Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Mendelian randomization

Abstract

Mendelian randomization (MR) is a term that applies to the use of genetic variation to address causal questions about how modifiable exposures influence different outcomes. The principles of MR are based on Mendel’s laws of inheritance and instrumental variable estimation methods, which enable the inference of causal effects in the presence of unobserved confounding. In this Primer, we outline the principles of MR, the instrumental variable conditions underlying MR estimation and some of the methods used for estimation. We go on to discuss how the assumptions underlying an MR study can be assessed and describe methods of estimation that are robust to certain violations of these assumptions. We give examples of a range of studies in which MR has been applied, the limitations of current methods of analysis and the outlook for MR in the future. The differences between the assumptions required for MR analysis and other forms of epidemiological studies means that MR can be used as part of a triangulation across multiple sources of evidence for causal inference.

This is a preview of subscription content

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Fig. 1: An overview of MR studies.
Fig. 2: Illustration of a randomized control study and instrumental variable estimation.
Fig. 3: Types of pleiotropy.
Fig. 4: Data visualization.
Fig. 5: Illustration of the multivariable MR model.
Fig. 6: Illustration of variants in linkage disequilibrium and shared causal variants identified by colocalization.

References

  1. Davey Smith, G. & Ebrahim, S. ‘Mendelian randomization’: can genetic epidemiology contribute to understanding environmental determinants of disease? Int. J. Epidemiol. 32, 1–22 (2003).

    Google Scholar 

  2. Angrist, J. D., Imbens, G. W. & Rubin, D. B. Identification of causal effects using instrumental variables. J. Am. Stat. Assoc. 91, 444–455 (1996).

    MATH  Google Scholar 

  3. Hernán, M. A. & Robins, J. M. Causal Inference: What If (Chapman & Hall/CRC, 2020).

  4. Greenland, S. An introduction to instrumental variables for epidemiologists. Int. J. Epidemiol. 29, 722–729 (2000).

    Google Scholar 

  5. Zuccolo, L. & Holmes, M. V. Commentary: Mendelian randomization-inspired causal inference in the absence of genetic data. Int. J. Epidemiol. 46, 962–965 (2017).

    Google Scholar 

  6. Munafò, M. R., Higgins, J. P. & Davey Smith, G. Triangulating evidence through the inclusion of genetically informed designs. Cold Spring Harb. Perspect. Med. 11, a040659 (2021).

    Google Scholar 

  7. Lawlor, D. A., Tilling, K. & Davey Smith, G. Triangulation in aetiological epidemiology. Int. J. Epidemiol. 45, 1866–1886 (2017).

    Google Scholar 

  8. Richmond, R. C. & Davey Smith, G. Mendelian randomization: concepts and scope. Cold Spring Harb. Perspect. Med. https://doi.org/10.1101/cshperspect.a040501 (2022).

    Article  Google Scholar 

  9. Davey Smith, G. & Ebrahim, S. Mendelian randomization: prospects, potentials, and limitations. Int. J. Epidemiol. 33, 30–42 (2004).

    Google Scholar 

  10. Gupta, S. K. Intention-to-treat concept: a review. Perspect. Clin. Res. 2, 109–112 (2011).

    Google Scholar 

  11. Ellenberg, J. H. Intent-to-treat analysis versus as-treated analysis. Drug Inf. J. 30, 535–544 (1996).

    Google Scholar 

  12. Glymour, M. M. Natural experiments and instrumental variable analyses in social epidemiology. Methods Soc. Epidemiol. 1, 429 (2006).

    Google Scholar 

  13. Martens, E. P., Pestman, W. R., de Boer, A., Belitser, S. V. & Klungel, O. H. Instrumental variables: application and limitations. Epidemiology 17, 260–267 (2006).

    Google Scholar 

  14. Lousdal, M. L. An introduction to instrumental variable assumptions, validation and estimation. Emerg. Themes Epidemiol. 15, 1 (2018).

    Google Scholar 

  15. Angrist, J. D. & Krueger, A. B. Instrumental variables and the search for identification: from supply and demand to natural experiments. J. Econ. Perspect. 15, 69–85 (2001).

    Google Scholar 

  16. Rassen, J. A., Brookhart, M. A., Glynn, R. J., Mittleman, M. A. & Schneeweiss, S. Instrumental variables I: instrumental variables exploit natural variation in nonexperimental data to estimate causal relationships. J. Clin. Epidemiol. 62, 1226–1232 (2009).

    Google Scholar 

  17. Didelez, V. & Sheehan, N. Mendelian randomization as an instrumental variable approach to causal inference. Stat. Methods Med. Res. 16, 309–330 (2007).

    MathSciNet  MATH  Google Scholar 

  18. Davey Smith, G. Capitalizing on Mendelian randomization to assess the effects of treatments. J. R. Soc. Med. 100, 432–435 (2007).

    Google Scholar 

  19. Carlson, C. S. et al. Polymorphisms within the C-reactive protein (CRP) promoter region are associated with plasma CRP levels. Am. J. Hum. Genet. 77, 64–77 (2005).

    Google Scholar 

  20. Davey Smith, G. et al. Association of C-reactive protein with blood pressure and hypertension: life course confounding and Mendelian randomization tests of causality. Arterioscler. Thromb. Vasc. Biol. 25, 1051–1056 (2005).

    Google Scholar 

  21. Morris, T. T., Heron, J., Sanderson, E., Davey Smith, G. & Tilling, K. Interpretation of Mendelian randomization using one measure of an exposure that varies over time. Preprint at medRxiv https://doi.org/10.1101/2021.11.18.21266515 (2021).

    Article  Google Scholar 

  22. Swanson, S. A., Tiemeier, H., Ikram, M. A. & Hernán, M. A. Nature as a trialist? Deconstructing the analogy between Mendelian randomization and randomized trials. Epidemiology 28, 653–659 (2017).

    Google Scholar 

  23. Didelez, V., Meng, S. & Sheehan, N. A. Assumptions of IV methods for observational epidemiology. Statist. Sci. 25, 22–40 (2010).

    MathSciNet  MATH  Google Scholar 

  24. Palmer, T. M. et al. Using multiple genetic variants as instrumental variables for modifiable risk factors. Stat. Methods Med. Res. 21, 223–242 (2011).

    MathSciNet  MATH  Google Scholar 

  25. Burgess, S. & Thompson, S. G. Use of allele scores as instrumental variables for Mendelian randomization. Int. J. Epidemiol. 42, 1134–1144 (2013).

    Google Scholar 

  26. Davies, N. M. et al. The many weak instruments problem and Mendelian randomization. Stat. Med. 34, 454–468 (2015).

    MathSciNet  Google Scholar 

  27. Hernán, M. A. & Robins, J. M. Instruments for causal inference: an epidemiologist’s dream? Epidemiology 17, 360–372 (2006).

