A More Credible Approach to Multivariable Mendelian Randomization

Multivariable Mendelian randomization (MVMR) uses genetic variants as instrumental variables to infer the direct effects of multiple exposures on an outcome. However, unlike univariable MR, MVMR often faces greater challenges with many weak instruments, which can lead to bias not necessarily toward zero and inflation of type I errors. In this work, we introduce a new asymptotic regime that allows exposures to have different degrees of instrument strength, providing a more credible theoretical framework for studying MVMR estimators. Our analysis of the widely used multivariable inverse-variance weighted method shows that it is often biased and tends to produce misleadingly narrow confidence intervals in the presence of many weak instruments. To address this, we propose a spectral regularized estimator and show that the estimator is consistent and asymptotically normal under many weak instruments. We demonstrate through simulations and real applications that our proposed estimator would bring more credibility to MVMR analysis.