A Review of Mendelian Randomization in the Presence of Weak Instrumental Variables; Statistical Methods and Challenges
Weak Instrumental Variables in Mendelian Randomization
Abstract
The genetic variant of interest is referred to be a weak instrumental variable in Mendelian randomization If the relevance assumption is not met. By and large, a weak instrument bias occurs when there is insufficient statistical evidence to support an association between IV and exposure. Weak instruments can result in a variety of problems, including (i) insufficient statistical power to hypothesis testing, (ii) increasing bias with deviation from IV assumptions, and (iii) asymptotic estimation of standard errors and confidence intervals. Several statistical techniques have been presented thus far for reducing weak instrumental bias. However, the absence of a comprehensive document comparing and reviewing all of these strategies is particularly evident. As such, we seek to present an overview of Mendelian Randomization, the challenges associated with weak instrumental bias, an adequate statistical remedy for weak instrumental bias, and the limits of MR, as well as a critical comparison.
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3. Berzuini C, Guo H, Burgess S, Bernardinelli L. A Bayesian approach to Mendelian randomization with multiple pleiotropic variants. Biostatistics. 2020;21(1):86–101.
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8. Habibi D, Daneshpour MS, Asgarian S, Kohansal K, Hadaegh F, Mansourian M, et al. Effect of C-reactive protein on the risk of Heart failure: a mendelian randomization study. BMC Cardiovasc Disord. 2023;23(1):1–7.
9. Habibi D, Teymoori F, Ebrahimi N, Fateh ST, Najd-Hassan-Bonab L, Saeidian AH, et al. Causal effect of serum 25 hydroxyvitamin D concentration on cardioembolic stroke: Evidence from Two-sample Mendelian randomization. Nutr Metab Cardiovasc Dis. 2024;
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11. Zheng J, Baird D, Borges M-C, Bowden J, Hemani G, Haycock P, et al. Recent developments in Mendelian randomization studies. Curr Epidemiol reports. 2017;4(4):330–45.
12. Evans DM, Davey Smith G. Mendelian randomization: new applications in the coming age of hypothesis-free causality. Annu Rev Genomics Hum Genet. 2015;16:327–50.
13. Burgess S, Swanson SA, Labrecque JA. Are Mendelian randomization investigations immune from bias due to reverse causation? Eur J Epidemiol. 2021;36(3):253–7.
14. Paternoster L, Tilling K, Davey Smith G. Genetic epidemiology and Mendelian randomization for informing disease therapeutics: Conceptual and methodological challenges. PLoS Genet. 2017;13(10):e1006944.
15. Bennett DA. An introduction to instrumental variables–part 2: Mendelian randomisation. Neuroepidemiology.
2010;35(4):307–10.
16. Lee K, Lim C-Y. Mendelian Randomization Analysis in Observational Epidemiology. J Lipid Atheroscler. 2019;8(2):67.
17. Sheehan NA, Didelez V. Epidemiology, genetic epidemiology and Mendelian randomisation: more need than ever to attend to detail. Hum Genet. 2020;139(1):121–36.
18. Lawlor DA, Harbord RM, Sterne JAC, Timpson N, Davey Smith G. Mendelian randomization: using genes as instruments for making causal inferences in epidemiology. Stat Med. 2008;27(8):1133–63.
19. Cano-Gamez E, Trynka G. From GWAS to function: using functional genomics to identify the mechanisms underlying complex diseases. Front Genet. 2020;11:424.
20. Burgess S, Davies NM, Thompson SG. Bias due to participant overlap in two‐sample Mendelian randomization. Genet Epidemiol. 2016;40(7):597–608.
21. Hartwig FP, Davies NM, Hemani G, Davey Smith G. Two-sample Mendelian randomization: avoiding the downsides of a powerful, widely applicable but potentially fallible technique. Int J Epidemiol. 2016;45(6):1717–1726.
22. Elston RC, Satagopan JM, Sun S. Statistical human genetics. Springer; 2012.
23. Rasooly D, Patel CJ. Conducting a Reproducible Mendelian Randomization Analysis using the R analytic statistical environment. Curr Protoc Hum Genet. 2019;101(1):e82.
