Statistical Science

Assumptions of IV Methods for Observational Epidemiology

Vanessa Didelez, Sha Meng, and Nuala A. Sheehan

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Abstract

Instrumental variable (IV) methods are becoming increasingly popular as they seem to offer the only viable way to overcome the problem of unobserved confounding in observational studies. However, some attention has to be paid to the details, as not all such methods target the same causal parameters and some rely on more restrictive parametric assumptions than others. We therefore discuss and contrast the most common IV approaches with relevance to typical applications in observational epidemiology. Further, we illustrate and compare the asymptotic bias of these IV estimators when underlying assumptions are violated in a numerical study. One of our conclusions is that all IV methods encounter problems in the presence of effect modification by unobserved confounders. Since this can never be ruled out for sure, we recommend that practical applications of IV estimators be accompanied routinely by a sensitivity analysis.

Article information

Source
Statist. Sci. Volume 25, Number 1 (2010), 22-40.

Dates
First available in Project Euclid: 3 August 2010

Permanent link to this document
http://projecteuclid.org/euclid.ss/1280841731

Digital Object Identifier
doi:10.1214/09-STS316

Mathematical Reviews number (MathSciNet)
MR2741813

Zentralblatt MATH identifier
1328.62587

Keywords
Causal inference instrumental variables Mendelian randomization relative bias structural mean models

Citation

Didelez, Vanessa; Meng, Sha; Sheehan, Nuala A. Assumptions of IV Methods for Observational Epidemiology. Statist. Sci. 25 (2010), no. 1, 22--40. doi:10.1214/09-STS316. http://projecteuclid.org/euclid.ss/1280841731.


