For example, if k=2, and βX1 is correlated with βX2, we require both of the weighted covariances of α′ with βX1 and βX2 to be zero to produce a consistent estimate of θ 1. The estimate of θ 1 from multivariable MR‐Egger with 2 risk factors where βX1 and βX2 are correlated is (12)θ^1ME=covw(β^Y,β^X1)varw(β^X2)−covw(β^Y,β^X2)covw(β^X1,β^X2)varw(β^X1)varw(β^X2)−covw(β^X1,β^X2)2→N→∞covw(βY,βX1)varw(βX2)−covw(βY,βX2)covw(βX1,βX2)varw(βX1)varw(βX2)−covw(βX1,βX2)2=θ1+covw(α′,βX1)varw(βX2)−covw(α′,βX2)covw(βX1,βX2)varw(βX1)varw(βX2)−covw(βX1,βX2)2, which is equal to θ 1 if the InSIDE assumption holds with respect to βX1 and βX2. As more risk factors with correlated sets of association parameters with βX1 are included in the multivariable MR‐Egger model, additional terms will be added to the bias term in Equation 12, and the InSIDE assumption must hold for these additional risk factors to obtain a consistent estimate of θ 1.
