Severity of bias of a simple estimator of the causal odds ratio in Mendelian randomization studies

Statistics in Medicine

Volumn 32, Issue 7, 2013, Pages 1246-1258

  Harbord, Roger M ^a   Didelez, Vanessa ^a   Palmer, Tom M ^a   Meng, Sha ^b   Sterne, Jonathan A C ^a   Sheehan, Nuala A ^b  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

^b UNIVERSITY OF LEICESTER   (United Kingdom)

Author keywords

Binary outcomes; Causal inference; Instrumental variables; Mendelian randomization; Odds ratios

Indexed keywords

ARTICLE; MENDELIAN RANDOMIZATION ANALYSIS; NORMAL DISTRIBUTION; QUANTITATIVE ANALYSIS; RISK; SAMPLING ERROR; SIMULATION; STATISTICAL MODEL;

BIAS (EPIDEMIOLOGY); BIOSTATISTICS; CAUSALITY; HUMANS; MENDELIAN RANDOMIZATION ANALYSIS; META-ANALYSIS AS TOPIC; MODELS, STATISTICAL; ODDS RATIO;

EID: 84874962114     PISSN: 02776715     EISSN: 10970258     Source Type: Journal    
DOI: 10.1002/sim.5659     Document Type: Article

References (59)

1. Thomas DC, Conti DV. Commentary: the concept of 'Mendelian Randomization'. International Journal of Epidemiology 2004; 33:21-25.
2. Didelez V, Sheehan NA. Mendelian randomisation as an instrumental variable approach to causal inference. Statistical Methods in Medical Research 2007; 16:309-330.
3. Lawlor DA, Harbord RM, Sterne JAC, Timpson N, Davey Smith G. Mendelian randomization: using genes as instruments for making causal inferences in epidemiology. Statistics in Medicine 2008; 27:1133-1163.
4. Davey Smith G, Harbord R, Milton J, Ebrahim S, Sterne JAC. Does elevated plasma fibrinogen increase the risk of coronary heart disease? Evidence from a meta-analysis of genetic association studies. Arteriosclerosis, Thrombosis, and Vascular Biology 2005; 25:2228-2233.
5. Lawlor DA, Harbord RM, Timpson NJ, Lowe GDO, Rumley A, Gaunt TR, Baker I, Yarnell JWG, Kivim kM, Kumari M, Norman PE, Jamrozik K, Hankey GJ, Almeida OP, Flicker L, Warrington N, Marmot MG, Ben-Shlomo Y, Palmer LJ, Day INM, Ebrahim S, Davey Smith G. The Association of C-reactive protein and CRP genotype with coronary heart disease: findings from five studies with 4, 610 cases amongst 18, 637 participants. PLoS ONE 2008; 3:e3011. DOI: 10.1371/journal.pone.0003011.
6. Timpson NJ, Harbord R, Davey Smith G, Zacho J, Tybjaerg-Hansen A, Nordestgaard BG. Does greater adiposity increase blood pressure and hypertension risk? Mendelian randomization using the FTO/MC4R genotype. Hypertension 2009; 54:84-90.
7. Casas JP, Bautista LE, Smeeth L, Sharma P, Hingorani AD. Homocysteine and stroke: evidence on a causal link from mendelian randomisation. Lancet 2005; 365:224-232.
8. Davey Smith G, Ebrahim S. 'Mendelian randomization': can genetic epidemiology contribute to understanding environmental determinants of disease? International Journal of Epidemiology 2003; 32:22.
9. Davey Smith G, Lawlor DA, Harbord R, Timpson N, Rumley A, Lowe GDO, Day INM, Ebrahim S. Association of C-reactive protein with blood pressure and hypertension-life course confounding and Mendelian randomization tests of causality. Arteriosclerosis, Thrombosis, and Vascular Biology 2005; 25:1051-1056.
10. Wald DS, Law M, Morris JK. Homocysteine and cardiovascular disease: evidence on causality from a meta-analysis. British Medical Journal 2002. DOI: 10.1136/bmj.325.7374-1202.
11. Youngman LD, Keavney BD, Palmer A, Parish S, Clark S, Danesh J, Delepine M, Lathrop M, Peto R, Collins R. Plasma fibrinogen and fibrinogen genotypes in 4685 cases of myocardial infarction and in 6002 controls: test of causality by 'Mendelian randomisation'. Circulation 2000; 102:II-31-II-32.
12. Bound J, Jaeger DA, Baker RM. Problems with instrumental variables estimation when the correlation between the instruments and the endogeneous explanatory variable is weak. Journal of the American Statistical Association 1995; 90:443-450.
