An alternative robust method for Mendelian randomization with summary data has been recently proposed by Bowden et al. [2015], referred to as “MR‐Egger regression.” This approach was motivated from a method in the meta‐analysis literature for the assessment of small‐study bias (often called “publication bias”) (Egger et al., 1997). This performs a weighted linear regression of the gene‐outcome coefficients Γ^j on the gene‐exposure coefficients γ^j: Γ^j=β0E+βEγ^jin which all the γ^j associations are orientated to be positive (the orientation of the Γ^j associations should be altered if necessary to match the orientation of the γ^j parameters), and the weights in the regression are the inverse variances of the gene‐outcome associations (σYj−2). Reorientation of the variants is performed as the orientation of genetic variants is arbitrary (i.e., estimates can be presented with reference to either the major or minor allele), and different orientations of genetic variants change the estimate of the intercept, as well as the sign and magnitude of the pleiotropic effect of the genetic variant. If there is no intercept term in the regression model, then the MR‐Egger slope estimate β^E will equal the IVW estimate (Burgess et al., 2015a).