    Google Scholar 

  28. Swanson, S. A., Hernán, M. A., Miller, M., Robins, J. M. & Richardson, T. S. Partial identification of the average treatment effect using instrumental variables: review of methods for binary instruments, treatments, and outcomes. J. Am. Stat. Assoc. 113, 933–947 (2018).

    MathSciNet  MATH  Google Scholar 

  29. Staley, J. R. & Burgess, S. Semiparametric methods for estimation of a nonlinear exposure–outcome relationship using instrumental variables with application to Mendelian randomization. Genet. Epidemiol. 41, 341–352 (2017).

    Google Scholar 

  30. Tyrrell, J. et al. Genetic predictors of participation in optional components of UK Biobank. Nat. Commun. 12, 886 (2021).

    ADS  Google Scholar 

  31. Davey Smith, G. Epigenesis for epidemiologists: does evo-devo have implications for population health research and practice? Int. J. Epidemiol. 41, 236–247 (2012).

    Google Scholar 

  32. Freeman, G., Cowling, B. J. & Schooling, C. M. Power and sample size calculations for Mendelian randomization studies using one genetic instrument. Int. J. Epidemiol. 42, 1157–1163 (2013).

    Google Scholar 

  33. Walker, V. M., Davies, N. M., Windmeijer, F., Burgess, S. & Martin, R. M. Power calculator for instrumental variable analysis in pharmacoepidemiology. Int. J. Epidemiol. 46, 1627–1632 (2017).

    Google Scholar 

  34. Burgess, S. Sample size and power calculations in Mendelian randomization with a single instrumental variable and a binary outcome. Int. J. Epidemiol. 43, 922–929 (2014).

    Google Scholar 

  35. Brion, M.-J. A., Shakhbazov, K. & Visscher, P. M. Calculating statistical power in Mendelian randomization studies. Int. J. Epidemiol. 42, 1497–1501 (2012).

    Google Scholar 

  36. Morris, T. P., White, I. R. & Crowther, M. J. Using simulation studies to evaluate statistical methods. Stat. Med. 38, 2074–2102 (2019).

    MathSciNet  Google Scholar 

  37. Burgess, S., Butterworth, A. & Thompson, S. G. Mendelian randomization analysis with multiple genetic variants using summarized data. Genet. Epidemiol. 37, 658–665 (2013).

    Google Scholar 

  38. Zhao, Q., Wang, J., Spiller, W., Bowden, J. & Small, D. S. Two-sample instrumental variable analyses using heterogeneous samples. Stat. Sci. 34, 317–333 (2019).

    MathSciNet  MATH  Google Scholar 

  39. Burgess, S. et al. Guidelines for performing Mendelian randomization investigations. Wellcome Open Res. 4, 186 (2019).

    Google Scholar 

  40. Pierce, B. L. & Burgess, S. Efficient design for Mendelian randomization studies: subsample and 2-sample instrumental variable estimators. Am. J. Epidemiol. 178, 1177–1184 (2013).

    Google Scholar 

  41. Holmes, M. V., Richardson, T. G., Ference, B. A., Davies, N. M. & Davey Smith, G. Integrating genomics with biomarkers and therapeutic targets to invigorate cardiovascular drug development. Nat. Rev. Cardiol. 18, 435–453 (2021).

    Google Scholar 

  42. Bound, J., Jaeger, D. A. & Baker, R. M. Problems with instrumental variables estimation when the correlation between the instruments and the endogenous explanatory variable is weak. J. Am. Stat. Assoc. 90, 443–450 (1995).

    Google Scholar 

  43. Burgess, S., Davies, N. M. & Thompson, S. G. Bias due to participant overlap in two-sample Mendelian randomization. Genet. Epidemiol. 40, 597–608 (2016).

    Google Scholar 

  44. Mounier, N. & Kutalik, Z. Correction for sample overlap, winner’s curse and weak instrument bias in two-sample Mendelian Randomization. Preprint at bioRxiv https://doi.org/10.1101/2021.03.26.437168 (2021).

    Article  Google Scholar 

  45. Angrist, J. D. & Krueger, A. B. Split-sample instrumental variables estimates of the return to schooling. J. Bus. Econ. Stat. 13, 225–235 (1995).

    Google Scholar 

  46. Fang, S., Hemani, G., Richardson, T. G., Gaunt, T. R. & Davey Smith, G. Evaluating and implementing block jackknife resampling Mendelian randomization to mitigate bias induced by overlapping samples. Preprint at medRxiv https://doi.org/10.1101/2021.12.03.21267246 (2021).

    Article  Google Scholar 

  47. Sadreev, I. I. et al. Navigating sample overlap, winner’s curse and weak instrument bias in Mendelian randomization studies using the UK Biobank. Preprint at medRxiv https://doi.org/10.1101/2021.06.28.21259622 (2021).

    Article  Google Scholar 

  48. Davies, N. M., Holmes, M. V. & Davey Smith, G. Reading Mendelian randomisation studies: a guide, glossary, and checklist for clinicians. BMJ 362, k601 (2018).

    Google Scholar 

  49. Holmes, M. V., Ala-Korpela, M. & Davey Smith, G. Mendelian randomization in cardiometabolic disease: challenges in evaluating causality. Nat. Rev. Cardiol. 14, 577–590 (2017).

    Google Scholar 

  50. Skrivankova, V. W. et al. Strengthening the reporting of observational studies in epidemiology using Mendelian randomisation (STROBE-MR): explanation and elaboration. BMJ 375, n2233 (2021).

    Google Scholar 

  51. Skrivankova, V. W. et al. Strengthening the reporting of observational studies in epidemiology using Mendelian randomization: the STROBE-MR statement. JAMA 326, 1614–1621 (2021).

    Google Scholar 

  52. Lawlor, D. A., Harbord, R. M., Sterne, J. A., Timpson, N. & Davey Smith, G. Mendelian randomization: using genes as instruments for making causal inferences in epidemiology. Stat. Med. 27, 1133–1163 (2008).

    MathSciNet  Google Scholar 

  53. Wooldridge, J. M. Econometric Analysis of Cross Section and Panel Data (MIT Press, 2010).

  54. Cole, S. R. et al. Illustrating bias due to conditioning on a collider. Int. J. Epidemiol. 39, 417–420 (2009).

    Google Scholar 

  55. Munafò, M. R., Tilling, K., Taylor, A. E., Evans, D. M. & Davey Smith, G. Collider scope: when selection bias can substantially influence observed associations. Int. J. Epidemiol. 47, 226–235 (2018).

    Google Scholar 

  56. Hernán, M. A., Hernández-Díaz, S. & Robins, J. M. A structural approach to selection bias. Epidemiology 15, 615–625 (2004).

