Going one step further, we also simulated in-silico phenotypes influenced by randomly selected causal SNPs. We explored two scenarios: one where 50 SNPs were randomly selected from the entire genome and another where random sampling was applied to gene regions only. The experiment was repeated 50 times and independent genetic data was used to generate the estimated pairwise correlation. Although in this case gene scores naturally deviate from the null distribution, we found that overall pathway p-values remain well calibrated (S14 and S15 Figs). Note that we explored only a limited set of simulation scenarios and cannot exclude that some settings might produce less well-calibrated results (see legend of S15 Fig).