24. Plotnikov D, Guggenheim JA. Mendelian randomisation and the goal of inferring causation from observational studies in the vision sciences. Ophthalmic Physiol Opt. 2019;39(1):11–25.
25. Pierce BL, Burgess S. Efficient design for Mendelian randomization studies: subsample and 2-sample instrumental variable estimators. Am J Epidemiol. 2013;178(7):1177–84.
26. Go T-H, Kang DR. Basic Concepts of a Mendelian Randomization Approach. Cardiovasc Prev Pharmacother. 2020;2(1):24–30.
27. Burgess S, Daniel RM, Butterworth AS, Thompson SG, Consortium E-I. Network Mendelian randomization: using genetic variants as instrumental variables to investigate mediation in causal pathways. Int J Epidemiol. 2015;44(2):484–95.
28. Sanderson E, Davey Smith G, Windmeijer F, Bowden J. An examination of 147 Vol 10 No 2 (2024) A Review of Mendelian Randomization in the Presence of Weak ... Habibi D et al. multivariable Mendelian randomization in the single-sample and two-sample summary data settings. Int J Epidemiol. 2019;48(3):713–27.
29. Rees JMB, Foley CN, Burgess S. Factorial Mendelian randomization: using genetic variants to assess interactions. Int J Epidemiol. 2020;49(4):1147–58.
30. VanderWeele TJ, Tchetgen EJT, Cornelis M, Kraft P. Methodological challenges in mendelian randomization. Epidemiology. 2014;25(3):427.
31. Pierce BL, Ahsan H, VanderWeele TJ. Power and instrument strength requirements for Mendelian randomization studies using multiple genetic variants. Int J Epidemiol. 2011;40(3):740–52.
32. Ebbes P, Wedel M, Böckenholt U. Frugal IV alternatives to identify the parameter for an endogenous regressor. J Appl Econom. 2009;24(3):446–68.
33. Burgess S, Thompson SG. Mendelian randomization: methods for using genetic variants in causal estimation. CRC Press; 2015.
34. Stock JH, Yogo M. Testing for weak instruments in linear IV regression. Identif inference Econom Model Essays Honor Thomas Rothenb. 2005;80(4.2):1.
35. Cragg JG, Donald SG. Testing identifiability and specification in instrumental variable models. Econom Theory. 1993;222–40.
36. Burgess S, Thompson SG. Use of allele scores as instrumental variables for Mendelian randomization. Int J Epidemiol. 2013;42(4):1134–44.
37. Burgess S, Thompson SG. Bias in causal estimates from Mendelian randomization studies with weak instruments. Stat Med. 2011;30(11):1312–23.
38. Burgess S, Thompson SG, Collaboration CRPCHDG. Avoiding bias from weak instruments in Mendelian randomization studies. Int J Epidemiol. 2011;40(3):755–64.
39. Burgess S. Sample size and power calculations in Mendelian randomization with a single instrumental variable and a binary outcome. Int J Epidemiol. 2014;43(3):922–9.
40. Burgess S, Dudbridge F, Thompson SG. Combining information on multiple instrumental variables in Mendelian randomization: comparison of allele score and summarized data methods. Stat Med. 2016;35(11):1880–906.
41. Nelson CR, Startz R. The distribution of the instrumental variables estimator and its t-ratio when the instrument is a poor one. J Bus. 1990;S125–40.
42. Angrist JD, Krueger AB. Split-sample instrumental variables estimates of the return to schooling. J Bus Econ Stat. 1995;13(2):225–35.
43. Zhao Q, Chen Y, Wang J, Small DS. Powerful three-sample genome-wide design and robust statistical inference in summary data Mendelian randomization. Int J Epidemiol. 2019;48(5):1478–92. 148 Vol 10 No 2 (2024) A Review of Mendelian Randomization in the Presence of Weak ... Habibi D et al.
