| Abstract |
Mendelian randomization uses genetic variants as instrumental variables (IV) to infer the causal effect of an exposure on the outcome of interest even in the presence of unmeasured confounding. However, the exclusion restriction and/or IV independence conditions can be violated in practice. Moreover, little work has been done for a binary outcome. In this paper, we first establish identification results for a binary outcome with a single possibly invalid IV. Second, we propose a novel model parameterization to resolve the variation dependence issue when estimating causal risk difference. Third, we propose maximum likelihood and doubly robust estimators for the causal risk difference that are guaranteed to lie in the interval (-1,1). Extensive simulation studies confirmed our theoretical results. We also apply the proposed method to estimate the causal effect of adiposity on the risk of hypertension in the UK Biobank. |
