Non-linear Mendelian randomization: evaluation of effect modification in the residual and doubly-ranked methods with simulated and empirical examples

Fergus W. Hamilton; David A. Hughes; Tianyuan Lu; Zoltán Kutalik; Apostolos Gkatzionis; Kate Tilling; Fernando P. Hartwig; George Davey Smith

doi:10.1007/s10654-025-01208-x

journal article Open Access Jun 01, 2025

Non-linear Mendelian randomization: evaluation of effect modification in the residual and doubly-ranked methods with simulated and empirical examples

Fergus W. Hamilton

David A. Hughes

Tianyuan Lu

Zoltán Kutalik

Apostolos Gkatzionis Kate Tilling

Fernando P. Hartwig

George Davey Smith

European Journal of Epidemiology Vol. 40 No. 6 pp. 631-647 · Springer Science and Business Media LLC

View at Publisher Save 10.1007/s10654-025-01208-x

Abstract

Abstract
Non-linear Mendelian randomisation (NLMR) is a relatively recently developed approach to estimate the causal effect of an exposure on an outcome where this is expected to be non-linear. Two commonly used techniques—based on stratifying the exposure and performing Mendelian randomisation (MR) within each strata—are the residual and doubly-ranked methods. The residual method is known to be biased in the presence of genetic effect heterogeneity—where the effect of the genotype on the exposure varies between individuals. The doubly-ranked method is considered to be less sensitive to genetic effect heterogeneity. In this paper, we simulate genetic effect heterogeneity and confounding of the exposure and outcome and identify that both methods are susceptible to likely unpredictable bias in this setting. Using UK Biobank, we identify empirical evidence of genetic effect heterogeneity and show via simulated outcomes that this leads to biased MR estimates within strata, whilst conventional MR across the full sample remains unbiased. We suggest that these biases are highly likely to be present in other empirical NLMR analyses using these methods and urge caution in current usage. Simulated outcome analyses may represent a useful test to identify if genetic effect heterogeneity is likely to bias NLMR estimates in future analyses.

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Citations

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References

Details

Published: Jun 01, 2025
Vol/Issue: 40(6)
Pages: 631-647
License: View

Authors

MRC Integrative Epidemiology Unit, Population Health Sciences University of Bristol Bristol UK

School of Social and Community Medicine, University of Bristol, Oakfield House, Oakfield Grove, Bristol, United Kingdom5Medical Research Council Integrative Epidemiology Unit at the University of Bristol, United Kingdom

Funding

Wellcome Trust Award: 222894/Z/21/Z

Medical Research Council Award: MC_UU_00032/2

Cite This Article

Fergus W. Hamilton, David A. Hughes, Tianyuan Lu, et al. (2025). Non-linear Mendelian randomization: evaluation of effect modification in the residual and doubly-ranked methods with simulated and empirical examples. European Journal of Epidemiology, 40(6), 631-647. https://doi.org/10.1007/s10654-025-01208-x

Non-linear Mendelian randomization: evaluation of effect modification in the residual and doubly-ranked methods with simulated and empirical examples

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