13. Durbin J. Errors in variables. Review of the International Statistical Institute 1954; 22:23-32.
14. Wald A. The fitting of straight lines if both variables are subject to error. The Annals of Mathematical Statistics 1940; 11:284-300.
15. Didelez V, Meng S, Sheehan NA. Assumptions of IV methods for observational epidemiology. Statistical Science 2010; 25:22-40.
16. Mullahy J. Instrumental-variable estimation of count data models: applications to models of cigarette smoking behavior. The Review of Economics and Statistics 1997; 79:586-593.
17. Thompson JR, Tobin MD, Minelli C. On the accuracy of estimates of the effect of phenotype on disease derived from Mendelian randomisation studies. Technical Report 2003/GE1, Centre for Biostatistics, Department of Health Sciences, University of Leicester.
18. Davey Smith G, Ebrahim S. Mendelian randomization: prospects, potentials, and limitations. Internation Journal of Epidemiology 2004; 33:30-42.
19. Sheehan NA, Didelez V, Burton PR, Tobin MD. Mendelian randomisation and causal inference in observational epidemiology. PLoS Medicine 2008. DOI: 10.1371/journal.pmed.0050177.
20. Hernan MA. A definition of causal effect for epidemiological research. Journal of Epidemiology and Community Health 2004; 58:265-271.
21. Hernán MA, Robins J. Instruments for causal inference: an epidemiologist's dream? Epidemiology 2006; 17:360-372.
22. Hernán MA, Robins JM. Estimating causal effects from epidemiological data. Journal of Epidemiology and Community Health 2006; 60:578-586.
23. Robins JM, Hern n MA, Brumback B. Marginal structural models and causal inference in epidemiology. Epidemiology 2000; 11:550-560.
24. Greenland S, Robins JM, Pearl J. Confounding and collapsibility in causal inference. Statistical Science 1999; 14:29-46.
25. Robinson LD, Jewell NP. Some surprising results about covariate adjustment in logistic regression models. International Statistical Review 1991; 59:227-240.
26. Didelez V, Kreiner S, Keiding N. Graphical models for inference under outcome dependent sampling. Statistical Science 2010; 25:368-387.
27. Abadie A. Semiparametric instrumental variable estimation of treatment response models. Journal of Econometrics 2003; 113:231-263.
28. Angrist JD. Estimation of limited dependent variable models with dummy endogenous regressors: simple strategies for empirical practice. Journal of Business & Economic Statistics 2001; 19:2-28.
29. Hardin J, Schmiediche H, Carroll RJ. Instrumental variables, bootstrapping, and generalized linear models. The Stata Journal 2003; 3:351-360.
30. Ding EL, Song Y, Manson JE, Hunter DJ, Lee CC, Rifai N, Buring JE, Gaziano JM, Liu S. Sex hormone-binding globulin and risk of type 2 diabetes in women and men. New England Journal of Medicine 2009; 361:1152-1163.
31. Qi L, Rifai N, Hu FB. Interleukin-6 receptor gene variations, plasma interleukin-6 levels, and type 2 diabetes in US women. Diabetes 2007; 56:3075-3081.
32. Bonet B. A calculus for causal relevance. In Proceedings of the Seventeenth Conference on Uncertainty and Artificial Intelligence. Morgan Kaufmann: San Francisco, 2001; 40-47.
33. Pearl J. On the testability of causal models with latent and instrumental variables. In Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence. Morgan Kaufmann: San Francisco, 1995; 435-443.
34. Palmer TM, Thompson JR, Tobin MD, Sheehan NA, Burton PR. Adjusting for bias and unmeasured confounding in Mendelian randomization studies with binary responses. Internation Journal of Epidemiology 2008; 37:1161-1168.
35. Wooldridge JM. Econometric Analysis of Cross Section and Panel Data. MIT: Cambridge, Massachusetts, 2002.
36. McDonald RP, Ho MHR. Principles and practice in reporting structural equation analyses. Psychological Methods 2002; 7:64-82.
37. Pearl J. Causal inference in statistics: an overview. Statistics Surveys 2009; 3:96-146.
