Abstract
Methods have been developed for Mendelian randomization that can obtain consistent causal estimates while relaxing the instrumental variable assumptions. These include multivariable Mendelian randomization, in which a genetic variant may be associated with multiple risk factors so long as any association with the outcome is via the measured risk factors (measured pleiotropy), and the MR‐Egger (Mendelian randomization‐Egger) method, in which a genetic variant may be directly associated with the outcome not via the risk factor of interest, so long as the direct effects of the variants on the outcome are uncorrelated with their associations with the risk factor (unmeasured pleiotropy). In this paper, we extend the MR‐Egger method to a multivariable setting to correct for both measured and unmeasured pleiotropy. We show, through theoretical arguments and a simulation study, that the multivariable MR‐Egger method has advantages over its univariable counterpart in terms of plausibility of the assumption needed for consistent causal estimation and power to detect a causal effect when this assumption is satisfied. The methods are compared in an applied analysis to investigate the causal effect of high‐density lipoprotein cholesterol on coronary heart disease risk. The multivariable MR‐Egger method will be useful to analyse high‐dimensional data in situations where the risk factors are highly related and it is difficult to find genetic variants specifically associated with the risk factor of interest (multivariable by design), and as a sensitivity analysis when the genetic variants are known to have pleiotropic effects on measured risk factors.
Highlights
Mendelian randomization (MR) uses genetic variants as instrumental variables to estimate the causal effect of a risk factor on an outcome using observational data.[1,2] Increases in the scale of genome-wide association studies have led to large numbers of genetic variants that are associated with candidate risk factors being discovered.[3]
The causal estimates for both multivariable inverse-variance weighted (IVW) and multivariable MR-Egger were biased under scenario 4, the magnitude of bias was less for multivariable MR-Egger, with the exception of when αj′ was generated from (0.01, 0.004)
In scenarios where there was no bias in the original set of simulations, the multivariable IVW and multivariable MR-Egger methods consistently estimated the direct effect of X1 on Y (θ1), while the univariable MR-Egger method consistently estimated the total causal effect of X1 on Y (θ1 + γθ2)
Summary
Mendelian randomization (MR) uses genetic variants as instrumental variables to estimate the causal effect of a risk factor on an outcome using observational data.[1,2] Increases in the scale of genome-wide association studies have led to large numbers of genetic variants that are associated with candidate risk factors being discovered.[3]. For some sets of risk factors, including lipid fractions, several risk factors have common genetic predictors Such genetic variants are pleiotropic, they can be used to estimate causal effects in a multivariable MR framework.[7]. In multivariable MR, the instrumental variable assumptions are extended to allow a genetic variant to be associated with multiple risk factors, provided all associated risk factors are included in the analysis. When genetic variants are suspected to violate the instrumental variable assumptions through unknown pleiotropic pathways, methods have been developed to estimate consistent causal effects under weaker assumptions. These include the weighted median and MR-Egger methods.[8,9]. There remains several methodological issues relating to the implementation of the method, and the assumptions required
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