A More Robust Approach to Multivariable Mendelian Randomization

TL;DR

This paper introduces a new theoretical framework and modified estimators for multivariable Mendelian randomization that are more robust to weak instruments, reducing bias and improving reliability in causal inference.

Contribution

It presents a novel asymptotic regime for MVMR, a simple bias-reduction modification, and a spectral regularization technique to enhance estimator performance with weak instruments.

Findings

Multivariable inverse-variance weighted method is biased with many weak instruments.

The proposed spectral-regularized estimator remains consistent and normal under weak instruments.

Simulations and real data show improved robustness of the new methods.

Abstract

Multivariable Mendelian randomization (MVMR) uses genetic variants as instrumental variables to infer the direct effects of multiple exposures on an outcome. However, unlike univariable Mendelian randomization, 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 varying degrees of instrument strength, providing a more accurate theoretical framework for studying MVMR estimators. Under this regime, 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 simple, closed-form modification to the multivariable inverse-variance weighted estimator to reduce bias from weak instruments, and additionally introduce a novel spectral regularization technique to improve finite-sample performance. We show that the resulting spectral-regularized estimator remains consistent and asymptotically normal under many weak instruments. Through simulations and real data applications, we demonstrate that our proposed estimator and asymptotic framework can enhance the robustness of MVMR analyses.