each association against a null-distribution created by repeating the analysis 100 times (permuting the sample labels for each iteration49). PCs that did not show significance at the FDR threshold of 0.0 were removed from the gene expression data by linear regression. In all but two very small datasets, the first 40 PCs were removed (excluding those components per cohort that showed a QTL effect). We observed that the removal of these 40 components revealed the highest number of eQTLs in each dataset. Although PC correction may remove some eQTL effects, we observed that the majority (95% when removing 35 PCs and 90% when removing 40 PCs) of trans-eQTL effects was independent of the number of PCs removed (Supplementary Figure 14).