44. Mikusheva A. Robust confidence sets in the presence of weak instruments. J Econom. 2010;157(2):236–47.
45. Brookhart MA, Rassen JA, Schneeweiss S. Instrumental variable methods in comparative safety and effectiveness research. Pharmacoepidemiol Drug Saf. 2010;19(6):537–54.
46. Ertefaie A, Small DS, Flory JH, Hennessy S. A tutorial on the use of instrumental variables in pharmacoepidemiology. Pharmacoepidemiol Drug Saf. 2017;26(4):357– 67.
47. Burgess S, Butterworth A, Thompson SG. Mendelian randomization analysis with multiple genetic variants using summarized data. Genet Epidemiol. 2013;37(7):658–65.
48. Hahn J, Hausman J. Weak instruments: Diagnosis and cures in empirical econometrics. Am Econ Rev. 2003;93(2):118–25.
49. Stock JH, Wright JH, Yogo M. A survey of weak instruments and weak identification in generalized method of moments. J Bus Econ Stat. 2002;20(4):518–29.
50. Hahn J, Hausman J. A new specification test for the validity of instrumental variables. Econometrica. 2002;70(1):163–89.
51. Hansen C, Hausman J, Newey W. Estimation with many instrumental variables. J Bus Econ Stat. 2008;26(4):398–422.
52. Davies NM, von Hinke Kessler Scholder S, Farbmacher H, Burgess S, Windmeijer F, Smith GD. The many weak instruments problem and Mendelian randomization. Stat Med. 2015;34(3):454–68.
53. Hausman JA, Newey WK, Woutersen T, Chao JC, Swanson NR. Instrumental variable estimation with heteroskedasticity and many instruments. Quant Econom. 2012;3(2):211– 55.
54. Jiang L, Oualkacha K, Didelez V, Ciampi A, Rosa‐Neto P, Benedet AL, et al. Constrained instruments and their application to Mendelian randomization with pleiotropy. Genet Epidemiol. 2019;43(4):373–401.
55. Wang S, Kang H. Weak-instrument robust tests in two-sample summary-data Mendelian randomization. Biometrics. 2021 Jul;
56. Ye T, Shao J, Kang H. Debiased inverse variance weighted estimator in two-sample summary-data mendelian randomization. Ann Stat. 2021;49(4):2079–100.
57. Bowden J, Holmes M V. Meta‐analysis and Mendelian randomization: A review. Res Synth Methods. 2019;10(4):486–96.
58. Bowden J, Del Greco M F, Minelli C, Davey Smith G, Sheehan NA, Thompson JR. Assessing the suitability of summary data for two-sample Mendelian randomization analyses using MR-Egger regression: the role of the I 2 statistic. Int J Epidemiol. 2016;45(6):1961–74.
59. Schmidt AF, Hingorani AD, Jefferis BJ, White J, Groenwold RHH, Dudbridge F. Comparison of variance estimators for meta- 149 Vol 10 No 2 (2024) A Review of Mendelian Randomization in the Presence of Weak ... Habibi D et al. analysis of instrumental variable estimates. Int J Epidemiol. 2016;45(6):1975–86. 60. Shea J. Instrument relevance in multivariate linear models: A simple measure. Rev Econ Stat. 1997;79(2):348–52.
61. Minică CC, Dolan C V, Boomsma DI, de Geus E, Neale MC. Extending causality tests with genetic instruments: an integration of Mendelian randomization with the classical twin design. Behav Genet. 2018;48(4):337–49.
62. Zou L, Guo H, Berzuini C. Overlapping-sample Mendelian randomisation with multiple exposures: a Bayesian approach. BMC Med Res Methodol. 2020;20(1):1–15.
63. Byrne BE, Rooshenas L, Lambert HS, Blazeby JM. A mixed methods case study investigating how randomised controlled trials (RCTs) are reported, understood and interpreted in practice. BMC Med Res Methodol. 2020;20:1–12.
64. Hosseini-Esfahani F, Zahedi AS, Akbarzadeh M, Seyedhamzehzadeh A, Daneshpour MS, Mirmiran P, et al. The resemblance of dietary intakes in three generations of parent-offspring pairs: Tehran lipid and glucose study. Appetite. 2021;105794.
