Fig. 1

a Multi-INTACT workflow. First, we perform multi-SNP fine-mapping analysis of eQTL, pQTL, and GWAS data (see Methods section). Then, we perform pairwise colocalization analysis of the eQTL and GWAS results, and separately, the pQTL and GWAS results. We generate eQTL TWAS weights and pQTL PWAS weights from the fine-mapping analysis. Using these weights, we compute the canonical correlation between the GWAS trait and imputed gene product levels. The canonical correlation and pairwise colocalization evidence serve as key inputs for Multi-INTACT analysis. Multi-INTACT utilizes an EM algorithm to determine the most relevant gene product based on the observed data. b Causal diagram that connects genetic variants G, expression levels of a candidate gene E, protein levels of a candidate gene P, and a complex trait Y. The node U represents latent confounders of effects between E, P, and Y. A similar diagram is assumed by multivariable Mendelian randomization methods. The edges that are highlighted in red are those that Multi-INTACT is designed to infer. The solid edges represent the graphical model assumed by most multivariable Mendelian randomization methods. The dashed lines emphasize that Multi-INTACT is designed to be robust to situations in which there are effects between gene products or there are violations of the exclusion restriction (i.e., direct-effect genetic variants)