For each analysis, single-SNP tests were carried out for each dataset by logistic regression for genotyped and imputed SNPs. For discrete genotypes without covariates, logistic regression is asymptotically equivalent to a trend test for additive effects, while permitting covariates. We used custom software to implement the same logistic regression approach for imputed non-integer genotype “dosages.” Covariates included the first ten ancestry-informative PCs, plus an indicator for sex for X chromosome SNPs. Combined analysis (“mega-analysis”) of genotypes was not straightforward because of the overlapping STAR*D/GenRED controls, with different numbers of genotyped SNPs for the two case groups. We could have assigned unique subsets of controls to GenRED and STAR*D, but some power is lost when imputation information content is much lower in one sample (see Supplementary Methods). Therefore, we used a meta-analysis procedure as described in Supplementary Methods. Briefly, for each SNP, the procedure weights the Z-score for each dataset by the case and control sample sizes and imputation r2 values (r2=1 for genotyped SNPs), while correcting for the shared controls between STAR*D and GenRED. Combined odds ratios were obtained with
