Improving the visualization, interpretation and analysis of two-sample summary data Mendelian randomization via the Radial plot and Radial regression
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Abstract
Background: data furnishing a two-sample Mendelian randomization (MR) study are often visualized with the aid of a scatter plot, in which single-nucleotide polymorphism (SNP)-outcome associations are plotted against the SNP-exposure associations to provide an immediate picture of the causal-effect estimate for each individual variant. It is also convenient to overlay the standard inverse-variance weighted (IVW) estimate of causal effect as a fitted slope, to see whether an individual SNP provides evidence that supports, or conflicts with, the overall consensus. Unfortunately, the traditional scatter plot is not the most appropriate means to achieve this aim whenever SNP-outcome associations are estimated with varying degrees of precision and this is reflected in the analysis. Methods: We propose instead to use a small modification of the scatter plot-the Galbraith Radial plot-for the presentation of data and results from an MR study, which enjoys many advantages over the original method. On a practical level, it removes the need to recode the genetic data and enables a more straightforward detection of outliers and influential data points. Its use extends beyond the purely aesthetic, however, to suggest a more general modelling framework to operate within when conducting an MR study, including a new form of MR-Egger regression. Results: We illustrate the methods using data from a two-sample MR study to probe the causal effect of systolic blood pressure on coronary heart disease risk, allowing for the possible effects of pleiotropy. The Radial plot is shown to aid the detection of a single outlying variant that is responsible for large differences between IVW and MR-Egger regression estimates. Several additional plots are also proposed for informative data visualization. Conclusions: The Radial plot should be considered in place of the scatter plot for visualizing, analysing and interpreting data from a two-sample summary data MR study. Software is provided to help facilitate its use.
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Papers reporting two-sample MR have grown rapidly over recent years and now constitute a large majority of published studies.
“Papers reporting two-sample MR have grown rapidly over recent years and now constitute a large majority of published studies.8,81”
From Mendelian randomization (2022) · cites this paper as [81]
Two-sample MR studies are relatively easy to conduct and can contain clear errors.
“These are relatively easy to conduct — perhaps too easy — and they can contain clear errors as discussed and demonstrated elsewhere.81”
From Mendelian randomization (2022) · cites this paper as [81]
Additional plots might also aid in the visualisation of results, assessing assumption violation, and detecting potential influential or outlier points.
“Additional plots might also aid in the visualisation of results, assessing assumption violation, and detecting potential influential or outlier points.”
From Strengthening the Reporting of Observational Studies in Epidemiology using Mendelian Randomisation (STROBE-MR): explanation and elaboration. (2021) · cites this paper as [105]
Combining a range of analyses with orthogonal validation is the most powerful way of addressing causal questions, within the triangulation of evidence framework.
“Combining this with orthogonal validation – such as through the use of positive and negative controls ( Section 7) – is the most powerful way of addressing causal questions, within the triangulation of evidence framework 96, 97 .”
From Guidelines for performing Mendelian randomization investigations (2020) · cites this paper as [97]
Mendelian randomization investigations are worthwhile in providing an alternative line of aetiological evidence even though the instrumental variable assumptions can never be proved beyond all doubt.
“Mendelian randomization investigations are worthwhile in providing an alternative line of aetiological evidence even though the instrumental variable assumptions can never be proved beyond all doubt 96, 97 .”
From Guidelines for performing Mendelian randomization investigations (2020) · cites this paper as [97]
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- Authors
- Bowden, J., Spiller, W., Del Greco M, F., Sheehan, N., Thompson, J., Minelli, C., & Davey Smith, G.
- Affiliations
- University of Bristol (GB)
- MRC Integrative Epidemiology Unit, Population Health Sciences, University of Bristol, Bristol, UK
- Institute for Biomedicine, Eurac Research, Bolzano, Italy
- University of Leicester (GB)
- Imperial College London (GB)
- Corresponding author
- Bowden, Jack
- Venue
- International Journal of Epidemiology
- Publisher
- Oxford University Press (OUP)
- Published
- 2018-06-28
- Volume
- 47
- Issue
- 4
- Pages
- 1264-1278
- ISSN
- 0300-5771 (ISSN-L)
- 1464-3685
- PMC
- PMC6124632
- OpenAlex
- W2761141539
- Cited by
- 880
- References
- 26
- Citations by year
- 2026: 81 · 2025: 188 · 2024: 274 · 2023: 146 · 2022: 83 · 2021: 47 · 2020: 35 · 2019: 17 · 2018: 5 · 2017: 1
- FWCI
- 15.84
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- Locations
- International Journal of Epidemiology (publishedVersion, cc-by)
- Europe PMC (PubMed Central) (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- Explore Bristol Research (submittedVersion, cc-by)
- Figshare (submittedVersion, cc-by)
- Bristol Research (University of Bristol) (submittedVersion, cc-by)
- Spiral (Imperial College London) (submittedVersion, other-oa)
- Open Research (University of Surrey) (submittedVersion)
- Funders
- Jack Bowden and George Davey Smith
- University of Bristol
- UK Medical Research Council (MCUU00011/1, MCUU00011/2)
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Genetics › Genetic Associations and Epidemiology
- Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Meta-analysis and systematic reviews
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Keywords
- two-sample Mendelian randomization, pleiotropy, causal effect estimation, data visualization, systolic blood pressure, coronary artery disease, single nucleotide polymorphisms
- MeSH terms
- Data Visualization, Humans, Genetic Variation, Genetic Predisposition to Disease, Polymorphism, Single Nucleotide, Mendelian Randomization Analysis, Genetic Pleiotropy
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