We further sought to quantify the significance of the expression-trait associations conditional on the SNP-trait effects at the locus with a permutation test (Methods). Comparing to this null assesses how much signal is added by the true expression given the specific architecture of the locus. Of the 69 genes, this permutation test was significant for 54 (after accounting for 69 tests). After excluding these individually significant genes, the P-values were still substantially elevated with λGC of 19 (ratio of median χ2 to the expected null). For these 54 genes, we can confidently conclude that integration of expression data significantly refined the association to trait. As before, more evidence of allelic heterogeneity of expression was observed at the loci that passed permutation (Supplementary Figure 17). Our results are consistent with a model of causality where these genes harbor inherited causal variants that modulate expression, which in turn has a complex effect on the cell and downstream impact on complex traits6.