38. Pearl J. An introduction to causal inference. International Journal of Biostatistics 2010. DOI: 10.2202/1557-4679.1203.
39. Maple. Maplesoft, 2007. Waterloo, Ontario, Canada.
40. Butrum R, Cannon G, Heggie S, Kroke A, Miles L, Norman H, El S N, James C, Stone E, Thompson R, Wiseman M. Systematic literature review specification manual version 15, World Cancer Research Fund/American Institute for Cancer Research, 2005. http:/www/dietandcancerreport.org/cancer_resource_center/downloads/SLR_Manual.pdf.
41. Danesh J, Collins R, Appleby P, Peto R. Association of fibrinogen, C-reactive protein, albumin, or leukocyte count with coronary heart disease: meta-analyses of prospective studies. Journal of the American Medical Association 1998; 279:1477-1482.
42. Rothman KJ, Greenland S, Lash TL. Modern Epidemiology. Lippincott Williams & Wilkins: Philadelphia, 2008.
43. Angrist JD. A note on bias in just identified IV with weak instruments, 2009.
44. IVPOIS. Stata module to Estimate an Instrumental Variables Poisson Regression via GMM. Boston College Department of Economics: Boston, MA, 2007.
45. Palmer TM, Sterne JAC, Harbord RM, Lawlor DA, Sheehan NA, Meng S, Granell R, Smith GD, Didelez V. Instrumental variable estimation of causal risk ratios and causal odds ratios in Mendelian randomization analyses. American Journal of Epidemiology 2011; 173:1392-1403.
46. Windmeijer FAG. GMM for panel count data models. Discussion Paper No.06/591, Department of Economics, University of Bristol, Bristol, UK, 2006.
47. Vansteelandt S, Goetghebeur E. Causal inference with generalized structural mean models. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 2003; 65:817-835.
48. McKeigue PM, Campbell H, Wild S, Vitart V, Hayward C, Rudan I, Wright AF, Wilson JF. Bayesian methods for instrumental variable analysis with genetic instruments ('Mendelian randomization'): example with urate transporter SLC2A9 as an instrumental variable for effect of urate levels on metabolic syndrome. International Journal of Epidemiology 2010; 39:907-918.
49. Burgess S, Thompson SG. Improving bias and coverage in instrumental variable analysis with weak instruments for continuous and binary outcomes. Statistics in Medicine 2012; 31:1582-1600.
50. Goetghebeur E. Commentary: to cause or not to cause confusion vs transparency with Mendelian Randomization. International Journal of Epidemiology 2010; 39:918-920.
51. Jones EM, Thompson JR, Didelez V, Sheehan NA. On the choice of parameterisation and priors for the Bayesian analyses of Mendelian randomisation studies. Statistics in Medicine 2012; 21:231-239.
52. Burgess S, Thompson SG. Bayesian methods for meta-analysis of causal relationships estimated using genetic instrumental variables. Statistics in Medicine 2010; 29:1298-1311.
53. Palmer TM, Thompson JR, Tobin MD. Meta-analysis of Mendelian randomization studies incorporating all three genotypes. Statistics in Medicine 2008; 27:6570-6582.
54. Thompson JR, Minelli C, Abrams KR, Tobin MD, Riley RD. Meta-analysis of genetic studies using Mendelian randomization-a multivariate approach. Statistics in Medicine 2005; 24:2241-2254.
55. Angrist JD, Imbens GW, Rubin DB. Identification of causal effects using instrumental variables (with discussion). Journal of the American Statistical Association 1996; 91:444-472.
56. Vansteelandt S, Bowden J, Babanezhad M, Goetghebeur E. On instrumental variable estimation of causal odds ratios. Statistical Science 2001; 26:403-422.
57. Zeger SL, Liang KY, Albert PS. Models for longitudinal data: a generalized estimating equation approach. Biometrics 1988; 44:1049-1060.
58. Johnson NL, Kotz S. Distributions in Statistics, Continuous Univariate Distributions. Houghton-Mifflin: Boston, 1970.
59. McCullagh P, Nelder JA. Generalized Linear Models. Chapman & Hall: Cambridge UK, 1989.