Abstract
Mendelian randomization (MR) is a popular instrumental variable (IV) approach, in which one or several genetic markers serve as IVs that can be leveraged to recover under certain conditions, 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 has no direct effect on the outcome that is not mediated by the exposure in view. In MR studies, such an assumption requires an unrealistic level of knowledge and understanding of the mechanism by which the genetic markers causally affect the outcome, particularly when a large number of genetic variants are considered as IVs. As a result, possible violation of the exclusion restriction can seldom be ruled out in such MR studies, and if present, such violation can invalidate IVbased inferences even if unbeknownst to the analyst, confounding is either negligible or absent. To address this concern, we introduce a new class of IV estimators which are robust to violation of the exclusion restriction under a large collection of data generating mechanisms consistent with parametric models commonly assumed in the MR literature. Our approach which we have named “MR G-Estimation under No Interaction with Unmeasured Selection” (MR GENIUS) may in fact be viewed as a modification to Robins’ G-estimation approach that is robust to both additive unmeasured confounding and violation of the exclusion restriction assumption. We also establish that estimation with MR GENIUS may also be viewed as a robust generalization of the well-known Lewbel estimator for a triangular system of structural equations with endogeneity. Specifically, we show that unlike Lewbel estimation, MR GENIUS is under fairly weak conditions also robust to unmeasured confounding of the effects of the genetic IVs on both the exposure and the outcome, another possible violation of a key IV Identification condition. Furthermore, while Lewbel estimation involves specification of linear models both for the outcome and the exposure, MR GENIUS generally does not require specification of a structural model for the direct effect of invalid IVs on the outcome, therefore allowing the latter model to be unrestricted. Finally, unlike Lewbel estimation, MR GENIUS is shown to equally apply for binary, discrete or continuous exposure and outcome variables and can be used under prospective sampling, or retrospective sampling such as in a case-control study, as well as for right censored time-to-event outcomes under an additive hazards model.
