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 MR-Egger method, we perform the same weighted linear regression with the intercept unconstrained. The intercept represents the average pleiotropic effect across the genetic variants (the average direct effect of a variant with the outcome). If the intercept differs from zero (the MR-Egger test), then there is evidence of directional pleiotropy. Under the assumption that the associations of the genetic variants with the exposure are independent of the direct effects of the genetic variants on the outcome (the InSIDE assumption), the slope coefficient from the MR-Egger regression is a consistent estimate of the causal effect. This is a weaker assumption than the assumption that all genetic variants are valid instrumental variables.The InSIDE assumption would be violated if the pleiotropic effects act via a confounder of the exposure—outcome association.R and Stata code to perform the inverse-variance weighted and MR-Egger methods is provided in the Web Appendix (available as Supplementary data at IJE online).
