Because the GWA scans used different genotyping platforms, we imputed genotypes for all polymorphic HapMap SNPs in each scan, using a hidden Markov model as implemented in MACH (Y. Li and G.R.A., unpublished data). This approach allowed us to evaluate association at the same SNPs in all scans. The imputation method combines genotype data from each sample with the HapMap CEU samples (July 2006 phased haplotype release) and then infers the unobserved genotypes probabilistically. The inference relies on the identification of stretches of haplotype shared between study samples and individuals in HapMap CEU reference panel. For each SNP in each individual, imputation results are summarized as an ‘allele dosage’ defined as the expected number of copies of the minor allele at that SNP (a fractional value between 0.0 and 2.0). As previously described, r2 between each imputed genotype and the true underlying genotype is estimated and serves as a quality-control metric (rsq_hat in Supplementary Table 7). We chose an estimated r2 >0.3 as a threshold to flag and discard low-quality imputed SNPs (ref. 13 and Y. Li and G.R.A., unpublished data).