We assessed the credibility of our findings using a standard Bayesian framework19,20 in which a positive fraction of SNPs have null effects and a positive fraction have non-null effects (Online Methods). For each phenotype, the non-null effect sizes are assumed to be drawn from a normal distribution whose variance is estimated from the GWAS summary statistics. As a first analysis, for each lead SNP’s association with its phenotype, we calculated the posterior probability of null association after having observed the GWAS results. We found that, for any assumption about the fraction of non-null SNPs in the range 1% to 99%, the probability of true association always exceeds 95% for all 16 loci (and always exceeds 98% for 14 of them).
