Heritable confounding in Mendelian randomization studies: structure, consequences and relevance for gene-environment equivalence

Mendelian randomization (MR) uses genetic variants to estimate the causal effect of an exposure on an outcome in the presence of unmeasured confounding. A key assumption of MR is that the genetic variants used influence the outcome only through the exposure. Violation of this assumption undermines the gene-environment equivalence principle, which posits that modifying the exposure via genetic variation is equivalent to modifying it through environmental factors. With increasing sample sizes in genome-wide association studies genetic instruments with smaller effect sizes are being identified as associated with a trait. Through simulation studies, we demonstrate that such variants may have greater liability to act through confounders of the exposure and outcome in a MR study, biasing effect estimates. This bias acts in the same direction as the confounded associations observed in linear regression, but often with greater magnitude and acts in the same direction across all of the most commonly used MR estimation methods, potentially leading to misleading confidence in the results. We further show that the magnitude of bias escalates as the proportion of genetic instruments associated with confounders increases. Importantly, when potential heritable confounders the genetic variants act through are known and can be instrumented, unbiased causal estimates can be obtained through pre-estimation filtering or by employing multivariable MR and adjusting for the confounder. We illustrate our approach through an application to estimate the effect of C Reactive protein on type 2 diabetes using a hypothesis free approach to identify and remove the effect of potential heritable confounders.