Title: The GENIUS Approach to Robust Mendelian Randomization Inference,
Abstract: Mendelian randomization (MR) is a popular instrumental variable (IV)
approach. A key IV identification condition known as the exclusion restriction
requires no direct effect of an IV on the outcome not through the exposure
which is unrealistic in most MR analyses. As a result, possible violation of
the exclusion restriction can seldom be ruled out in such studies. 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 named "MR G-Estimation under No Interaction with
Unmeasured Selection" (MR GENIUS) may 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, 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.