20 principal components (Supplementary Fig. 1). Thus, we interpret this deviation as indicative of a large number of weakly associated SNPs consistent with polygenic inheritance4. We also examined 298 ancestry-informative markers (AIMs) that reflect European-ancestry population substructure5. Unadjusted analyses showed greater inflation in the test statistics than we saw for all markers (AIMs λ = 2.26 compared to all markers λ = 1.56). After inclusion of principal components, the distributions of the test statistics did not differ between AIMs (λ = 1.18) and all markers (λ = 1.23), a result inconsistent with population stratification explaining the residual deviation seen in Supplementary Figure 1. Moreover, the results of a meta-analysis using summary results generated using study specific principal components (Supplementary Note) were highly correlated with those from the mega-analysis (Pearson correlation = 0.94, with a similar λ = 1.20; Supplementary Fig. 2). Of the ten SNPs in Table 2, four increased and six decreased in significance, suggesting that the most extreme values did not result from systematic inflation artifacts. Therefore, our primary analysis used unadjusted P values (nevertheless, see Table 2 for stage 1 P values adjusted for λ (ref. 6).