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References

  • [1] Angrist, J. and Imbens, G. (1995). Two-stage least squares estimation of average causal effects in models with variable treatment intensity. J. Amer. Statist. Assoc. 90 431–442.
  • [2] Angrist, J., Imbens, G. and Rubin, D. (1996). Identification of causal effects using instrumental variables. J. Amer. Statist. Assoc. 91 444–455.
  • [3] Babanezhad, M., Vansteelandt, S. and Goetghebeur, E. (2010). On the perfomance of IV-estimators for the causal odds ratio. Technical report, Univ. Ghent.
  • [4] Balke, A. A. and Pearl, J. (1994). Counterfactual probabilities: Computational methods, bounds and applications. In Proceedings of the 10th Conference on Uncertainty in Artificial Intelligence (R. Mantaras and D. Poole, eds.) 46–54. Morgan Kaufmann, San Francisco, CA.
  • [5] Bonet, B. (2001). Instrumentality tests revisited. In Proceedings of the 17th Conference on Uncertainty in Artificial Intelligence 48–55. Morgan Kaufmann, San Francisco, CA.
  • [6] Bosron, W. F. and Li, T. K. (1986). Genetic polymorphism of human liver alcohol and aldehyde dehydrogenases, and their relationship to alcohol metabolism and alcoholism. Hepatology 6 502–510.
  • [7] Bound, J., Jaeger, D. A. and Baker, R. M. (1995). Problems with instrumental variables estimation when the correlation between the instruments and the endogenous explanatory variable is weak. J. Amer. Statist. Assoc. 90 443–450.
  • [8] Brookhart, M. A. and Schneeweiss, S. (2007). Preference-based instrumental variable methods for the estimation of treatment effects: Assessing validity and interpreting results. Int. J. Biostat. 3 Article 14.
  • [9] Cardon, L. R. and Palmer, L. J. (2003). Population stratification and spurious allelic association. Lancet 361 598–604.
  • [10] Casas, J., Bautista, L., Smeeth, L., Sharma, P. and Hingorani, A. (2005). Homocysteine and stroke: Evidence on a causal link from Mendelian randomisation. Lancet 365 224–232.
  • [11] Casas, J., Shah, T., Cooper, J., Hawe, E., McMahon, A. D., Gaffney, D., Packard, C. J., O’Reilly, D. S., Juhan-Vague, I., Yudkin, J. D., Tremoli, E., Margaglione, M., Di Minno, D., Hamsten, A., Kooistra, T., Stephens, J. W., Hurel, S. J., Livingstpne, S., Colhoun, H. M., Miller, G. J., Bautista, L., Meade, T., Sattar, N., Humphries, S. E. and Hingorani, A. (2006). Insight into the nature of the CRP-coronary event association using Mendelian randomisation. International Journal of Epidemiology 35 922–931.
  • [12] Chen, L., Davey Smith, G., Harbord, R. and Lewis, S. (2008). Genotype influencing alcohol consumption is positively associated with blood pressure and the risk of hypertension: A systematic review implementing a Mendelian randomization approach. PLoS Medicine 5 e52.
  • [13] Clarke, P. and Windmeijer, F. (2009). Instrumental variable estimators for binary outcomes. Working Paper 09/209, Centre for Market and Public Organisation, Univ. Bristol.
  • [14] Cowell, R. G., Dawid, A. P., Lauritzen, S. L. and Spiegelhalter, D. J. (1999). Probabilistic Networks and Expert Systems. Springer, New York.
  • [15] Davey Smith, G. (2007). Capitalizing on Mendelian randomization to assess the effects of treatments. Journal of the Royal Society of Medicine 100 432–435.
  • [16] Davey Smith, G. and Ebrahim, S. (2003). Mendelian randomization: Can genetic epidemiology contribute to understanding environmental determinants of disease? International Journal of Epidemiology 32 1–22.
  • [17] Davey Smith, G., Harbord, R., Milton, J., Ebrahim, S. and Sterne, J. (2005). Does elevated plasma fibrinogen increase the risk of coronary heart disease? Arteriosclerosis, Thrombosis and Vascular Biology 25 2228–2233.
  • [18] Davey Smith, G., Lawlor, D., Harbord, R., Rumley, A., Lowe, G., Day, I. and Ebrahim, S. (2005). Association of C-reactive protein with blood pressure and hypertension. Life course confounding and Mendelian randomisation tests of causality. Arteriosclerosis, Thrombosis and Vascular Biology 25 1051–1056.
  • [19] Davey Smith, G., Lawlor, D., Harbord, R., Timpson, N., Day, I. and Ebrahim, S. (2007). Clustered environments and randomized genes: A fundamental distinction between conventional and genetic epidemiology. PLoS Medicine 4 e352.
  • [20] Dawid, A. P. (2000). Causal inference without counterfactuals. J. Amer. Statist. Assoc. 95 407–448.
  • [21] Dawid, A. P. (2002). Influence diagrams for causal modelling and inference. International Statistical Review 70 161–189.
  • [22] Dawid, A. P. (2003). Causal inference using influence diagrams: The problem of partial compliance. In Highly Structured Stochastic Systems (P. J. Green, N. L. Hjort and S. Richardson, eds.) 45–81. Oxford Univ. Press, Oxford, UK.
  • [23] Didelez, V. and Sheehan, N. A. (2007). Mendelian randomisation as an instrumental variable approach to causal inference. Stat. Methods Med. Res. 16 309–330.
