MR-MAGIC: Robust Causal Inference Using Many Weak Genetic Interactions

Abstract: Mendelian randomization (MR) studies commonly use genetic variants as instrumental variables to estimate causal effects of exposures on outcomes. However, the presence of invalid instruments-even when numerous-can lead to biased causal estimates. We propose a novel identification strategy that remains valid even when all candidate instruments are invalid by leveraging genetic interactions that collectively explain substantial exposure variation. Recognizing that individual interaction effects may be weak, we develop MR-MAGIC (Mendelian Randomization with MAny weak Genetic Interactions for Causality), a robust method that simultaneously addresses instrument invalidity and improves estimation efficiency. MR-MAGIC provides consistent and asymptotically normal estimates under a many-weak-interactions asymptotic framework. Comprehensive simulations and applications to UK Biobank data demonstrate that MR-MAGIC outperforms conventional MR methods in practice, offering reliable causal inference when standard approaches fail.