression slope of one indicates “ideal” replication of all loci in the regression, whereas a slope of zero indicates no replication.