  • [24] Didelez, V. and Sheehan, N. A. (2007). Mendelian randomisation: Why epidemiology needs a formal language for causality. In Causality and Probability in the Sciences (F. Russo and J. Williamson, eds.). Texts in Philosophy 5 263–292. London College Publications.
  • [25] Elwood, M. (2007). Critical Appraisal of Epidemiological Studies and Clinical Trials, 3rd ed. Oxford Univ. Press, Oxford.
  • [26] Enomoto, N., Takase, S., Yasuhara, M. and Takada, A. (1991). Acetaldehyde metabolism in different aldehyde dehydrogenase-2 genotypes. Alcohol Clin. Exp. Res. 15 141–144.
  • [27] Fischer, K. and Goetghebeur, E. (2004). Structural mean effects of noncompliance: Estimating interaction with baseline prognosis and selection effects. J. Amer. Statist. Assoc. 99 918–928.
  • [28] Geneletti, S. and Dawid, A. P. (2010). The effect of treatment on the treated: A decision theoretic perspective. In Casuality in the Sciences (M. Illari, F. Russo and J. Williamson, eds.). Oxford Univ. Press, Oxford, UK. To appear.
  • [29] Greenland, S. (2000). An introduction to instrumental variables for epidemiologists. International Journal of Epidemiology 29 722–729.
  • [30] Greenland, S., Pearl, J. and Robins, J. M. (1999). Causal diagrams for epidemiologic research. Epidemiology 10 37–48.
  • [31] Hernán, M. (2004). A definition of causal effect for epidemiologic research. Journal of Epidemiology and Community Health 58 265–271.
  • [32] Hernán, M. and Robins, J. (2006). Instruments for causal inference. An epidemiologist’s dream? Epidemiology 17 360–372.
  • [33] Imbens, G. W. and Angrist, J. (1994). Identification and estimation of local average treatment effects. Econometrica 62 467–475.
  • [34] Katan, M. B. (1986). Apolipoprotein E isoforms, serum cholesterol, and cancer. Lancet I 507–508.
  • [35] Keavney, B. D., Danesh, J., Parish, S., Palmer, A., Clark, S., Youngman, L., Delépine, M., Lathrop, M., Peto, R. and Collins, R. (2006). Fibrinogen and coronoary heart disease: Test of causality by ‘Mendelian randomization.’ International Journal of Epidemiology 35 935–943.
  • [36] Kivimaki, M., Lawlor, D. A., Eklund, C., Smith, G. D., Hurme, M., Lehtimaki, T., Viikari, J. S. and Raitakari, O. T. (2007). Mendenlian randomization suggests no causal association between C-reactive protein and carotid intima-media thickness in the young Finns study. Arteriosclerosis, Thrombosis and Vascular Biology 27 978–979.
  • [37] Lauritzen, S. L. (2000). Causal inference from graphical models. In Complex Stochastic Systems (O. E. Barndorff-Nielsen, D. R. Cox and C. Kluppelberg, eds.) 63–107. Chapman & Hall, Boca Raton, FL.
  • [38] Lawlor, D. A. and Davey Smith, G. (2006). Cardiovascular risk and hormone replacement therapy. Current Opinion in Obstetrics and Gynaecology 18 658–665.
  • [39] Lawlor, D. A., Harbord, R. M., Sterne, J. A. C., Timpson, N. and Davey Smith, G. (2008). Mendelian randomization: Using genes as instruments for making causal inferences in epidemiology. Stat. Med. 27 1133–1163.
  • [40] Lawlor, D. A., Timpson, N. J., Harbord, R. M., Leary, S., Ness, A., McCarthy, M. I., Frayling, T. M., Hattersley, A. T. and Davey Smith, G. (2008). Exploring the developmental overnutrition hypothesis using parent-offspring associations and FTO as an instrumental variable. PLoS Medicine 5 e33.
  • [41] Leigh, P. and Schembri, M. (2004). Instrumental variables technique: Cigarette price provided better estimate of effects of smoking on sf-12. Journal of Clinical Epidemiology 57 284–293.
  • [42] Lewis, S. J. and Davey Smith, G. (2005). Alcohol, ALDH2, and esophageal cancer: A meta-analysis which illustrates the potentials and limitations of a Mendenlian randomization approach. Cancer Epidemiology Biomarkers and Prevention 14 2228–2233.
  • [43] Lewis, S. J., Harbord, R. M. and Smith, R. H. G. D. (2006). Meta-analyses of observational and genetic association studies of folate intakes or levels and breast cancer risk. J. Natl. Cancer Inst. 98 1607–1622.
  • [44] Manski, C. F. (1990). Nonparametric bounds on treatment effects. American Economic Review, Papers and Proceedings 80 319–323.
  • [45] Martens, E. P., Pestman, W. R., de Boer, A., Belitser, S. V. and Klungel, O. H. (2006). Instrumental variables: Application and limitations. Epidemiology 17 260–267.
  • [46] Minelli, C., Thompson, J., Tobin, M. and Abrams, K. (2004). An integrated approach to the Meta-Analysis of genetic association studies using Mendelian randomization. American Journal of Epidemiology 160 445–452.
  • [47] Mullahy, J. (1997). Instrumental variable estimation of count data models: Application to models of cigarette smoking behaviour. Review of Economics and Statistics 79 586–593.
