Fig. 7
Histograms of I2 distribution for validating exclusion restriction from PTWAS scan signals. Panel a shows the histogram of the I2 statistics computed from 2.09 million trait-gene-tissue combinations, where the gene has at least two independent eQTLs with individual signal-level PIP >0.50. For each trait-gene-tissue pair, the I2 index measures the consistency of the causal effects estimated from each independent eQTL. Panels b and c show the histograms with at least 3 and 5 eligible independent eQTLs, respectively. The overall patterns of the distributions are the same in all panels, where majority of the test cases show strong consistency among independent instruments. However, the ability of identifying violations of ER improves with the increasing availability of independent eQTL instruments