Bias from Heritable Confounding in Mendelian Randomization Studies

Mendelian randomization (MR) is an approach to causal inference that utilises genetic variants to obtain estimates of the causal effect of an exposure on an outcome in the presence of unobserved confounding. MR relies on a set of assumptions to obtain unbiased effect estimates, one of these assumptions is that there is no pathway from the genetic variants to the outcome that does not act through the exposure. Increasing genome-wide association study (GWAS) sample sizes for the exposure enables discovery of instrumental variables with smaller effect sizes. We illustrate through simulations how smaller effect sizes could arise from genetic variants that act through traits that have greater liability to confound an exposure-outcome relationship. When such genetic variants are selected as instruments this can bias the MR effect estimate obtained from that instrument in the same direction as the confounded observational association but with larger magnitude. Through simulation we illustrate how the total bias of the MR estimates increases across a range of standard MR estimation methods increases as the proportion of the genetic instruments that are associated with the confounder increases. However, if such heritable confounders are known and can be instrumented, the confounder free effect estimate can be obtained through applying a pre-estimation filtering to standard MR methods, removing instruments that explain more variation in that confounder than the exposure, or by estimating effects through multivariable MR. We highlight the potential for SNPs identified in GWAS to be associated with potential confounders through examination of a recent GWAS of C-Reactive Protein. Finally, we illustrate our approach through estimation of the causal effect of age at menarche on type 2 diabetes, hypothesising that the MR effect estimate may be biased by confounding due to the inclusion of genetic variants associated with early life adiposity as instruments. ### Competing Interest Statement The authors have declared no competing interest. ### Funding Statement Medical Research Council (MC\_UU\_00032/1, MC\_UU\_00032/2) ### Author Declarations I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained. Yes The details of the IRB/oversight body that provided approval or exemption for the research described are given below: MRC IEU OpenGWAS https://gwas.mrcieu.ac.uk I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals. Yes I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance). Yes I have followed all appropriate research reporting guidelines, such as any relevant EQUATOR Network research reporting checklist(s) and other pertinent material, if applicable. Yes All code used is available online at https://github.com/eleanorsanderson/confounding. Summary data used is available at https://gwas.mrcieu.ac.uk.