65. Akbarzadeh M, Dehkordi SR, Roudbar MA, Sargolzaei M, Guity K, Sedaghati Khayat B, et al. GWAS findings improved genomic prediction accuracy of lipid profile traits: Tehran Cardiometabolic Genetic Study. Sci Rep. 2021;11(1):1–9.
66. Burgess S, Foley CN, Allara E, Staley JR, Howson JMM. A robust and efficient method for Mendelian randomization with hundreds of genetic variants. Nat Commun. 2020;11(1):1–11.
67. Rees JMB, Wood AM, Burgess S. Extending the MR‐Egger method for multivariable Mendelian randomization to correct for both measured and unmeasured pleiotropy. Stat Med. 2017;36(29):4705–18.
68. Akbarzadeh M, Moghimbeigi A, Morris N, Daneshpour MS, Mahjub H, Soltanian AR. A Bayesian structural equation model in general pedigree data analysis. Stat Anal Data Min ASA Data Sci J. 2019;12(5):404–11.
69. Boef AGC, Dekkers OM, Le Cessie S. Mendelian randomization studies: a review of the approaches used and the quality of reporting. Int J Epidemiol. 2015;44(2):496– 511.
70. Myers JA, Rassen JA, Gagne JJ, Huybrechts KF, Schneeweiss S, Rothman KJ, et al. Effects of adjusting for instrumental variables on bias and precision of effect estimates. Am J Epidemiol. 2011;174(11):1213–22.
71. Davies NM, Holmes M V, Smith GD. Reading Mendelian randomisation studies: a guide, glossary, and checklist for clinicians. Bmj. 2018;362.
72. Hartwig FP, Davies NM. Why internal weights should be avoided (not only) in MR-Egger regression
2. Cornish AJ, Tomlinson IPM, Houlston RS. Mendelian randomisation: a powerful and inexpensive method for identifying and excluding non-genetic risk factors for colorectal cancer. Mol Aspects Med. 2019;69:41–7.
3. Berzuini C, Guo H, Burgess S, Bernardinelli L. A Bayesian approach to Mendelian randomization with multiple pleiotropic variants. Biostatistics. 2020;21(1):86–101.
4. Davey Smith G, Hemani G. Mendelian randomization: genetic anchors for causal inference in epidemiological studies. Hum Mol Genet. 2014;23(R1):R89–98.
5. Jepsen P, Johnsen SP, Gillman MW, Sørensen HT. Interpretation of observational studies. Heart [Internet]. 2004 Aug;90(8):956–60. Available from: https://pubmed.ncbi.nlm.nih.gov/15253985
6. DiPrete TA, Burik CAP, Koellinger PD. Genetic instrumental variable regression: Explaining socioeconomic and health
outcomes in nonexperimental data. Proc Natl Acad Sci. 2018;115(22):E4970–9.
7. Greenland S. An introduction to instrumental variables for epidemiologists. Int J Epidemiol. 2000;29(4):722–9.
8. Habibi D, Daneshpour MS, Asgarian S, Kohansal K, Hadaegh F, Mansourian M, et al. Effect of C-reactive protein on the risk of Heart failure: a mendelian randomization study. BMC Cardiovasc Disord. 2023;23(1):1–7.
9. Habibi D, Teymoori F, Ebrahimi N, Fateh ST, Najd-Hassan-Bonab L, Saeidian AH, et al. Causal effect of serum 25 hydroxyvitamin D concentration on cardioembolic stroke: Evidence from Two-sample Mendelian randomization. Nutr Metab Cardiovasc Dis. 2024;
10. Gala H, Tomlinson I. The use of Mendelian randomisation to identify causal cancer risk factors: promise and limitations. J Pathol. 2020;250(5):541–54.
11. Zheng J, Baird D, Borges M-C, Bowden J, Hemani G, Haycock P, et al. Recent developments in Mendelian randomization studies. Curr Epidemiol reports. 2017;4(4):330–45.