    Google Scholar 

  57. Staiger, D. & Stock, J. H. Instrumental variables regression with weak instruments. Report No. 0898-2937 (National Bureau of Economic Research, 1994).

  58. Stock, J. H. & Yogo, M. Testing for weak instruments in linear IV regression. Report No. 0898-2937 (National Bureau of Economic Research, 2002).

  59. Brumpton, B. et al. Within-family studies for Mendelian randomization: avoiding dynastic, assortative mating, and population stratification biases. Nat. Commun. 11, 1–13 (2020).

    Google Scholar 

  60. Hemani, G., Bowden, J. & Davey Smith, G. Evaluating the potential role of pleiotropy in Mendelian randomization studies. Hum. Mol. Genet. 27, R195–R208 (2018).

    Google Scholar 

  61. Davey Smith, G. & Hemani, G. Mendelian randomization: genetic anchors for causal inference in epidemiological studies. Hum. Mol. Genet. 23, R89–R98 (2014).

    Google Scholar 

  62. Burgess, S., Swanson, S. A. & Labrecque, J. A. Are Mendelian randomization investigations immune from bias due to reverse causation? Eur. J. Epidemiol. 36, 253–257 (2021).

    Google Scholar 

  63. Griffith, G. J. et al. Collider bias undermines our understanding of COVID-19 disease risk and severity. Nat. Commun. 11, 5749 (2020).

    ADS  Google Scholar 

  64. Hughes, R. A., Davies, N. M., Davey Smith, G. & Tilling, K. Selection bias when estimating average treatment effects using one-sample instrumental variable analysis. Epidemiology 30, 350–357 (2019).

    Google Scholar 

  65. Sargan, J. D. The estimation of economic relationships using instrumental variables. Econometrica 26, 393–415 (1958).

    MathSciNet  MATH  Google Scholar 

  66. Glymour, M. M., Tchetgen Tchetgen, E. J. & Robins, J. M. Credible Mendelian randomization studies: approaches for evaluating the instrumental variable assumptions. Am. J. Epidemiol. 175, 332–339 (2012).

    Google Scholar 

  67. Diemer, E. W., Labrecque, J., Tiemeier, H. & Swanson, S. A. Application of the instrumental inequalities to a Mendelian randomization study with multiple proposed instruments. Epidemiology 31, 65–74 (2020).

    Google Scholar 

  68. Yang, Q., Sanderson, E., Tilling, K., Borges, M. C. & Lawlor, D. A. Exploring and mitigating potential bias when genetic instrumental variables are associated with multiple non-exposure traits in Mendelian randomization. Preprint at medRxiv https://doi.org/10.1101/19009605 (2019).

    Article  Google Scholar 

  69. Lawlor, D. A. et al. Exploring the developmental overnutrition hypothesis using parental–offspring associations and FTO as an instrumental variable. PLoS Med. 5, e33 (2008).

    Google Scholar 

  70. Kang, H., Zhang, A., Cai, T. T. & Small, D. S. Instrumental variables estimation with some invalid instruments and its application to Mendelian randomization. J. Am. Stat. Assoc. 111, 132–144 (2016).

    MathSciNet  Google Scholar 

  71. Windmeijer, F., Farbmacher, H., Davies, N. & Davey Smith, G. On the use of the lasso for instrumental variables estimation with some invalid instruments. J. Am. Stat. Assoc. 114, 1339–1350 (2019).

    MathSciNet  MATH  Google Scholar 

  72. Jiang, L. et al. Constrained instruments and their application to Mendelian randomization with pleiotropy. Genet. Epidemiol. 43, 373–401 (2019).

    Google Scholar 

  73. Sanderson, E., Davey Smith, G., Windmeijer, F. & Bowden, J. An examination of multivariable Mendelian randomization in the single-sample and two-sample summary data settings. Int. J. Epidemiol. 48, 713–727 (2019).

    Google Scholar 

  74. Chen, L., Davey Smith, G., Harbord, R. M. & Lewis, S. J. Alcohol intake and blood pressure: a systematic review implementing a Mendelian randomization approach. PLoS Med. 5, e52 (2008).

    Google Scholar 

  75. Spiller, W., Hartwig, F. P., Sanderson, E., Davey Smith, G. & Bowden, J. Interaction-based Mendelian randomization with measured and unmeasured gene-by-covariate interactions. Preprint at medRxiv https://doi.org/10.1101/2020.07.27.20162909 (2020).

    Article  Google Scholar 

  76. Spiller, W., Slichter, D., Bowden, J. & Davey Smith, G. Detecting and correcting for bias in Mendelian randomization analyses using gene-by-environment interactions. Int. J. Epidemiol. 48, 702–712 (2019).

    Google Scholar 

  77. Tchetgen Tchetgen, E. J., Sun, B. & Walter, S. The GENIUS approach to robust Mendelian randomization inference. Stat. Sci. 36, 443–464 (2019).

    MathSciNet  Google Scholar 

  78. Burgess, S., Dudbridge, F. & Thompson, S. G. Combining information on multiple instrumental variables in Mendelian randomization: comparison of allele score and summarized data methods. Stat. Med. 35, 1880–1906 (2016).

    MathSciNet  Google Scholar 

  79. Zhu, Z. et al. Causal associations between risk factors and common diseases inferred from GWAS summary data. Nat. Commun. 9, 224 (2018).

    ADS  Google Scholar 

  80. Hartwig, F. P., Davies, N. M., Hemani, G. & Davey Smith, G. Two-sample Mendelian randomization: avoiding the downsides of a powerful, widely applicable but potentially fallible technique. Int. J. Epidemiol. 45, 1717–1726 (2017).

    Google Scholar 

  81. Bowden, J. et al. Improving the visualization, interpretation and analysis of two-sample summary data Mendelian randomization via the radial plot and radial regression. Int. J. Epidemiol. 47, 1264–1278 (2018).

    Google Scholar 

  82. Bowden, J., Davey Smith, G., Haycock, P. C. & Burgess, S. Consistent estimation in Mendelian randomization with some invalid instruments using a weighted median estimator. Genet. Epidemiol. 40, 304–314 (2016).

    Google Scholar 

  83. Hartwig, F. P., Davey Smith, G. & Bowden, J. Robust inference in summary data Mendelian randomization via the zero modal pleiotropy assumption. Int. J. Epidemiol. 46, 1985–1998 (2017).

    Google Scholar 

  84. Rees, J. M., Wood, A. M., Dudbridge, F. & Burgess, S. Robust methods in Mendelian randomization via penalization of heterogeneous causal estimates. PloS ONE 14, e0222362 (2019).

    Google Scholar 

  85. Cho, Y. et al. Exploiting horizontal pleiotropy to search for causal pathways within a Mendelian randomization framework. Nat. Commun. 11, 1010 (2020).

