We proposed a novel omnibus test for significant association across predictions from all three cohorts. Because the imputation is made into the same GWAS cohort, correlation between predictors must be accounted for. For each gene i, we estimated a correlation matrix Ci by predicting from the three tissues into the ~5,500 unrelated METSIM GWAS individuals (though any large panel from the study population could be used). This correlation includes both the genetic correlation of expression as well as any correlated error in the predictors, thus capturing all redundancy. On average, a correlation of 0.01, 0.01, and 0.43 was observed between YFS:METSIM, NTR:METSIM, and YFS:NTR, highlighting the same tissue of origin the last pair. We then used the three-entry vector of TWAS predictions, Zi, to compute the statistic omnibusi = Zi′ Ci−1 Zi which is approximately χ2 (3-dof) distributed and provides an omnibus test for effect in any tissue while accounting for correlation57,58. Though the correlation observed in our data was almost entirely driven by the YFS:NTR blood datasets, we expect this to be an especially useful strategy for future studies
