The parameters used in the simulations are: (i) Gene set size of 25, 100 or 1000 genes; (ii) Fraction of genes in a gene set that got assigned a SNP with a modest effect size: 0 (negative control), 1%, 5%, and 10%, 20%, 30%, 40%, 50% and 60%; (iii) The small effect size of each spiked-in SNP was estimated by randomly sampling from a noncentral chi-square distribution with one degree of freedom (assuming an additive allelic test). The non-centrality parameters (NCP) used were: NCP = 0 for estimating specificity or false positive rate of our GSEA method, NCP = 2.5 for a very weak effect size (equivalent to 1% power of detection at p≤1e-4 using single SNP analysis; e.g. odds ratio of 1.03–1.04 for an allele frequency of 0.2–0.3 and sample size of 10,000 individuals [41]; Figure S6A), and NCP = 10 for a modest effect size (equivalent to 1% power of detection at genome-wide significance (p≤5e-8) using single SNP analysis; e.g. odds ratio of 1.07 for an allele frequency of 0.2–0.3 and sample size of 10,000 individuals [41]; Figure
