  Mendelian randomization (MR) is a popular instrumental variable (IV)
approach, in which one or several genetic markers serve as IVs that can
sometimes be leveraged to recover valid inferences about a given
exposure-outcome causal association subject to unmeasured confounding. A key IV
identification condition known as the exclusion restriction states that the IV
cannot have a direct effect on the outcome which is not mediated by the
exposure in view. In MR studies, such an assumption requires an unrealistic
level of prior knowledge about the mechanism by which genetic markers causally
affect the outcome. As a result, possible violation of the exclusion
restriction can seldom be ruled out in practice. To address this concern, we
introduce a new class of IV estimators which are robust to violation of the
exclusion restriction under data generating mechanisms commonly assumed in MR
literature. The proposed approach named "MR G-Estimation under No Interaction
with Unmeasured Selection" (MR GENIUS) improves on Robins' G-estimation by
making it robust to both additive unmeasured confounding and violation of the
exclusion restriction assumption. In certain key settings, MR GENIUS reduces to
the estimator of Lewbel (2012) which is widely used in econometrics but appears
largely unappreciated in MR literature. More generally, MR GENIUS generalizes
Lewbel's estimator to several key practical MR settings, including
multiplicative causal models for binary outcome, multiplicative and odds ratio
exposure models, case control study design and censored survival outcomes.
