Summary-based imputation was performed using the ImpG-Summary algorithm4 extended to train on the cis-genetic component of expression. Let Z be a vector of standardized effect sizes (z-scores) of SNP on trait at a given cis-locus (i.e. Wald statistics β/se(β) ). We impute the z-score of the expression and trait as a linear combination of elements of Z with weights W (these weights are precompiled from the reference panel as Σe,sΣ−1s,s for ImpG-Summary or directly from BSLMM). Σe,s is the covariance matrix between all SNPs at the locus and gene expression and Σs,s is the covariance among all SNPs (i.e. linkage disequilibrium). Under null data (no association) and a multi-variate normal assumption Z ~ N(0,Σs,s). It follows that imputed z-score of expression and trait (WZ) has variance W Σs,s Wt; therefore, we use WZ/(W Σs,s Wt )1/2 as the imputation Z-score of cis-genetic effect on trait. In practice, for each gene, all SNPs within 1Mb of the gene present in the GWAS study were selected, and Σs,s and Σe,s were computed in the reference panel (i.e. expression and SNP data). To
