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Methods have been developed for Mendelian randomization that can obtainconsistent causal estimates while relaxing the instrumental variableassumptions. These include multivariable Mendelian randomization, in which agenetic variant may be associated with multiple risk factors so long as anyassociation with the outcome is via the measured risk factors (measuredpleiotropy), and the MR-Egger (Mendelian randomization-Egger) method, in whicha genetic variant may be directly associated with the outcome not via the riskfactor of interest, so long as the direct effects of the variants on theoutcome are uncorrelated with their associations with the risk factor(unmeasured pleiotropy). In this paper, we extend the MR-Egger method to amultivariable setting to correct for both measured and unmeasured pleiotropy.We show, through theoretical arguments and a simulation study, that themultivariable MR-Egger method has advantages over its univariable counterpartin terms of plausibility of the assumption needed for consistent causalestimation, and power to detect a causal effect when this assumption issatisfied. The methods are compared in an applied analysis to investigate thecausal effect of high-density lipoprotein cholesterol on coronary heart diseaserisk. The multivariable MR-Egger method will be useful to analysehigh-dimensional data in situations where the risk factors are highly relatedand it is difficult to find genetic variants specifically associated with therisk factor of interest (multivariable by design), and as a sensitivityanalysis when the genetic variants are known to have pleiotropic effects onmeasured risk factors.

Extending the MR-Egger method for multivariable Mendelian randomization to correct for both measured and unmeasured pleiotropy