MR-AHC: a fast, efficient and robust method for two-sample summary data Mendelian randomization based on agglomerative hierarchical clustering

Mendelian randomization (MR) is an epidemiological approach that uses genetic variants as instrumental variables for estimating the causal effect of a modifiable but likely confounded exposure on an outcome. Standard MR usually assumes that all included genetic variants are valid instruments and there is a single homogeneous causal effect of the exposure on the outcome. We allow violations of both assumptions such that the variants can be divided into clusters identifying distinct causal effects driven by different biological mechanisms and/or horizontal pleiotropy. We adapted the Agglomerative Hierarchical Clustering (AHC) method developed for individual-level data to the summary data MR setting, enabling the detection of such variant clusters using only genome-wide summary statistics. We also extend the method to handle two outcomes and a common exposure to aid investigation of the mechanisms of multimorbidity. We conduct Monte Carlo simulations to evaluate the performance of our ‘MR-AHC’ algorithm compared to the existing MR-Clust method, showing that it is both reliable and computationally efficient: it detects variant clusters with high accuracy and is much faster than MR-Clust. In an applied example, we use our method to analyze the causal effects of high body fat percentage on a pair of well-known multimorbid conditions, type 2 diabetes and osteoarthritis, discovering distinct variant clusters reflecting the heterogeneous shared pathways. ### Competing Interest Statement The authors have declared no competing interest. ### Funding Statement This work was funded by the Strategic Priority Fund Tackling multimorbidity at scale programme (grant number MC/MR/WO14548/1) delivered by the Medical Research Council and the National Institute for Health and Care Research in partnership with the Economic and Social Research Council and in collaboration with the Engineering and Physical Sciences Research Council. Nicolas Apfel is supported by the ESRC grant EST013567/1. ### 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: 1. GWAS summary data from the online supplementary (file name: elife-72452-supp1.doc) of the paper "Disease consequences of higher adiposity uncoupled from its adverse metabolic effects using Mendelian randomisation". Link: 2. GWAS summary data from the paper "Fine-mapping type 2 diabetes loci to single-variant resolution534 using high-density imputation and islet-specific epigenome maps". Link: [http://diagram-consortium.org/downloads.html][1] 3. GWAS summary data from FinnGen. Link: [https://r8.risteys.finngen.fi/phenocode/M13\_ARTHROSIS\_INCLAVO][2] 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 data used in the applied examples in the present study are available upon reasonable request to the authors. The R code that generates the simulation datasets are available online at [1]: https://diagram-consortium.org/downloads.html [2]: https://r8.risteys.finngen.fi/phenocode/M13_ARTHROSIS_INCLAVO