0.50 or minimum r2 < 0.30 in any imputation batch, as well as SNPs that had strong evidence of an imputation batch effect. The batch effect test is an F test from an ANOVA of the SNP dosages against a factor representing imputation batch; we removed results with P < 1 × 10−50. We also removed linear regression results for SNPs with MAF < 0.1% because tests of low frequency variants can be sensitive to violations of the regression assumption of normally distributed residuals. We performed association tests by linear regression assuming an additive model. We included age (inverse-normal transformed), sex, the top five principal components of genotype, and indicator variables for genotype platforms as covariates (Supplementary Table 4).