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 Lewbels 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.
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