assigned a SNP of small effect size were also randomly chosen from all genes in the gene set. The remaining number of causal SNPs was randomly assigned to genes outside the gene set. The small effects were randomly assigned to SNPs within the ±50kb extended gene boundaries (see above for boundary definition). To eliminate artifacts that could arise from using one specific vector of permuted , each simulation run was done on a different GWA study permutation background that was randomly chosen from 1,000 different DGI phenotype permutations. For each of the 1,000 simulation runs, gene p-values corrected with multivariate regression analysis (see above), were calculated for all genes g in the genome. The GSEA algorithm in MAGENTA was then applied to the simulated gene set with a given fraction of causal genes of weak effect. Finally, GSEA power (i.e. sensitivity) was estimated as the fraction of 1,000 spike-in simulations whose gene set enrichment p-value, exceeded a given significance level (in this study ≤0.01, a suitable cutoff for the few hypotheses tested in the mitochondrial gene set analysis). The power does not decrease significantly when a more stringent cutoff is used: ≤0.001 (Figure S9).
