Figure 1 shows histograms of the P values from the association tests. Under the null hypothesis assuming no replication, the histograms would have had equal heights. The skewed histograms therefore indicated considerable enrichment of small P values. To quantify this enrichment, we divided the observed median test statistic value by the expected median under the null hypothesis. This index, which has an expected value of 1.00 if SNPs do not replicate, equaled 1.19, 1.12, and 1.07 for subjects from European, Asian, and African ancestry, respectively, and was 1.15 for the (signed) combined analysis that required the same direction of effects in all 3 groups. Next, we tested whether this enrichment for small P values was statistically significant (eMethods 3). Owing to the large number of SNPs, large sample size, and family-based association tests allowing for missing genotypes, it was computationally not feasible to perform a sufficiently large number of permutations to obtain empirical P values. Instead, we obtained the lower and upper bounds assuming no linkage disequilibrium (LD) and very high LD, respectively, among the SNPs. When we assumed no
