Estimating and visualising multivariable Mendelian randomization analyses within a radial framework

Background
Mendelian randomization (MR) is a statistical approach using genetic variants as instrumental variables to estimate causal effects of a single exposure on an outcome. Multivariable MR (MVMR) extends this to estimate the direct effect of multiple exposures simulatiously. MR and MVMR can be biased by the presence of pleiotropic genetic variants in the set used as instrumental variables, violating one of the core IV assumptions. Genetic variants that give outlying estimates are often considered to be potentially pleiotropic variants. Radial plots can be used in MR to help identify these variants. Analogous plots for MVMR have so far been unavailable due to the multidimensional nature of the analysis.

Methods
We propose a radial formulation of MVMR, and an adapted Galbraith radial plot, which allows for the estimated effect of each exposure within an MVMR analysis to be visualised. Radial MVMR additionally includes an option for removal of outlying SNPs which may violate one or more assumptions of MVMR. A RMVMR R package is presented as accompanying software for implementing the methods described.

Results
We demonstrate the effectiveness of the radial MVMR approach through simulations and applied analyses. We highlight how outliers with respect to all exposures can be visualised and removed through Radial MVMR. We present simulations that illustrate how outlier removal decreases the bias in estimated effects under various forms of pleiotropy. We apply Radial MVMR to estimate the effect of lipid fractions on coronary heart disease (CHD). In combination with simulated examples, we highlight how important features of MVMR analyses can be explored using a range of tools incorporated within the RMVMR R package.

Conclusions
Radial MVMR effectively visualises causal effect estimates, and provides valuable diagnostic information with respect to the underlying assumptions of MVMR.