Consistent Estimation in Mendelian Randomization with Some Invalid Instruments Using a Weighted Median Estimator

TLDR

Genome‑wide association studies and abundant summary genetic data have simplified Mendelian randomization, yet reliable results remain difficult because the conventional inverse‑variance weighted method requires all genetic variants to be valid instruments. The authors introduce a weighted median estimator to combine multiple genetic variants into a single causal estimate. The estimator aggregates individual variant estimates by computing a weighted median, yielding consistency even when up to half the instruments are invalid. Simulations show the weighted median has superior finite‑sample Type 1 error rates compared to the inverse‑variance weighted method and complements MR‑Egger regression; in LDL/HDL analyses it indicates a causal effect of LDL but a null effect of HDL, aligning with experimental evidence, and the authors recommend using median‑based and MR‑Egger methods as sensitivity analyses.

Abstract

ABSTRACT Developments in genome‐wide association studies and the increasing availability of summary genetic association data have made application of Mendelian randomization relatively straightforward. However, obtaining reliable results from a Mendelian randomization investigation remains problematic, as the conventional inverse‐variance weighted method only gives consistent estimates if all of the genetic variants in the analysis are valid instrumental variables. We present a novel weighted median estimator for combining data on multiple genetic variants into a single causal estimate. This estimator is consistent even when up to 50% of the information comes from invalid instrumental variables. In a simulation analysis, it is shown to have better finite‐sample Type 1 error rates than the inverse‐variance weighted method, and is complementary to the recently proposed MR‐Egger (Mendelian randomization‐Egger) regression method. In analyses of the causal effects of low‐density lipoprotein cholesterol and high‐density lipoprotein cholesterol on coronary artery disease risk, the inverse‐variance weighted method suggests a causal effect of both lipid fractions, whereas the weighted median and MR‐Egger regression methods suggest a null effect of high‐density lipoprotein cholesterol that corresponds with the experimental evidence. Both median‐based and MR‐Egger regression methods should be considered as sensitivity analyses for Mendelian randomization investigations with multiple genetic variants.