    ADS  Google Scholar 

  86. Verbanck, M., Chen, C.-Y., Neale, B. & Do, R. Detection of widespread horizontal pleiotropy in causal relationships inferred from Mendelian randomization between complex traits and diseases. Nat. Genet. 50, 693–698 (2018).

    Google Scholar 

  87. Zhao, Q., Wang, J., Hemani, G., Bowden, J. & Small, D. S. Statistical inference in two-sample summary-data Mendelian randomization using robust adjusted profile score. Ann. Stat. 48, 1742–1769 (2020).

    MathSciNet  MATH  Google Scholar 

  88. Wang, J. et al. Causal inference for heritable phenotypic risk factors using heterogeneous genetic instruments. PLoS Genet. 17, e1009575 (2021).

    Google Scholar 

  89. Morrison, J., Knoblauch, N., Marcus, J. H., Stephens, M. & He, X. Mendelian randomization accounting for correlated and uncorrelated pleiotropic effects using genome-wide summary statistics. Nat. Genet. 52, 740–747 (2020).

    Google Scholar 

  90. Bowden, J., Davey Smith, G. & Burgess, S. Mendelian randomization with invalid instruments: effect estimation and bias detection through Egger regression. Int. J. Epidemiol. 44, 512–525 (2015).

    Google Scholar 

  91. Burgess, S. & Thompson, S. G. Multivariable Mendelian randomization: the use of pleiotropic genetic variants to estimate causal effects. Am. J. Epidemiol. 181, 251–260 (2015).

    Google Scholar 

  92. Bowden, J. & Vansteelandt, S. Mendelian randomization analysis of case-control data using structural mean models. Stat. Med. 30, 678–694 (2011).

    MathSciNet  Google Scholar 

  93. Hemani, G., Tilling, K. & Davey Smith, G. Orienting the causal relationship between imprecisely measured traits using GWAS summary data. PLoS Genet. 13, e1007081 (2017).

    Google Scholar 

  94. Brown, B. C. & Knowles, D. A. Welch-weighted Egger regression reduces false positives due to correlated pleiotropy in Mendelian randomization. Am. J. Hum. Genet. 108, 2319–2335 (2021).

    Google Scholar 

  95. O’Connor, L. J. & Price, A. L. Distinguishing genetic correlation from causation across 52 diseases and complex traits. Nat. Genet. 50, 1728–1734 (2018).

    Google Scholar 

  96. Elsworth, B. L. et al. The MRC IEU OpenGWAS data infrastructure. Preprint at bioRxiv https://doi.org/10.1101/2020.08.10.244293 (2020).

    Article  Google Scholar 

  97. Livingston, G. et al. Dementia prevention, intervention, and care: 2020 report of the Lancet Commission. Lancet 396, 413–446 (2020).

    Google Scholar 

  98. Snoeckx, R. L. et al. GJB2 mutations and degree of hearing loss: a multicenter study. Am. J. Hum. Genet. 77, 945–957 (2005).

    Google Scholar 

  99. Hoffmann, T. J. et al. A large genome-wide association study of age-related hearing impairment using electronic health records. PLoS Genet. 12, e1006371 (2016).

    Google Scholar 

  100. Lambert, J.-C. et al. Meta-analysis of 74,046 individuals identifies 11 new susceptibility loci for Alzheimer’s disease. Nat. Genet. 45, 1452–1458 (2013).

    Google Scholar 

  101. Burgess, S., Dudbridge, F. & Thompson, S. G. Re: “Multivariable Mendelian randomization: the use of pleiotropic genetic variants to estimate causal effects”. Am. J. Epidemiol. 181, 290–291 (2015).

    Google Scholar 

  102. Zuber, V., Colijn, J. M., Klaver, C. & Burgess, S. Selecting likely causal risk factors from high-throughput experiments using multivariable Mendelian randomization. Nat. Commun. 11, 29 (2020).

    ADS  Google Scholar 

  103. Sanderson, E. Multivariable Mendelian randomization and mediation. Cold Spring Harb. Perspect. Med. 11, a038984 (2020).

    Google Scholar 

  104. Carter, A. R. et al. Mendelian randomisation for mediation analysis: current methods and challenges for implementation. Eur. J. Epidemiol. 36, 465–478 (2021).

    Google Scholar 

  105. Relton, C. L. & Davey Smith, G. Two-step epigenetic Mendelian randomization: a strategy for establishing the causal role of epigenetic processes in pathways to disease. Int. J. Epidemiol. 41, 161–176 (2012).

    Google Scholar 

  106. Burgess, S., Daniel, R. M., Butterworth, A. S., Thompson, S. G. & Consortium, E.-I. Network Mendelian randomization: using genetic variants as instrumental variables to investigate mediation in causal pathways. Int. J. Epidemiol. 44, 484–495 (2015).

    Google Scholar 

  107. Burgess, S., Davies, N. M. & Thompson, S. G. Instrumental variable analysis with a nonlinear exposure–outcome relationship. Epidemiology 25, 877 (2014).

    Google Scholar 

  108. Sun, Y.-Q. et al. Body mass index and all cause mortality in HUNT and UK Biobank studies: linear and non-linear mendelian randomisation analyses. BMJ 364, l1042 (2019).

    Google Scholar 

  109. North, T.-L. et al. Using genetic instruments to estimate interactions in Mendelian randomization studies. Epidemiology 30, e33–e35 (2019).

    Google Scholar 

  110. Rees, J., Foley, C. N. & Burgess, S. Factorial Mendelian randomization: using genetic variants to assess interactions. Int. J. Epidemiol. 49, 1147–1158 (2019).

    Google Scholar 

  111. Plagnol, V., Smyth, D. J., Todd, J. A. & Clayton, D. G. Statistical independence of the colocalized association signals for type 1 diabetes and RPS26 gene expression on chromosome 12q13. Biostatistics 10, 327–334 (2009).

    MATH  Google Scholar 

  112. Wallace, C. Statistical testing of shared genetic control for potentially related traits. Genet. Epidemiol. 37, 802–813 (2013).

    Google Scholar 

  113. Pavlides, J. M. W. et al. Predicting gene targets from integrative analyses of summary data from GWAS and eQTL studies for 28 human complex traits. Genome Med. 8, 84–84 (2016).

    Google Scholar 

  114. Hormozdiari, F. et al. Colocalization of GWAS and eQTL signals detects target genes. Am. J. Hum. Genet. 99, 1245–1260 (2016).

    Google Scholar 

  115. Giambartolomei, C. et al. Bayesian test for colocalisation between pairs of genetic association studies using summary statistics. PLoS Genet. 10, e1004383 (2014).

    Google Scholar 

  116. Wallace, C. Eliciting priors and relaxing the single causal variant assumption in colocalisation analyses. PLoS Genet. 16, e1008720 (2020).

