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Instrumental Variables: Application and Limitations
Abstract
To correct for confounding, the method of instrumental variables (IV) has been proposed. Its use in medical literature is still rather limited because of unfamiliarity or inapplicability. By introducing the method in a nontechnical way, we show that IV in a linear model is quite easy to understand and easy to apply once an appropriate instrumental variable has been identified. We also point out some limitations of the IV estimator when the instrumental variable is only weakly correlated with the exposure. The IV estimator will be imprecise (large standard error), biased when sample size is small, and biased in large samples when one of the assumptions is only slightly violated. For these reasons, it is advised to use an IV that is strongly correlated with exposure. However, we further show that under the assumptions required for the validity of the method, this correlation between IV and exposure is limited. Its maximum is low when confounding is strong, such as in case of confounding by indication. Finally, we show that in a study in which strong confounding is to be expected and an IV has been used that is moderately or strongly related to exposure, it is likely that the assumptions of IV are violated, resulting in a biased effect estimate. We conclude that instrumental variables can be useful in case of moderate confounding but are less useful when strong confounding exists, because strong instruments cannot be found and assumptions will be easily violated.
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“IV analyses are an alternative estimation method that can be used to derive an estimate of the causal effect of the treatment (here, CRP) on the outcome (SBP) by accounting for the size of the association between randomization and CRP.3,4,12–15”
From Mendelian randomization (2022) · cites this paper as [13]
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BackgroundDecreased survival in cystic fibrosis patients with a positive screen for depression
Schechter, M. S., Ostrenga, J. S., Fink, A. K., Barker, D. H., Sawicki, G. S., & Quittner, A. L. (2021) · Journal of Cystic Fibrosis · doi:10.1016/j.jcf.2020.07.020 · Cited by 71
Estimating the Effects of Wages on Obesity
Kim, D., & Leigh, J. P. (2010) · Journal of Occupational and Environmental Medicine · doi:10.1097/jom.0b013e3181dbc867 · Cited by 69
Developmental Science in 2025: A Predictive Review
Lerner, R. M., Agans, J. P., DeSouza, L. M., & Hershberg, R. M. (2014) · Research in Human Development · doi:10.1080/15427609.2014.967046 · Cited by 76
Ramkumar, N., Martínez‐Camblor, P., Columbo, J. A., Osborne, N. H., Goodney, P. P., & O’Malley, A. J. (2019) · Journal of the American Heart Association · doi:10.1161/jaha.119.012081 · Cited by 68
“This was supported by statistical confirmation using the F statistic adjusted for measured confounders, for which a value >10 indicates a strong instrument.(34,35) The other IV assumptions cannot be verified from the data; therefore, we relied on our expert’s subject matter knowledge to assess the potential for an ass…”
Statistical Causality from a Decision-Theoretic Perspective
Dawid, A. P. (2014) · Annual Review of Statistics and Its Application · doi:10.1146/annurev-statistics-010814-020105 · Cited by 63
Estimating treatment effects in randomised controlled trials with non-compliance: a simulation study
Ye, C., Beyene, J., BROWNE, G. B., & Thabane, L. (2014) · BMJ Open · doi:10.1136/bmjopen-2014-005362 · Cited by 68
Pierce, B. L., & VanderWeele, T. J. (2012) · International Journal of Epidemiology · doi:10.1093/ije/dys141 · Cited by 65
Boef, A. G. C., Dekkers, O. M., Vandenbroucke, J. P., & le Cessie, S. (2014) · Journal of Clinical Epidemiology · doi:10.1016/j.jclinepi.2014.05.019 · Cited by 66
Kutcher, S., Brophy, J. M., Banack, H. R., Kaufman, J. S., & Samuel, M. (2021) · Canadian Journal of Cardiology · doi:10.1016/j.cjca.2021.05.012 · Cited by 71
African-American/white differences in the age of menarche: Accounting for the difference
Reagan, P. B., Salsberry, P. J., Fang, M. Z., Gardner, W. P., & PAJER, K. A. (2012) · Social Science & Medicine · doi:10.1016/j.socscimed.2012.05.018 · Cited by 69
Instrumental Variable Analyses and Selection Bias
Canan, C. E., Lesko, C. R., & Lau, B. M. (2017) · Epidemiology · doi:10.1097/ede.0000000000000639 · Cited by 65
Martínez‐Camblor, P., Mackenzie, T., Staiger, D. O., Goodney, P. P., & O’Malley, A. J. (2017) · Biostatistics · doi:10.1093/biostatistics/kxx062 · Cited by 63
“IV procedures have subsequently been used to estimate causal effects from observational studies (Martens et al., 2006) in statistics, biomedicine, and many other applied research fields.”
