To find additional independent SNPs at each locus, we ran a conditional stepwise regression analysis at all SNPs with rinfo2>0.8 in the GERA meta-analysis, around each previously-described and novel GERA SNP. We looked for additional genome-wide significant SNPs within a 1Mb window (±0.5Mb) of the lead SNP. While this generally worked well, certain portions of the genome have stronger LD (we noted particularly at ends of chromosomes and centromeres, where recombination is suppressed), which we assessed via visual inspection of the Manhattan plots to form an expanded window size, and repeated the stepwise regression on the expanded window. In these analyses we adjusted for ancestry PCs (see below) instead of the mixed model approach, both for simplicity and computational efficiency.