    Google Scholar 

  117. Marmot, M. & Brunner, E. Alcohol and cardiovascular disease: the status of the U shaped curve. BMJ 303, 565–568 (1991).

    Google Scholar 

  118. Corrao, G., Rubbiati, L., Bagnardi, V., Zambon, A. & Poikolainen, K. Alcohol and coronary heart disease: a meta-analysis. Addiction 95, 1505–1523 (2000).

    Google Scholar 

  119. Mukamal, K. J. & Rimm, E. B. Alcohol’s effects on the risk for coronary heart disease. Alcohol. Res. Health 25, 255–261 (2001).

    Google Scholar 

  120. US National Library of Medicine. ClinicalTrials.gov https://clinicaltrials.gov/ct2/show/NCT03169530 (2019).

  121. Dyer, O. $100m alcohol study is cancelled amid pro-industry “bias”. BMJ 361, k2689 (2018).

    Google Scholar 

  122. Mitchell, G., Lesch, M. & McCambridge, J. Alcohol industry involvement in the moderate alcohol and cardiovascular health trial. Am. J. Public Health 110, 485–488 (2020).

    Google Scholar 

  123. National Institutes of Health. NIH to end funding for Moderate Alcohol and Cardiovascular Health trial. National Institutes of Health https://www.nih.gov/news-events/news-releases/nih-end-funding-moderate-alcohol-cardiovascular-health-trial (2018).

  124. Wild, C. in World Cancer Report 2014 (eds Wild, C. P. & Stewart, B. W.) (World Health Organization, 2014).

  125. Secretan, B. et al. A review of human carcinogens — Part E: tobacco, areca nut, alcohol, coal smoke, and salted fish. Lancet Oncol. 10, 1033–1034 (2009).

    Google Scholar 

  126. Lawlor, D. A. et al. Exploring causal associations between alcohol and coronary heart disease risk factors: findings from a Mendelian randomization study in the Copenhagen General Population Study. Eur. Heart J. 34, 2519–2528 (2013).

    Google Scholar 

  127. Holmes, M. V. et al. Association between alcohol and cardiovascular disease: Mendelian randomisation analysis based on individual participant data. BMJ 349, g4164 (2014).

    Google Scholar 

  128. Silverwood, R. J. et al. Testing for non-linear causal effects using a binary genotype in a Mendelian randomization study: application to alcohol and cardiovascular traits. Int. J. Epidemiol. 43, 1781–1790 (2014).

    Google Scholar 

  129. Millwood, I. Y. et al. Conventional and genetic evidence on alcohol and vascular disease aetiology: a prospective study of 500 000 men and women in China. Lancet 393, 1831–1842 (2019).

    Google Scholar 

  130. Goldstein, J. L. & Brown, M. S. A century of cholesterol and coronaries: from plaques to genes to statins. Cell 161, 161–172 (2015).

    Google Scholar 

  131. Miller, G. & Miller, N. Plasma-high-density-lipoprotein concentration and development of ischaemic heart-disease. Lancet 305, 16–19 (1975).

    Google Scholar 

  132. Castelli, W. P. et al. HDL cholesterol and other lipids in coronary heart disease. The cooperative lipoprotein phenotyping study. Circulation 55, 767–772 (1977)

    Google Scholar 

  133. Emerging Risk Factors Collaboration et al. Major lipids, apolipoproteins, and risk of vascular disease. JAMA 302, 1993–2000 (2009).

    Google Scholar 

  134. Davey Smith, G. & Phillips, A. N. Correlation without a cause: an epidemiological odyssey. Int. J. Epidemiol. 49, 4–14 (2020).

    Google Scholar 

  135. Voight, B. F. et al. Plasma HDL cholesterol and risk of myocardial infarction: a Mendelian randomisation study. Lancet 380, 572–580 (2012).

    Google Scholar 

  136. Do, R. et al. Common variants associated with plasma triglycerides and risk for coronary artery disease. Nat. Genet. 45, 1345–1352 (2013).

    Google Scholar 

  137. Holmes, M. V. et al. Mendelian randomization of blood lipids for coronary heart disease. Eur. Heart J. 36, 539–550 (2015).

    Google Scholar 

  138. Holmes, M. V. & Davey Smith, G. REVEALing the effect of CETP inhibition in cardiovascular disease. Nat. Rev. Cardiol. 14, 635–636 (2017).

    Google Scholar 

  139. Barter, P. J. et al. Effects of torcetrapib in patients at high risk for coronary events. N. Engl. J. Med. 357, 2109–2122 (2007).

    Google Scholar 

  140. Riaz, H. et al. Effects of high-density lipoprotein targeting treatments on cardiovascular outcomes: a systematic review and meta-analysis. Eur. J. Prev. Cardiol. 26, 533–543 (2019).

    Google Scholar 

  141. Richardson, T. G., Sanderson, E., Elsworth, B., Tilling, K. & Davey Smith, G. Use of genetic variation to separate the effects of early and later life adiposity on disease risk: Mendelian randomisation study. BMJ 369, m1203 (2020).

    Google Scholar 

  142. Bycroft, C. et al. The UK Biobank resource with deep phenotyping and genomic data. Nature 562, 203–209 (2018).

    ADS  Google Scholar 

  143. Schooling, C. M. Selection bias in population-representative studies? A commentary on Deaton and Cartwright. Soc. Sci. Med. 210, 70 (2018).

    Google Scholar 

  144. Dixon, P., Davey Smith, G., von Hinke, S., Davies, N. M. & Hollingworth, W. Estimating marginal healthcare costs using genetic variants as instrumental variables: Mendelian randomization in economic evaluation. PharmacoEconomics 34, 1075–1086 (2016).

    Google Scholar 

  145. Dixon, P., Hollingworth, W., Harrison, S., Davies, N. M. & Davey Smith, G. Mendelian randomization analysis of the causal effect of adiposity on hospital costs. J. Health Econ. 70, 102300 (2020).

    Google Scholar 

  146. Xu, Z. M. & Burgess, S. Polygenic modelling of treatment effect heterogeneity. Genet. Epidemiol. 44, 868–879 (2020).

    Google Scholar 

  147. Holmes, M. V. Human genetics and drug development. N. Engl. J. Med. 380, 1076–1079 (2019).

    Google Scholar 

  148. Kyriacou, D. N. & Lewis, R. J. Confounding by indication in clinical research. JAMA 316, 1818–1819 (2016).

    Google Scholar 

  149. Schmidt, A. F. et al. Genetic drug target validation using Mendelian randomisation. Nat. Commun. 11, 3255 (2020).

    ADS  Google Scholar 

  150. Schmidt, A. F., Hingorani, A. D. & Finan, C. Human genomics and drug development. Cold Spring Harb. Perspect. Med. https://doi.org/10.1101/cshperspect.a039230 (2021).