MethodPotentially Preventable Hospitalizations in Medicare Patients With Diabetes
Kuo, Y., Chen, N.-W., Baillargeon, J., Raji, M. A., & Goodwin, J. S. (2015) · Medical Care · doi:10.1097/mlr.0000000000000406 · Cited by 62
Tiro, J., Kamineni, A., Levin, T., Zheng, Y.-Y., Schottinger, J., Rutter, C., Corley, D., Skinner, C., Chubak, J., Doubeni, C. A., et al. (2014) · Cancer Epidemiology, Biomarkers and Prevention · doi:10.1158/1055-9965.epi-13-1217 · Cited by 63
“For example, instrumental variable analysis (47, 48) or propensity score adjustment (49, 50) are approaches used to minimize selection bias (51, 52).”
MethodLiquid Nitrogen or Phenolization for Giant Cell Tumor of Bone?
van der Heijden, L., van der Geest, I. C. M., Schreuder, H. W. B., van de Sande, M. A. J., & Dijkstra, P. D. S. (2014) · Journal of Bone and Joint Surgery · doi:10.2106/jbjs.m.00516 · Cited by 61
“In observational studies, analysis of instrumental variables can estimate the therapeutic effects of various standard treatments and deal with controlled and uncontrolled confounding [44-46].”
Systemic inflammation, genetic susceptibility and lung function
Sunyer, J., Pistelli, R., Plana, E., Andreani, M., Baldari, F., Kolz, M., Köenig, W., Pekkanen, J., Peters, A., & Forastiere, F. (2008) · European Respiratory Journal · doi:10.1183/09031936.00052507 · Cited by 59
Kern, D., Auchincloss, A., Stehr, M., Diez Roux, A., Moore, L., Kanter, G., & Robinson, L. (2017) · International Journal of Environmental Research and Public Health · doi:10.3390/ijerph14111394 · Cited by 58
“The IV analysis adds some face validity to the standard regression results; however, as with all models, IV methods have assumptions [66], some of which are not verifiable—notably the third assumption prohibiting any association between the IV and unmeasured cofounders [65].”
Quantitative assessment of unobserved confounding is mandatory in nonrandomized intervention studies
Groenwold, R. H. H., Hak, E., & Hoes, A. W. (2008) · Journal of Clinical Epidemiology · doi:10.1016/j.jclinepi.2008.02.011 · Cited by 58
Holz, F. G., Tadayoni, R., Beatty, S., Berger, A. R., Cereda, M. G., Hykin, P. G., Staurenghi, G., Wittrup-Jensen, K. U., Nilsson, J., Kim, K., et al. (2016) · Eye · doi:10.1038/eye.2016.90 · Cited by 56
Furosemide Exposure and Prevention of Bronchopulmonary Dysplasia in Premature Infants
Greenberg, R. G., Gayam, S., Savage, D., Tong, A., Gorham, D., Sholomon, A., Clark, R. H., Benjamin, D. K., Laughon, M. M., & Smith, P. B. (2018) · The Journal of Pediatrics · doi:10.1016/j.jpeds.2018.11.043 · Cited by 56
“001 White 48 48 Black 31 29 Hispanic 21 23 Percentage risk of BPD/death on postnatal day 7, median (25th-75th percentile) 63 (38-79) 35 (17-64) <.”
Metadata
- Authors
- Martens, E. P., Pestman, W. R., de Boer, A., Belitser, S. V., & Klungel, O. H.
- Affiliations
- Utrecht University (NL)
- Corresponding author
- Martens, Edwin P.
- Belitser, Svetlana V.
- Klungel, Olaf H.
- Venue
- Epidemiology
- Published
- 2006-05
- Volume
- 17
- Issue
- 3
- Pages
- 260-267
- ISSN
- 1044-3983 (ISSN-L)
- OpenAlex
- W2127065386
- Cited by
- 464
- References
- 37
- Citations by year
- 2026: 19 · 2025: 35 · 2024: 31 · 2023: 29 · 2022: 35 · 2021: 29 · 2020: 26 · 2019: 26 · 2018: 21 · 2017: 22 · 2016: 18 · 2015: 28 · 2014: 24 · 2013: 22 · 2012: 27
- FWCI
- 10.31
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Epidemiology (publishedVersion)
- PubMed (publishedVersion)
- Utrecht University Repository (Utrecht University) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Meta-analysis and systematic reviews
- Keywords
- instrumental variables, confounding, confounding by indication, weak instruments, linear regression, exposure measurement error
- MeSH terms
- United States, Models, Statistical, Bias, Confounding Factors, Epidemiologic, Epidemiologic Studies
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