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

Genet Epidemiol. 2016 May;40(4):304-14. doi: 10.1002/gepi.21965. Epub 2016 Apr 7.


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.

Keywords: Egger regression; Mendelian randomization; instrumental variables; pleiotropy; robust statistics.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Cholesterol, HDL / analysis
  • Cholesterol, LDL / analysis
  • Coronary Artery Disease / genetics
  • Coronary Artery Disease / metabolism
  • Genetic Predisposition to Disease
  • Genetic Variation / genetics*
  • Genome-Wide Association Study
  • Humans
  • Mendelian Randomization Analysis / methods*
  • Models, Genetic
  • Regression Analysis
  • Research Design


  • Cholesterol, HDL
  • Cholesterol, LDL