    Article  Google Scholar 

  151. Munafò, M. R. et al. A manifesto for reproducible science. Nat. Hum. Behav. 1, 0021 (2017).

    Google Scholar 

  152. Munafò, M. R. & Davey Smith, G. Robust research needs many lines of evidence. Nature 553, 399–401 (2018).

    ADS  Google Scholar 

  153. Davies, N. M., Dickson, M., Davey Smith, G., van den Berg, G. J. & Windmeijer, F. The causal effects of education on health outcomes in the UK Biobank. Nat. Hum. Behav. 2, 117–125 (2018).

    Google Scholar 

  154. Sanderson, E., Davey Smith, G., Bowden, J. & Munafò, M. R. Mendelian randomisation analysis of the effect of educational attainment and cognitive ability on smoking behaviour. Nat. Commun. 10, 2949 (2019).

    ADS  Google Scholar 

  155. Davies, N. M. et al. Multivariable two-sample Mendelian randomization estimates of the effects of intelligence and education on health. eLife 8, e43990 (2019).

    Google Scholar 

  156. Tillmann, T. et al. Education and coronary heart disease: mendelian randomisation study. BMJ 358, j3542 (2017).

    Google Scholar 

  157. Davies, N. M., Dickson, M., Davey Smith, G., Windmeijer, F. & van den Berg, G. J. The causal effects of education on adult health, mortality and income: evidence from Mendelian randomization and the raising of the school leaving age. Preprint at SSRN https://doi.org/10.2139/ssrn.3390179 (2019).

    Article  Google Scholar 

  158. Baldwin, J., Pingault, J.-B., Schoeler, T., Sallis, H. M. & Munafo, M. R. Protecting against researcher bias in secondary data analysis: challenges and solutions. Eur. J. Epidemiol. 37, 1–10 (2022).

    Google Scholar 

  159. Sallis, H. Triangulation protocol; intergenerational effects of parental substance use on child substance use and mental health outcomes. Preprint at https://osf.io/s6jv4/ (2021).

  160. Hartwig, F. P., Davies, N. M. & Davey Smith, G. Bias in Mendelian randomization due to assortative mating. Genet. Epidemiol. 42, 608–620 (2018).

    Google Scholar 

  161. Brumpton, B. et al. Avoiding dynastic, assortative mating, and population stratification biases in Mendelian randomization through within-family analyses. Nat. Commun. 11, 3519 (2020).

    ADS  Google Scholar 

  162. Morris, T. T., Davies, N. M., Hemani, G. & Davey Smith, G. Population phenomena inflate genetic associations of complex social traits. Sci. Adv. 6, eaay0328 (2020).

    ADS  Google Scholar 

  163. Minică, C. C., Boomsma, D. I., Dolan, C. V., de Geus, E. & Neale, M. C. Empirical comparisons of multiple Mendelian randomization approaches in the presence of assortative mating. Int. J. Epidemiol. 49, 1185–1193 (2020).

    Google Scholar 

  164. Davies, N. M. et al. Within family Mendelian randomization studies. Hum. Mol. Genet. 28, R170–R179 (2019).

    Google Scholar 

  165. Minică, C. C., Dolan, C. V., Boomsma, D. I., de Geus, E. & Neale, M. C. Extending causality tests with genetic instruments: an integration of Mendelian randomization with the classical twin design. Behav. Genet. 48, 337–349 (2018).

    Google Scholar 

  166. Howe, L. J. et al. Within-sibship genome-wide association analyses decrease bias in estimates of direct genetic effects. Nat. Genet. (in the press).

  167. Taylor, A. E. et al. Exploring the association of genetic factors with participation in the Avon Longitudinal Study of Parents and Children. Int. J. Epidemiol. 47, 1207–1216 (2018).

    Google Scholar 

  168. Fry, A. et al. Comparison of sociodemographic and health-related characteristics of UK Biobank participants with those of the general population. Am. J. Epidemiol. 186, 1026–1034 (2017).

    Google Scholar 

  169. Pirastu, N. et al. Genetic analyses identify widespread sex-differential participation bias. Nat. Genet. 53, 663–671 (2021).

    Google Scholar 

  170. Smit, R. A., Trompet, S., Dekkers, O. M., Jukema, J. W. & le Cessie, S. Survival bias in Mendelian randomization studies: a threat to causal inference. Epidemiology 30, 813 (2019).

    Google Scholar 

  171. Schooling, C. M. et al. Use of multivariable Mendelian randomization to address biases due to competing risk before recruitment. Front. Genet. 11, 610852 (2020).

    Google Scholar 

  172. Vansteelandt, S., Dukes, O. & Martinussen, T. Survivor bias in Mendelian randomization analysis. Biostatistics 19, 426–443 (2017).

    MathSciNet  Google Scholar 

  173. Hernán, M. A. Invited commentary: selection bias without colliders. Am. J. Epidemiol. 185, 1048–1050 (2017).

    Google Scholar 

  174. Mahmoud, O., Dudbridge, F., Davey Smith, G., Munafo, M. & Tilling, K. Slope-Hunter: a robust method for index-event bias correction in genome-wide association studies of subsequent traits. Nat. Commun. (in the press).

  175. Waddington, C. H. Canalization of development and the inheritance of acquired characters. Nature 150, 563–565 (1942).

    ADS  Google Scholar 

  176. Debat, V. & David, P. Mapping phenotypes: canalization, plasticity and developmental stability. Trends Ecol. Evol. 16, 555–561 (2001).

    Google Scholar 

  177. Kitami, T. & Nadeau, J. H. Biochemical networking contributes more to genetic buffering in human and mouse metabolic pathways than does gene duplication. Nat. Genet. 32, 191–194 (2002).

    Google Scholar 

  178. Gu, Z. et al. Role of duplicate genes in genetic robustness against null mutations. Nature 421, 63–66 (2003).

    ADS  Google Scholar 

  179. Hemani, G. et al. Automating Mendelian randomization through machine learning to construct a putative causal map of the human phenome. Preprint at bioRxiv https://doi.org/10.1101/173682 (2017).

    Article  Google Scholar 

  180. Ioannidis, J. P. The mass production of redundant, misleading, and conflicted systematic reviews and meta-analyses. Milbank Q. 94, 485–514 (2016).

    Google Scholar 

  181. Martin, A. R. et al. Clinical use of current polygenic risk scores may exacerbate health disparities. Nat. Genet. 51, 584–591 (2019).

    Google Scholar 

  182. Paternoster, L., Tilling, K. & Davey Smith, G. Genetic epidemiology and Mendelian randomization for informing disease therapeutics: conceptual and methodological challenges. PLoS Genet. 13, e1006944 (2017).