12. Evans DM, Davey Smith G. Mendelian randomization: new applications in the coming age of hypothesis-free causality. Annu Rev Genomics Hum Genet. 2015;16:327–50.
13. Burgess S, Swanson SA, Labrecque JA. Are Mendelian randomization investigations immune from bias due to reverse causation? Eur J Epidemiol. 2021;36(3):253–7.
14. Paternoster L, Tilling K, Davey Smith G. Genetic epidemiology and Mendelian randomization for informing disease therapeutics: Conceptual and methodological challenges. PLoS Genet. 2017;13(10):e1006944.
15. Bennett DA. An introduction to instrumental variables–part 2: Mendelian randomisation. Neuroepidemiology.
2010;35(4):307–10.
16. Lee K, Lim C-Y. Mendelian Randomization Analysis in Observational Epidemiology. J Lipid Atheroscler. 2019;8(2):67.
17. Sheehan NA, Didelez V. Epidemiology, genetic epidemiology and Mendelian randomisation: more need than ever to attend to detail. Hum Genet. 2020;139(1):121–36.
18. Lawlor DA, Harbord RM, Sterne JAC, Timpson N, Davey Smith G. Mendelian randomization: using genes as instruments for making causal inferences in epidemiology. Stat Med. 2008;27(8):1133–63.
19. Cano-Gamez E, Trynka G. From GWAS to function: using functional genomics to identify the mechanisms underlying complex diseases. Front Genet. 2020;11:424.
20. Burgess S, Davies NM, Thompson SG. Bias due to participant overlap in two‐sample Mendelian randomization. Genet Epidemiol. 2016;40(7):597–608.
21. Hartwig FP, Davies NM, Hemani G, Davey Smith G. Two-sample Mendelian randomization: avoiding the downsides of a powerful, widely applicable but potentially fallible technique. Int J Epidemiol. 2016;45(6):1717–1726.
22. Elston RC, Satagopan JM, Sun S. Statistical human genetics. Springer; 2012.
23. Rasooly D, Patel CJ. Conducting a Reproducible Mendelian Randomization Analysis using the R analytic statistical environment. Curr Protoc Hum Genet. 2019;101(1):e82.
24. Plotnikov D, Guggenheim JA. Mendelian randomisation and the goal of inferring causation from observational studies in the vision sciences. Ophthalmic Physiol Opt. 2019;39(1):11–25.
25. Pierce BL, Burgess S. Efficient design for Mendelian randomization studies: subsample and 2-sample instrumental variable estimators. Am J Epidemiol. 2013;178(7):1177–84.
26. Go T-H, Kang DR. Basic Concepts of a Mendelian Randomization Approach. Cardiovasc Prev Pharmacother. 2020;2(1):24–30.
27. Burgess S, Daniel RM, Butterworth AS, Thompson SG, Consortium E-I. Network Mendelian randomization: using genetic variants as instrumental variables to investigate mediation in causal pathways. Int J Epidemiol. 2015;44(2):484–95.
28. Sanderson E, Davey Smith G, Windmeijer F, Bowden J. An examination of 147 Vol 10 No 2 (2024) A Review of Mendelian Randomization in the Presence of Weak ... Habibi D et al. multivariable Mendelian randomization in the single-sample and two-sample summary data settings. Int J Epidemiol. 2019;48(3):713–27.
29. Rees JMB, Foley CN, Burgess S. Factorial Mendelian randomization: using genetic variants to assess interactions. Int J Epidemiol. 2020;49(4):1147–58.
30. VanderWeele TJ, Tchetgen EJT, Cornelis M, Kraft P. Methodological challenges in mendelian randomization. Epidemiology. 2014;25(3):427.
31. Pierce BL, Ahsan H, VanderWeele TJ. Power and instrument strength requirements for Mendelian randomization studies using multiple genetic variants. Int J Epidemiol. 2011;40(3):740–52.
32. Ebbes P, Wedel M, Böckenholt U. Frugal IV alternatives to identify the parameter for an endogenous regressor. J Appl Econom. 2009;24(3):446–68.
