Multivariate mendelian randomization for joint inferences of correlated outcomes

Mendelian randomization (MR) typically analyzes causal relationships between exposures and outcomes independently, potentially missing important correlations among related outcomes. Few methods exist to jointly analyze multiple outcomes in MR studies. We propose two novel multivariate approaches for handling correlated outcomes in MR. Multivariate inverse-variance weighted MR (multivariate MR-IVW) incorporates outcome correlations through multivariate meta-analysis. Multivariate MR pleiotropy residual sum and outlier (multivariate MR-PRESSO) test leverages Mahalanobis distance to detect heterogeneous instruments across correlated outcomes. We evaluated these methods through comprehensive simulation study. Multivariate methods were applied to investigate causal relationships between DNA methylation at cg11294513 and five zinc finger gene expressions using Framingham Heart Study and Genotype-Tissue Expression project data. Simulation study demonstrated that multivariate MR-IVW consistently achieved lower bias and mean squared error compared to univariate method. For global hypothesis testing, multivariate MR-IVW showed substantially higher sensitivity than univariate method (e.g., 95% vs. 52% at r = 0.8 with two outcomes) while maintaining controlled false positive rates. Multivariate MR-PRESSO detected outlying SNPs with substantially higher sensitivity compared to univariate method (e.g., 85-90% vs. 35-40% with four outcomes and balanced pleiotropy). In real data application, MR analysis revealed significant causal effects of DNA methylation at cg11294513 on all five zinc finger genes. Multivariate MR-PRESSO identified additional heterogeneous instruments that were undetected by univariate analysis. Multivariate MR methods provide superior causal effect estimation and pleiotropy detection, as well as more flexible hypothesis testing by leveraging outcome correlations. These approaches enable comprehensive analysis of complex multi-omics data.