To evaluate what these quasi-replication results imply about the credibility of the 16 GWAS associations, we compared the observed quasi-replication record to the quasi-replication record expected given our statistical power. We calculated statistical power using our Bayesian framework, under the hypothesis that each lead SNP has a non-null effect on both the first- and second-stage phenotypes. Our calculations take into account both the imperfect genetic correlation between the first- and second-stage phenotypes and inflation of the first-stage estimates due to the well-known problem of winner’s curse (Online Methods). Of the 19 quasi-replication tests, our calculations imply that 16.7 would be expected to yield the anticipated sign and 6.9 would be significant at the 5% level. The observed numbers are 16 and 7. Our quasi-replication results are thus consistent with the hypothesis that none of the 16 genome-wide significant associations are chance findings, and in fact strengthen the credibility of our GWAS results (Supplementary Table 14).