33. Burgess S, Thompson SG. Mendelian randomization: methods for using genetic variants in causal estimation. CRC Press; 2015.
34. Stock JH, Yogo M. Testing for weak instruments in linear IV regression. Identif inference Econom Model Essays Honor Thomas Rothenb. 2005;80(4.2):1.
35. Cragg JG, Donald SG. Testing identifiability and specification in instrumental variable models. Econom Theory. 1993;222–40.
36. Burgess S, Thompson SG. Use of allele scores as instrumental variables for Mendelian randomization. Int J Epidemiol. 2013;42(4):1134–44.
37. Burgess S, Thompson SG. Bias in causal estimates from Mendelian randomization studies with weak instruments. Stat Med. 2011;30(11):1312–23.
38. Burgess S, Thompson SG, Collaboration CRPCHDG. Avoiding bias from weak instruments in Mendelian randomization studies. Int J Epidemiol. 2011;40(3):755–64.
39. Burgess S. Sample size and power calculations in Mendelian randomization with a single instrumental variable and a binary outcome. Int J Epidemiol. 2014;43(3):922–9.
40. Burgess S, Dudbridge F, Thompson SG. Combining information on multiple instrumental variables in Mendelian randomization: comparison of allele score and summarized data methods. Stat Med. 2016;35(11):1880–906.
41. Nelson CR, Startz R. The distribution of the instrumental variables estimator and its t-ratio when the instrument is a poor one. J Bus. 1990;S125–40.
42. Angrist JD, Krueger AB. Split-sample instrumental variables estimates of the return to schooling. J Bus Econ Stat. 1995;13(2):225–35.
43. Zhao Q, Chen Y, Wang J, Small DS. Powerful three-sample genome-wide design and robust statistical inference in summary data Mendelian randomization. Int J Epidemiol. 2019;48(5):1478–92. 148 Vol 10 No 2 (2024) A Review of Mendelian Randomization in the Presence of Weak ... Habibi D et al.
44. Mikusheva A. Robust confidence sets in the presence of weak instruments. J Econom. 2010;157(2):236–47.
45. Brookhart MA, Rassen JA, Schneeweiss S. Instrumental variable methods in comparative safety and effectiveness research. Pharmacoepidemiol Drug Saf. 2010;19(6):537–54.
46. Ertefaie A, Small DS, Flory JH, Hennessy S. A tutorial on the use of instrumental variables in pharmacoepidemiology. Pharmacoepidemiol Drug Saf. 2017;26(4):357– 67.
47. Burgess S, Butterworth A, Thompson SG. Mendelian randomization analysis with multiple genetic variants using summarized data. Genet Epidemiol. 2013;37(7):658–65.
48. Hahn J, Hausman J. Weak instruments: Diagnosis and cures in empirical econometrics. Am Econ Rev. 2003;93(2):118–25.
49. Stock JH, Wright JH, Yogo M. A survey of weak instruments and weak identification in generalized method of moments. J Bus Econ Stat. 2002;20(4):518–29.
50. Hahn J, Hausman J. A new specification test for the validity of instrumental variables. Econometrica. 2002;70(1):163–89.
51. Hansen C, Hausman J, Newey W. Estimation with many instrumental variables. J Bus Econ Stat. 2008;26(4):398–422.
52. Davies NM, von Hinke Kessler Scholder S, Farbmacher H, Burgess S, Windmeijer F, Smith GD. The many weak instruments problem and Mendelian randomization. Stat Med. 2015;34(3):454–68.
53. Hausman JA, Newey WK, Woutersen T, Chao JC, Swanson NR. Instrumental variable estimation with heteroskedasticity and many instruments. Quant Econom. 2012;3(2):211– 55.
54. Jiang L, Oualkacha K, Didelez V, Ciampi A, Rosa‐Neto P, Benedet AL, et al. Constrained instruments and their application to Mendelian randomization with pleiotropy. Genet Epidemiol. 2019;43(4):373–401.
55. Wang S, Kang H. Weak-instrument robust tests in two-sample summary-data Mendelian randomization. Biometrics. 2021 Jul;
56. Ye T, Shao J, Kang H. Debiased inverse variance weighted estimator in two-sample summary-data mendelian randomization. Ann Stat. 2021;49(4):2079–100.
