In the GWAS and replication analysis, we computed association test results by logistic regression assuming additive allelic effects. For tests using imputed data, we use the imputed dosages rather than best-guess genotypes. We included covariates for age, gender, and the top 5 principal components to account for residual population structure. While we could justify the choice of 5 PCs based on the preceding ancestry analysis, we actually chose to use 5 based on computational considerations, and others have noted this to be a reasonable choice35.