  • [48] Nitsch, D., Molokhia, M., Smeeth, L., DeStavola, B. L., Whittaker, J. C. and Leon, D. A. (2006). Limits to causal inference based on Mendelian randomization: A comparison with randomised controlled trials. American Journal of Epidemiology 163 397–403.
  • [49] Pearl, J. (1995). Causal diagrams for empirical research. Biometrika 82 669–710.
  • [50] Pearl, J. (1995). Causal inference from indirect experiments. Artifical Intelligence in Medicine 7 561–582.
  • [51] Pearl, J. (2000). Causality. Cambridge Univ. Press, Cambridge.
  • [52] Ramsahai, R. R. (2007). Causal bounds and instruments. In Proceedings of the 23rd Conference on Uncertainty in Artificial Inteligence 310–317. AUAI Press, Corvallis, OR.
  • [53] Ramsahai, R. R. (2009). Causal inference with instruments and other supplementary variables. Ph.D. thesis, Univ. Oxford, UK.
  • [54] Rassen, J. A., Brookhart, M. A., Glynn, R. J., Mittleman, M. A. and Schneeweiss (2009). Instrumental variables I: Instrumental variables exploit natural variation in nonexperimental data to estimate causal relationships. Journal of Clinical Epidemiology 62 1226–1232.
  • [55] Rassen, J. A., Brookhart, M. A., Glynn, R. J., Mittleman, M. A. and Schneeweiss (2009). Instrumental variables II: Instrumental variable application—In 25 variations, the physician prescribing preference generally was strong and reduced covariate imbalance. Journal of Clinical Epidemiology 62 1233–1241.
  • [56] Rassen, J. A., Schneeweiss, S., Glynn, R. J., Mittleman, M. A. and Brookhart, A. A. (2009). Instrumental variable analysis for estimation of treatment effects with dichotomous outcomes. American Journal of Epidemiology 169 273–284.
  • [57] Robins, J. (1989). The analysis of randomized and nonrandomized AIDS treatment trials using a new approach to causal inference in longitudinal studies. In Health Service Research Methodology. A Focus on AIDS (L. Sechrest, H. Freeman and A. Mulley, eds.) 113–159. U.S. Public Health Service, Washington, DC.
  • [58] Robins, J. (1994). Correcting for non-compliance in randomized trials using structural nested mean models. Comm. Statist. Theory Methods 23 2379–2412.
  • [59] Robins, J. and Rotnitzky, A. (2004). Estimation of treatment effects in randomised trials with non-compliance and dichotomous outcomes using structural mean models. Biometrika 91 763–783.
  • [60] Robins, J. M. and Greenland, S. (2000). Comment on “Causal inference without counterfactuals” by A. P. Dawid. J. Amer. Statist. Assoc. 95 431–435.
  • [61] Robins, J. M., VanderWeele, T. J. and Richardson, T. S. (2006). Comment on: Causal effects in the presence of non compliance: A latent variable interpretation. Metron 64 288–298.
  • [62] Rubin, D. (1974). Estimating causal effects of treatments in randomized and nonrandomized studies. Journal of Educational Psychology 66 688–701.
  • [63] Rubin, D. (1978). Bayesian inference for causal effects: The role of randomization. Ann. Statist. 6 34–58.
  • [64] Sheehan, N. A., Didelez, V., Burton, P. R. and Tobin, M. D. (2008). Mendelian randomisation and causal inference in observational epidemiology. PLoS Medicine 5 1205–1210.
  • [65] Thomas, D. and Conti, D. (2004). Commentary: The concept of “Mendelian randomization.” International Journal of Epidemiology 33 21–25.
  • [66] Thompson, J. R., Minelli, C., Abrams, K. R., Tobin, M. D. and Riley, R. D. (2005). Meta-analysis of genetic studies using Mendelian randomization—A multivariate approach. Stat. Med. 24 2241–2254.
  • [67] Vansteelandt, S. and Goetghebeur, E. (2003). Causal inference with generalized structural mean models. J. R. Stat. Soc. Ser. B Stat. Methodol. 65 817–835.
  • [68] Vansteelandt, S., Babanezhad, M. and Goetghebeur, E. (2007). Correcting instrumental variables estimators for systematic measurement error. Statist. Sinica 19 1223–1246.
  • [69] Wald, A. (1940). The fitting of straight lines if both variables are subject to error. Ann. Math. Statist. 11 284–300.
  • [70] Windmeijer, F. and Silva, J. M. C. S. (1997). Endogeneity in count data models: An application to demand for health care. J. Appl. Econometrics 12 281–294.
  • [71] Wooldridge, J. M. (2002). Econometric Analysis of Cross Section and Panel Data. MIT Press, Cambridge.
  • [72] Writing Committee for the Women’s Health Iinitiative Randomized Controlled Trial (2002). Risks and benefits of estrogen plus progestin in healthy postmenopausal women: Principal results from the Women’s Health Initiative randomized controlled trial. Journal of the American Medical Association 288 321–333.
  • [73] Yoshida, A., Huang, I. Y. and Ikawa, M. (1984). Molecular abnormality of an inactive aldehyde dehydrogenase variant commonly found in orientals. Proc. Natl. Acad. Sci. USA 81 258–261.
  • [74] Zohoori, N. and Savitz, D. A. (1997). Econometric approaches to epidemiological data: Relating endogeneity and unobserved heterogeneity to confounding. Annals of Epidemiology 7 251–257.