Figure 2. Explicit and implicit adjustment of confounding with higher-order conditional independence tests Empirical type-I error rate for conditional independence tests from simulated data at a nominal level α0.05 (dotted horizontal line) as function of the conditioning order $q$. Panel (A) shows results on testing for an absent eQTL association while panel (B) shows them for an absent gene-gene association. Solid lines correspond to the model under which confounding affects only the tested genes while dashed lines correspond to a confounding effect on all genes. Dotted lines from both confounding models overlap because they correspond to the inclusion of the confounding effect in the conditioning subsets, thereby explicitly adjusting for it.