Examining the evidence for Mendelian randomization homogeneity assumption violation using instrument association with exposure variance

Background Estimation of the average causal effect using instrumental variable (IV) analyses requires homogeneity of instrument-exposure and/or exposure-outcome relationships. Previous research explored the validity of homogeneity assumptions by testing IV-exposure interaction effects using a set of effect modifiers. However, this approach requires that modifiers are known and measured but evidence for interaction may also be observed through IV association with exposure variance without knowledge of the modifier. Methods We explored the utility of testing for IV-exposure variance effects as evidence against homogeneity through simulation. We also evaluated the approach of removing IVs from Mendelian randomization (MR) analyses that show strong association with exposure variance (hence are likely to have heterogeneous effects). Our methodology was applied to evaluate homogeneity assumptions of LDL, urate and glucose on cardiovascular disease, gout, and type 2 diabetes, respectively. Results Under simulation, interaction of IV-exposure and exposure-outcome effects by a single modifier led to bias of the estimated average causal effect (ACE) which could be partially assessed by testing for IV-exposure variance effects. Bias of the ACE attenuated after removing instruments with strong exposure variance effects. In applied analyses, we found no strong evidence of bias from the ACE. Conclusions We find no strong evidence against estimating the ACE for LDL, urate and glucose on cardiovascular disease, gout, and type 2 diabetes. These approaches could be used in future MR analyses to gain improved understanding of the causal estimand. Key messages ### Competing Interest Statement The authors declare no competing non-financial interests but the following competing financial interests: T.R.G receives funding from Biogen for unrelated research. K.T has been paid for consultancy for CHDI. The remaining authors declare no competing financial interests. ### Funding Statement This study was funded by the NIHR Biomedical Research Centre at University Hospitals Bristol and Weston NHS Foundation Trust and the University of Bristol. The views expressed are those of the author(s) and not necessarily those of the NIHR or the Department of Health and Social Care. This work was also funded by the UK Medical Research Council as part of the MRC Integrative Epidemiology Unit (MC\_UU\_00011/1 and MC\_UU\_00011/3 and MC\_UU\_00011/4). L.A.C.M is funded by a University of Bristol Vice-Chancellor's fellowship. ### 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: The study used only openly available GWAS summary statistics that were originally located at . 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 and uploaded the relevant EQUATOR Network research reporting checklist(s) and other pertinent material as supplementary files, if applicable. Yes GWAS summary statistics are available from .