inference compared with standard approaches which rely on the stronger assumption that there is no pleiotropy. This renders it an important sensitivity analysis tool in the Mendelian randomization context. In Box 1 we re-state the critical assumptions required for the valid application of MR-Egger regression and provide a step-by-step guide to its application in practice. Box 1. Summary of assumptions for application of MR-Egger regression We take summarized genetic association estimates with the exposure (γ^1,…,γ^J), with the outcome (Γ^1,…,Γ^J), and standard errors of the genetic associations with the outcome (σY1,…,σYJ) for J genetic variants which are: (i) robustly associated with the exposure, (ii) uncorrelated with each other and (iii) in Hardy-Weinberg equilibrium. All variants must be orientated such that the genetic associations with the exposure have the same sign (that is, they must all be positive or all negative).For the standard inverse-variance weighted method, we perform a weighted linear regression of the genetic associations with the outcome on the genetic associations with the exposure, weighting by the inverse-variance of the genetic associations with the outcome (σYj−2). In this regression model, the intercept is constrained to equal zero. This analysis assumes that all genetic variants are valid instrumental variables.For the proposed
