title: Consistent Estimation in Mendelian Randomization with Some Invalid Instruments Using a Weighted Median Estimator.
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.
authors.affiliation: Integrative Epidemiology Unit, University of Bristol, Bristol, United Kingdom.
authors.forename: Jack
authors.initials: J
authors.lastname: Bowden
authors.affiliation: Integrative Epidemiology Unit, University of Bristol, Bristol, United Kingdom.
authors.forename: George
authors.initials: G
authors.lastname: Davey Smith
authors.affiliation: Integrative Epidemiology Unit, University of Bristol, Bristol, United Kingdom.
authors.forename: Philip C
authors.initials: PC
authors.lastname: Haycock
authors.affiliation: Department of Public Health and Primary Care, University of Cambridge, Cambridge, United Kingdom.
authors.forename: Stephen
authors.initials: S
authors.lastname: Burgess
mesh_terms: D008076:Cholesterol, HDL / Q000032:analysis; D008078:Cholesterol, LDL / Q000032:analysis; D003324:Coronary Artery Disease / Q000235:genetics / Q000378:metabolism; D020022:Genetic Predisposition to Disease; D014644:Genetic Variation / Q000235:genetics*; D055106:Genome-Wide Association Study; D006801:Humans; D057182:Mendelian Randomization Analysis / Q000379:methods*; D008957:Models, Genetic; D012044:Regression Analysis; D012107:Research Design
chemical_list: D008076:Cholesterol, HDL; D008078:Cholesterol, LDL
keywords: Egger regression; Mendelian randomization; instrumental variables; pleiotropy; robust statistics