If the βX1 parameters are independent of the βXk parameters for all k=2,3,…,K, then the second term in Equation 13 (the measured direct effect) does not contribute to the value of covw(α,βX1). Under this scenario, bias for the univariable and multivariable MR‐Egger estimates depends on the same covariance term covw(α′,βX1). As a consequence, the estimates of the causal effects from univariable MR‐Egger θ^UE and multivariable MR‐Egger θ^1ME will be asymptotically the same. In this case, multivariable MR‐Egger may improve precision of the causal estimate but will not affect the asymptotic bias.
