Improving the accuracy of two-sample summary-data Mendelian randomization: moving beyond the NOME assumption
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Abstract
Background: Two-sample summary-data Mendelian randomization (MR) incorporating multiple genetic variants within a meta-analysis framework is a popular technique for assessing causality in epidemiology. If all genetic variants satisfy the instrumental variable (IV) and necessary modelling assumptions, then their individual ratio estimates of causal effect should be homogeneous. Observed heterogeneity signals that one or more of these assumptions could have been violated. Methods: Causal estimation and heterogeneity assessment in MR require an approximation for the variance, or equivalently the inverse-variance weight, of each ratio estimate. We show that the most popular ‘first-order’ weights can lead to an inflation in the chances of detecting heterogeneity when in fact it is not present. Conversely, ostensibly more accurate ‘second-order’ weights can dramatically increase the chances of failing to detect heterogeneity when it is truly present. We derive modified weights to mitigate both of these adverse effects. Results: Using Monte Carlo simulations, we show that the modified weights outperform first- and second-order weights in terms of heterogeneity quantification. Modified weights are also shown to remove the phenomenon of regression dilution bias in MR estimates obtained from weak instruments, unlike those obtained using first- and second-order weights. However, with small numbers of weak instruments, this comes at the cost of a reduction in estimate precision and power to detect a causal effect compared with first-order weighting. Moreover, first-order weights always furnish unbiased estimates and preserve the type I error rate under the causal null. We illustrate the utility of the new method using data from a recent two-sample summary-data MR analysis to assess the causal role of systolic blood pressure on coronary heart disease risk. Conclusions: We propose the use of modified weights within two-sample summary-data MR studies for accurately quantifying heterogeneity and detecting outliers in the presence of weak instruments. Modified weights also have an important role to play in terms of causal estimation (in tandem with first-order weights) but further research is required to understand their strengths and weaknesses in specific settings.
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The variants included were examined for instrument strength (mean F-statistic > 10).
“The variants included were examined for instrument strength79 (mean F-statistic > 10; Supplementary Table 18).”
From Locus for severity implicates CNS resilience in progression of multiple sclerosis (2023) · cites this paper as [79]
All selected variants for MR had an estimated F-statistic >15.
“All the selected variants had an estimated F-statistic >1569.”
From Integrative genomic analyses identify candidate causal genes for calcific aortic valve stenosis involving tissue-specific regulation (2024) · cites this paper as [69]
The Methods section reports mean F-statistics for simulated MR studies, while the Discussion gives hypothetical SNP-selection examples with F-statistics of approximately 20 or 30 and above. Neither passage reports that all selected variants in the citing study had estimated F-statistics above 15; searches for that threshold and for selected-variant F-statistics found no such result. (LLM, conf=0.73)
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- Authors
- Bowden, J., Del Greco M, F., Minelli, C., Zhao, Q., Lawlor, D. A., Sheehan, N. A., Thompson, J., & Davey Smith, G.
- Affiliations
- University of Bristol (GB)
- Institute for Biomedicine, Eurac Research, Bolzano, Italy
- Imperial College London (GB)
- University of Pennsylvania (US)
- University of Leicester (GB)
- MRC Integrative Epidemiology Unit, University of Bristol, Bristol, UK
- Corresponding author
- Bowden, Jack
- Venue
- International Journal of Epidemiology
- Publisher
- Oxford University Press (OUP)
- Published
- 2018-12-18
- Volume
- 48
- Issue
- 3
- Pages
- 728-742
- ISSN
- 0300-5771 (ISSN-L)
- 1464-3685
- PMC
- PMC6659376
- OpenAlex
- W2953121869
- Cited by
- 995
- References
- 23
- Citations by year
- 2026: 102 · 2025: 267 · 2024: 340 · 2023: 121 · 2022: 55 · 2021: 37 · 2020: 35 · 2019: 23 · 2018: 13 · 2017: 2
- FWCI
- 16.29
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- Locations
- International Journal of Epidemiology (publishedVersion, cc-by)
- bioRxiv (Cold Spring Harbor Laboratory) (acceptedVersion, cc-by)
- Europe PMC (PubMed Central) (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- Explore Bristol Research (publishedVersion, cc-by)
- Figshare (submittedVersion, cc-by)
- Leicester Research Archive (University of Leicester) (submittedVersion, cc-by)
- Spiral (Imperial College London) (submittedVersion, cc-by)
- Open Research (University of Surrey) (submittedVersion, other-oa)
- Funders
- University of Bristol
- Medical Research Council (MCUU00011/1, MCUU00011/2, MCUU00011/6)
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Genetics › Genetic Associations and Epidemiology
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Meta-analysis and systematic reviews
- Keywords
- heterogeneity, inverse variance weighting, weak instruments, regression dilution bias, causal effect estimation, systolic blood pressure, coronary artery disease
- MeSH terms
- Blood Pressure, Coronary Disease, Humans, Monte Carlo Method, Polymorphism, Single Nucleotide, Mendelian Randomization Analysis
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