Prediction of causal genes at GWAS loci with pleiotropic gene regulatory effects using sets of correlated instrumental variables

Multivariate Mendelian randomization (MVMR) is a statistical technique that uses sets of genetic instruments to estimate the direct causal effects of multiple exposures on an outcome of interest. At genomic loci with pleiotropic gene regulatory effects, that is, loci where the same genetic variants are associated to multiple nearby genes, MVMR can potentially be used to predict candidate causal genes. However, consensus in the field dictates that the genetic instruments in MVMR must be independent (not in linkage disequilibrium), which is usually not possible when considering a group of candidate genes from the same locus. Here we used causal inference theory to show that MVMR with correlated instruments satisfies the instrumental set condition. This is a classical result by Brito and Pearl (2002) for structural equation models that guarantees the identifiability of individual causal effects in situations where multiple exposures collectively, but not individually, separate a set of instrumental variables from an outcome variable. Extensive simulations confirmed the validity and usefulness of these theoretical results. Importantly, the causal effect estimates remained unbiased and their variance small even when instruments are highly correlated, while bias introduced by horizontal pleiotropy or LD matrix sampling error was comparable to standard MR. We applied MVMR with correlated instrumental variable sets at genome-wide significant loci for coronary artery disease (CAD) risk using expression Quantitative Trait Loci (eQTL) data from seven vascular and metabolic tissues in the STARNET study. Our method predicts causal genes at twelve loci, each associated with multiple colocated genes in multiple tissues. We confirm causal roles for PHACTR1 and ADAMTS7 in arterial tissues, among others. However, the extensive degree of regulatory pleiotropy across tissues and the limited number of causal variants in each locus still require that MVMR is run on a tissue-by-tissue basis, and testing all gene-tissue pairs with cis-eQTL associations at a given locus in a single model to predict causal gene-tissue combinations remains infeasible. Our results show that within tissues, MVMR with dependent, as opposed to independent, sets of instrumental variables significantly expands the scope for predicting causal genes in disease risk loci with pleiotropic regulatory effects. However, considering risk loci with regulatory pleiotropy that also spans across tissues remains an unsolved problem.