    Google Scholar 

  183. Zhou, W. et al. Causal relationships between body mass index, smoking and lung cancer: univariable and multivariable Mendelian randomization. Int. J. Cancer 148, 1077–1086 (2021).

    Google Scholar 

  184. Lee, J. C. et al. Genome-wide association study identifies distinct genetic contributions to prognosis and susceptibility in Crohn’s disease. Nat. Genet. 49, 262–268 (2017).

    Google Scholar 

  185. Kim, Y.-I. Role of folate in colon cancer development and progression. J. Nutr. 133, 3731S–3739S (2003).

    Google Scholar 

  186. Davey Smith, G., Paternoster, L. & Relton, C. When will Mendelian randomization become relevant for clinical practice and public health? JAMA 317, 589–591 (2017).

    Google Scholar 

  187. Ye, T., Shao, J. & Kang, H. Debiased inverse-variance weighted estimator in two-sample summary-data Mendelian randomization. Ann. Stat. 49, 2079–2100 (2021).

    MathSciNet  MATH  Google Scholar 

  188. Bowden, J. et al. Improving the accuracy of two-sample summary-data Mendelian randomization: moving beyond the NOME assumption. Int. J. Epidemiol. 48, 728–742 (2018).

    Google Scholar 

  189. Wang, S. & Kang, H. Weak-instrument robust tests in two-sample summary-data Mendelian randomization. Biometrics https://doi.org/10.1111/biom.13524 (2021).

    Article  Google Scholar 

  190. Minelli, C. et al. The use of two-sample methods for Mendelian randomization analyses on single large datasets. Int. J. Epidemiol. 50, 1651–1659 (2021).

    Google Scholar 

  191. Burgess, S., Foley, C. N., Allara, E., Staley, J. R. & Howson, J. M. M. A robust and efficient method for Mendelian randomization with hundreds of genetic variants. Nat. Commun. 11, 376 (2020).

    ADS  Google Scholar 

  192. Foley, C. N., Mason, A. M., Kirk, P. D. W. & Burgess, S. MR-Clust: clustering of genetic variants in Mendelian randomization with similar causal estimates. Bioinformatics 37, 531–541 (2020).

    Google Scholar 

  193. Berzuini, C., Guo, H., Burgess, S. & Bernardinelli, L. A Bayesian approach to Mendelian randomization with multiple pleiotropic variants. Biostatistics 21, 86–101 (2018).

    MathSciNet  Google Scholar 

  194. Xu, S., Fung, W. K. & Liu, Z. MRCIP: a robust Mendelian randomization method accounting for correlated and idiosyncratic pleiotropy. Brief. Bioinform. 22, bbab019 (2021).

    Google Scholar 

  195. Qi, G. & Chatterjee, N. Mendelian randomization analysis using mixture models for robust and efficient estimation of causal effects. Nat. Commun. 10, 1941 (2019).

    ADS  Google Scholar 

  196. Cheng, Q. et al. MR-LDP: a two-sample Mendelian randomization for GWAS summary statistics accounting for linkage disequilibrium and horizontal pleiotropy. NAR Genom. Bioinform 2, lqaa028 (2020).

    Google Scholar 

  197. Zhu, X., Li, X., Xu, R. & Wang, T. An iterative approach to detect pleiotropy and perform Mendelian randomization analysis using GWAS summary statistics. Bioinformatics 37, 1390–1400 (2020).

    Google Scholar 

  198. Grant, A. J. & Burgess, S. An efficient and robust approach to Mendelian randomization with measured pleiotropic effects in a high-dimensional setting. Biostatistics https://doi.org/10.1093/biostatistics/kxaa045 (2020).

    Article  Google Scholar 

  199. Iong, D., Zhao, Q. & Chen, Y. A latent mixture model for heterogeneous causal mechanisms in mendelian randomization. Preprint at https://arxiv.org/abs/2007.06476 (2020).

  200. van der Graaf, A. et al. Mendelian randomization while jointly modeling cis genetics identifies causal relationships between gene expression and lipids. Nat. Commun. 11, 4930 (2020).

    ADS  Google Scholar 

  201. Jiang, L., Xu, S., Mancuso, N., Newcombe, P. J. & Conti, D. V. A hierarchical approach using marginal summary statistics for multiple intermediates in a Mendelian randomization or transcriptome analysis. Am. J. Epidemiol. 190, 1148–1158 (2021).

    Google Scholar 

  202. DiPrete, T. A., Burik, C. A. P. & Koellinger, P. D. Genetic instrumental variable regression: explaining socioeconomic and health outcomes in nonexperimental data. Proc. Natl Acad. Sci. USA 115, E4970–E4979 (2018).

    Google Scholar 

  203. Howey, R., Shin, S.-Y., Relton, C., Davey Smith, G. & Cordell, H. J. Bayesian network analysis incorporating genetic anchors complements conventional Mendelian randomization approaches for exploratory analysis of causal relationships in complex data. PLoS Genet. 16, e1008198 (2020).

    Google Scholar 

  204. Schmidt, A. F. & Dudbridge, F. Mendelian randomization with Egger pleiotropy correction and weakly informative Bayesian priors. Int. J. Epidemiol. 47, 1217–1228 (2017).

    Google Scholar 

  205. Bucur, I. G., Claassen, T. & Heskes, T. Inferring the direction of a causal link and estimating its effect via a Bayesian Mendelian randomization approach. Stat. Methods Med. Res. 29, 1081–1111 (2019).

    MathSciNet  Google Scholar 

  206. Davey Smith, G., Holmes, M. V., Davies, N. M. & Ebrahim, S. Mendel’s laws, Mendelian randomization and causal inference in observational data: substantive and nomenclatural issues. Eur. J. Epidemiol. 35, 99–111 (2020).

    Google Scholar 

  207. Davey Smith, G. et al. Clustered environments and randomized genes: a fundamental distinction between conventional and genetic epidemiology. PLoS Med. 4, 1985–1992 (2007).

    Google Scholar 

  208. Pearl, J. Causality (Cambridge Univ. Press, 2009).

  209. Keele, L., Zhao, Q., Kelz, R. R. & Small, D. Falsification tests for instrumental variable designs with an application to tendency to operate. Med. Care 57, 167–171 (2019).

    Google Scholar 

  210. Brookhart, M. A., Rassen, J. A. & Schneeweiss, S. Instrumental variable methods in comparative safety and effectiveness research. Pharmacoepidemiol. Drug Saf. 19, 537–554 (2010).

    Google Scholar 

  211. Burgess, S. & Labrecque, J. A. Mendelian randomization with a binary exposure variable: interpretation and presentation of causal estimates. Eur. J. Epidemiol. 33, 947–952 (2018).