57. Bowden J, Holmes M V. Meta‐analysis and Mendelian randomization: A review. Res Synth Methods. 2019;10(4):486–96.
58. Bowden J, Del Greco M F, Minelli C, Davey Smith G, Sheehan NA, Thompson JR. Assessing the suitability of summary data for two-sample Mendelian randomization analyses using MR-Egger regression: the role of the I 2 statistic. Int J Epidemiol. 2016;45(6):1961–74.
59. Schmidt AF, Hingorani AD, Jefferis BJ, White J, Groenwold RHH, Dudbridge F. Comparison of variance estimators for meta- 149 Vol 10 No 2 (2024) A Review of Mendelian Randomization in the Presence of Weak ... Habibi D et al. analysis of instrumental variable estimates. Int J Epidemiol. 2016;45(6):1975–86. 60. Shea J. Instrument relevance in multivariate linear models: A simple measure. Rev Econ Stat. 1997;79(2):348–52.
61. Minică CC, Dolan C V, Boomsma DI, de Geus E, Neale MC. Extending causality tests with genetic instruments: an integration of Mendelian randomization with the classical twin design. Behav Genet. 2018;48(4):337–49.
62. Zou L, Guo H, Berzuini C. Overlapping-sample Mendelian randomisation with multiple exposures: a Bayesian approach. BMC Med Res Methodol. 2020;20(1):1–15.
63. Byrne BE, Rooshenas L, Lambert HS, Blazeby JM. A mixed methods case study investigating how randomised controlled trials (RCTs) are reported, understood and interpreted in practice. BMC Med Res Methodol. 2020;20:1–12.
64. Hosseini-Esfahani F, Zahedi AS, Akbarzadeh M, Seyedhamzehzadeh A, Daneshpour MS, Mirmiran P, et al. The resemblance of dietary intakes in three generations of parent-offspring pairs: Tehran lipid and glucose study. Appetite. 2021;105794.
65. Akbarzadeh M, Dehkordi SR, Roudbar MA, Sargolzaei M, Guity K, Sedaghati Khayat B, et al. GWAS findings improved genomic prediction accuracy of lipid profile traits: Tehran Cardiometabolic Genetic Study. Sci Rep. 2021;11(1):1–9.
66. Burgess S, Foley CN, Allara E, Staley JR, Howson JMM. A robust and efficient method for Mendelian randomization with hundreds of genetic variants. Nat Commun. 2020;11(1):1–11.
67. Rees JMB, Wood AM, Burgess S. Extending the MR‐Egger method for multivariable Mendelian randomization to correct for both measured and unmeasured pleiotropy. Stat Med. 2017;36(29):4705–18.
68. Akbarzadeh M, Moghimbeigi A, Morris N, Daneshpour MS, Mahjub H, Soltanian AR. A Bayesian structural equation model in general pedigree data analysis. Stat Anal Data Min ASA Data Sci J. 2019;12(5):404–11.
69. Boef AGC, Dekkers OM, Le Cessie S. Mendelian randomization studies: a review of the approaches used and the quality of reporting. Int J Epidemiol. 2015;44(2):496– 511.
70. Myers JA, Rassen JA, Gagne JJ, Huybrechts KF, Schneeweiss S, Rothman KJ, et al. Effects of adjusting for instrumental variables on bias and precision of effect estimates. Am J Epidemiol. 2011;174(11):1213–22.
71. Davies NM, Holmes M V, Smith GD. Reading Mendelian randomisation studies: a guide, glossary, and checklist for clinicians. Bmj. 2018;362.
72. Hartwig FP, Davies NM. Why internal weights should be avoided (not only) in MR-Egger regression
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How to Cite
1.
Habibi D, S Daneshpour M, Mansourian M, Akbarzadeh M. A Review of Mendelian Randomization in the Presence of Weak Instrumental Variables; Statistical Methods and Challenges. JBE. 2024;10(2):132-149.
