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

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

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Integrative Epidemiology Unit, University of Bristol, Bristol, United Kingdom.
Department of Public Health and Primary Care, University of Cambridge, Cambridge, United Kingdom.


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.


Egger regression; Mendelian randomization; instrumental variables; pleiotropy; robust statistics

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