    Google Scholar 

  212. Wang, L. & Tchetgen Tchetgen, E. Bounded, efficient and multiply robust estimation of average treatment effects using instrumental variables. J. R. Stat. Soc. Ser. B 80, 531–550 (2018).

    MathSciNet  MATH  Google Scholar 

  213. Mills, H. L. et al. Detecting heterogeneity of intervention effects using analysis and meta-analysis of differences in variance between arms of a trial. Epidemiology 32, 846–854 (2021).

    Google Scholar 

  214. West-Eberhard, M. J. Developmental Plasticity and Evolution (Oxford Univ. Press, 2003).

  215. Zuckerkandl, E. & Villet, R. Concentration-affinity equivalence in gene regulation: convergence of genetic and environmental effects. Proc. Natl Acad. Sci. USA 85, 4784–4788 (1988).

    ADS  Google Scholar 

  216. Ebrahim, S. & Davey Smith, G. Mendelian randomization: can genetic epidemiology help redress the failures of observational epidemiology? Hum. Genet. 123, 15–33 (2008).

    Google Scholar 

  217. Hill, W. D. et al. Molecular genetic contributions to social deprivation and household income in UK Biobank. Curr. Biol. 26, 3083–3089 (2016).

    Google Scholar 

  218. Labrecque, J. A. & Swanson, S. A. Interpretation and potential biases of mendelian randomization estimates with time-varying exposures. Am. J. Epidemiol. 188, 231–238 (2018).

    Google Scholar 

  219. Sanderson, E., Richardson, T. G., Morris, T. T., Tilling, K. & Davey Smith, G. Estimation of causal effects of a time-varying exposure at multiple time points through Multivariable Mendelian randomization. Preprint at medRxiv https://doi.org/10.1101/2022.01.04.22268740 (2022).

    Article  Google Scholar 

  220. Cardon, L. R. & Palmer, L. J. Population stratification and spurious allelic association. Lancet 361, 598–604 (2003).

    Google Scholar 

  221. Loh, P.-R. et al. Efficient Bayesian mixed-model analysis increases association power in large cohorts. Nat. Genet. 47, 284 (2015).

    Google Scholar 

  222. Zhou, W. et al. Efficiently controlling for case-control imbalance and sample relatedness in large-scale genetic association studies. Nat. Genet. 50, 1335–1341 (2018).

    Google Scholar 

  223. Price, A. L. et al. Principal components analysis corrects for stratification in genome-wide association studies. Nat. Genet. 38, 904–909 (2006).

    Google Scholar 

  224. Lawson, D. J. et al. Is population structure in the genetic biobank era irrelevant, a challenge, or an opportunity? Hum. Genet. 139, 23–41 (2020).

    Google Scholar 

  225. Haworth, S. et al. Apparent latent structure within the UK Biobank sample has implications for epidemiological analysis. Nat. Commun. 10, 1–9 (2019).

    Google Scholar 

  226. Howe, L. J. et al. Genetic evidence for assortative mating on alcohol consumption in the UK Biobank. Nat. Commun. 10, 5039 (2019).

    ADS  Google Scholar 

  227. Nordsletten, A. E. et al. Patterns of nonrandom mating within and across 11 major psychiatric disorders. JAMA Psychiat. 73, 354–361 (2016).

    Google Scholar 

  228. Bochud, M., Chiolero, A., Elston, R. C. & Paccaud, F. A cautionary note on the use of Mendelian randomization to infer causation in observational epidemiology. Int. J. Epidemiol. 37, 414–416 (2008).

    Google Scholar 

Download references

Acknowledgements

E.S., M.R.M., T.P. and G.D.S. are members of the UK Medical Research Council (MRC) Integrative Epidemiology unit, which is funded by the MRC (MC_UU_00011/1, MC_UU_00011/3 and MC_UU_00011/7) and the University of Bristol. M.M.G. is supported by the National Institutes of Health/National Institute on Aging (NIH/NIA) grant R01AG057869. M.V.H. works in a unit that receives funding from the MRC and is supported by a British Heart Foundation Intermediate Clinical Research Fellowship (FS/18/23/33512) and the National Institute for Health Research Oxford Biomedical Research Centre. H.K. is supported by the National Science Foundation grant DMS-1811414. C.W. is funded by the MRC (MC UU 00002/4, MC UU 00002/13) and the Wellcome Trust (WT107881).

Author information

Authors and Affiliations

Authors

Contributions

Introduction (E.S.); Experimentation (E.S., M.M.G. and T.P); Results (E.S., M.M.G., T.P. and C.W); Applications (E.S. and M.V.H.); Reproducibility and data deposition (M.R.M.); Limitations and optimizations (E.S.); Outlook (G.D.S.); Overview of the Primer (E.S., H.K., J.M., C.M.S., Q.Z. and G.D.S.).

Corresponding author

Correspondence to Eleanor Sanderson.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information

Nature Reviews Methods Primers thanks Marianne Benn, Frida Emanuelsson, Sarah Gagliano Taliun and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Related links

ivonesamplemr: https://github.com/remlapmot/ivonesamplemr

MendelianRandomization: https://cran.r-project.org/package=MendelianRandomization

MR dictionary: https://mr-dictionary.mrcieu.ac.uk/

mrrobust: https://github.com/remlapmot/mrrobust

OneSampleMR: https://remlapmot.github.io/OneSampleMR/

STROBE-MR: https://www.strobe-mr.org/

The OpenGWAS project: https://gwas.mrcieu.ac.uk/

TwoSampleMR: https://github.com/MRCIEU/TwoSampleMR

UK Biobank: https://www.ukbiobank.ac.uk/

Supplementary information

Glossary

Instrumental variable

(IV). A variable associated with an exposure that is not associated with the outcome through any other pathway.

Natural experiment

Natural experiments are variation in any exposures or risk factors that occurred by chance in the population without conscious or deliberate intervention from investigators or scientists.

Confounder

A trait that influences both the exposure and outcome of interest.

First-stage F statistic

Test statistic used to test the strength of association between the instrument(s) and the exposure in an instrumental variable estimation.

Linkage disequilibrium

Correlation between genetic variants located closely together on the genome.

Vertical pleiotropy

The phenomenon of a genetic variant associated with multiple phenotypes on the same pathway.

Horizontal pleiotropy

The phenomenon of a genetic variant associated with multiple phenotypes on different pathways.

Bidirectional relationship

Where an effect acts in both directions between a pair of traits so that changing one will change the other.

Collider bias

Bias occurring owing to conditioning on a variable that is dependent on both the exposure and outcome or is dependent on causes of the exposure and outcome.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Sanderson, E., Glymour, M.M., Holmes, M.V. et al. Mendelian randomization. Nat Rev Methods Primers 2, 6 (2022). https://doi.org/10.1038/s43586-021-00092-5

Download citation

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1038/s43586-021-00092-5

Further reading

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing