Skip to main content

Instrumental Variable Analysis

  • Reference work entry
  • First Online:
Health Services Evaluation

Part of the book series: Health Services Research ((HEALTHSR))

  • 1889 Accesses

Abstract

A goal of many health services research studies is to determine the causal effect of a treatment or intervention on health outcomes. Often, it is not ethically or practically possible to conduct a perfectly randomized experiment, and instead an observational study must be used. A major difficulty with observational studies is that there might be unmeasured confounding, i.e., unmeasured ways in which the treatment and control groups differ before treatment that affect the outcome. Instrumental variable analysis is a method for controlling for unmeasured confounding. Instrumental variable analysis requires the measurement of a valid instrumental variable, which is a variable that is independent of the unmeasured confounding and encourages a subject to take one treatment level versus another, while having no effect on the outcome beyond its encouragement of a certain treatment level. This chapter discusses the types of causal effects that can be estimated by instrumental variable analysis, the assumptions needed for instrumental variable analysis to provide valid estimates of causal effects and sensitivity analysis for those assumptions, methods of estimation of causal effects using instrumental variables, and sources of instrumental variables in health services research studies.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 649.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 899.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Abadie A. Bootstrap tests for distributional treatment effects in instrumental variable models. J Am Stat Assoc. 2002;97:284–92.

    Article  Google Scholar 

  • Abadie A. Semiparametric instrumental variable estimation of treatment response models. J Econ. 2003;113:231–63.

    Article  Google Scholar 

  • Aidoo M, Terlouw D, Kolczak M, McElroy P, ter Kuile F, Kariuki S, Nahlen B, Lal A, Udhayakumar V. Protective effects of the sickle cell gene against malaria morbidity and mortality. Lancet. 2002;359:1311–2.

    Article  PubMed  CAS  Google Scholar 

  • Anderson J. Multivariate logistic compounds. Biometrika. 1979;66:17–26.

    Article  Google Scholar 

  • Angrist J. Estimation of limited dependent variable models with dummy endogenous regressors. J Bus Econ Stat. 2001;19:2–28.

    Article  Google Scholar 

  • Angrist J, Imbens G. Two-stage least squares estimation of average causal effects in models with variable treatment intensity. J Am Stat Assoc. 1995;90:430–42.

    Article  Google Scholar 

  • Angrist J, Krueger A. Does compulsory school attendance affect schooling and earnings? Q J Econ. 1991;106:979–1014.

    Article  Google Scholar 

  • Angrist J, Krueger A. The effect of age at school entry on educational attainment: an application of instrumental variables with moments from two samples. J Am Stat Assoc. 1992;87:328–36.

    Article  Google Scholar 

  • Angrist J, Krueger A. Why do World War II veterans earn more than nonveterans? J Labor Econ. 1994;12:74–97.

    Article  Google Scholar 

  • Angrist J, Pischke J-S. Mostly harmless econometrics: an empiricist’s companion. Princeton/Oxford: Princeton University Press; 2009.

    Google Scholar 

  • Angrist J, Imbens G, Rubin D. Identification of causal effects using instrumental variables. J Am Stat Assoc. 1996;91:444–55.

    Article  Google Scholar 

  • Baiocchi M, Small D, Lorch S, Rosenbaum P. Building a stronger instrument in an observational study of perinatal care for premature infants. J Am Stat Assoc. 2010;105:1285–96.

    Article  CAS  Google Scholar 

  • Baiocchi M, Small D, Yang L, Polsky D, Groeneveld P. Near/far matching: a study design approach to instrumental variables. Health Serv Outcome Res Methodol. 2012;12:237–53.

    Article  Google Scholar 

  • Baker S. Analysis of survival data from a randomized trial with all-or-none compliance: estimating the cost-effectiveness of a cancer screening program. J Am Stat Assoc. 1998;93:929–34.

    Article  Google Scholar 

  • Balke A, Pearl J. Bounds on treatment effects for studies with imperfect compliance. J Am Stat Assoc. 1997;92:1171–6.

    Article  Google Scholar 

  • Basu A, Heckman J, Navarro-Lozano S, Urzua S. Use of instrumental variables in the presence of heterogeneity and self-selection: an application to treatments of breast cancer patients. Health Econ. 2007;16:1133–57.

    Article  PubMed  Google Scholar 

  • Bhattacharya J, Goldman D, McCaffrey D. Estimating probit models with self-selected treatments. Stat Med. 2006;25:389–413.

    Article  PubMed  Google Scholar 

  • Bhattacharya J, Shaikh A, Vytlacil E. Treatment effect bounds under monotonicity assumptions: an application to Swan-Ganz catheterization. Am Econ Rev. 2008;98:351–6.

    Article  Google Scholar 

  • Bound JD, Jaeger DA, Baker RM. Problems with instrumental variables estimation when the correlation between the instruments and the endogenous explanatory variables is weak. J Am Stat Assoc. 1995;90:443–50.

    Google Scholar 

  • Brookhart M, Schneeweiss S. Preference-based instrumental variable methods for the estimation of treatment effects: assessing validity and interpreting results. Int J Biostat. 2007;3:14.

    Article  Google Scholar 

  • Brookhart M, Wang P, Solomon D, Schneeweiss S. Evaluating short-term drug effects using a physician-specific prescribing preference as an instrumental variable. Epidemiology. 2006;17:268–75.

    Article  PubMed  PubMed Central  Google Scholar 

  • Brookhart M, Rassen J, Schneeweiss S. Instrumental variable methods in comparative safety and effectiveness research. Pharmacoepidemiol Drug Saf. 2010;19:537–54.

    Article  PubMed  PubMed Central  Google Scholar 

  • Brooks J, Chrischilles E, Scott S, Chen-Hardee S. Was breast conserving surgery underutilized for early stage breast cancer? Instrumental variables evidence for stage II patients from Iowa. Health Serv Res. 2004;38:1385–402.

    Article  Google Scholar 

  • Bruce M, Ten Have T, Reynolds C III, Katz I, Schulberg H, Mulsant B, Brown G, McAvay G, Pearson J, Alexopoulos G. Reducing suicidal ideation and depressive symptoms in depressed older primary care patients: a randomized trial. J Am Med Assoc. 2004;291:1081–91.

    Article  CAS  Google Scholar 

  • Cai B, Small D, Ten Have T. Two-stage instrumental variable methods for estimating the causal odds ratio: analysis of bias. Stat Med. 2011;30:1809–24.

    Article  PubMed  Google Scholar 

  • Cai B, Hennessy S, Flory JH, Sha D, Ten Have TR, Small DS. Simulation study of instrumental variable approaches with an application to a study of the antidiabetic effect of bezafibrate. Pharmacoepidemiol Drug Saf. 2012;21:114–20.

    Article  PubMed  CAS  Google Scholar 

  • Card D. Using geographic variation in college proximity to estimate the return to schooling. Toronto: University of Toronto Press; 1995. p. 201–22.

    Google Scholar 

  • Cheng J. Estimation and inference for the causal effect of receiving treatment on a multinomial outcome. Biometrics. 2009;65:96–103.

    Article  PubMed  Google Scholar 

  • Cheng J, Small D. Bounds on causal effects in three-arm trials with noncompliance. J R Stat Soc Ser B. 2006;68:815–36.

    Article  Google Scholar 

  • Cheng J, Qin J, Zhang B. Semiparametric estimation and inference for distributional and general treatment effects. J R Stat Soc Ser B Stat Methodol. 2009a;71:881–904.

    Article  Google Scholar 

  • Cheng J, Small D, Tan Z, Ten Have T. Efficient nonparametric estimation of causal effects in randomized trials with noncompliance. Biometrika. 2009b;96:19–36.

    Article  Google Scholar 

  • Clarke P, Windmeijer F. Instrumental variable estimators for binary outcomes. J Am Stat Assoc. 2012;107:1638–52.

    Article  CAS  Google Scholar 

  • Cole J, Norman H, Weatherby L, Walker A. Drug copayment and adherence in chronic heart failure: effect on costs and outcomes. Pharmacotherapy. 2006;26:1157–64.

    Article  PubMed  Google Scholar 

  • Cox D. Planning of experiments. New York: Wiley; 1958.

    Google Scholar 

  • Cuzick J, Sasieni P, Myles J, Tyler J. Estimating the effect of treatment in a proportional hazards model in the presence of non-compliance and contamination. J R Stat Soc Ser B Methodol. 2007;69:565–88.

    Article  Google Scholar 

  • Davidson R, MacKinnon J. Estimation and inference in econometrics. New York: Oxford University Press; 1993.

    Google Scholar 

  • Demissie K, Rhoads G, Ananth C, Alexander G, Kramer M, Kogan M, Joseph K. Trends in preterm birth and neonatal mortality among blacks and whites in the United States from 1989 to 1997. Am J Epidemiol. 2001;154:307–15.

    Article  PubMed  CAS  Google Scholar 

  • Didelez V, Sheehan N. Mendelian randomization as an instrumental variable approach to causal inference. Stat Methods Med Res. 2007;16:309–30.

    Article  PubMed  Google Scholar 

  • Durbin J. Errors in variables. Rev Inst Int Stat. 1954;22:23–32.

    Article  Google Scholar 

  • Fisher R. Design of experiments. Edinburgh: Oliver and Boyd; 1949.

    Google Scholar 

  • Freedman D. Statistical models: theory and practice. Cambridge: Cambridge University Press; 2009.

    Book  Google Scholar 

  • Freedman D, Sekhon J. Endogeneity in probit response models. Polit Anal. 2010;18:138–50.

    Article  Google Scholar 

  • Goedde H, Agarwal D, Fritze G, Meier-Tackmann D, Singh S, Beckmann G, Bhatia K, Chen L, Fang B, Lisker R. Distribution of ADH2 and ALDH2 genotypes in different populations. Hum Genet. 1992;88:344–6.

    Article  PubMed  CAS  Google Scholar 

  • Goyal N, Zubizarreta J, Small D, Lorch S. Length of stay and readmission among late preterm infants: an instrumental variable approach. Hosp Pediatr. In press.

    Google Scholar 

  • Heckman J, Robb R. Alternative methods for evaluating the impacts of interventions: an overview. J Econ. 1985;30:239–67.

    Article  Google Scholar 

  • Heckman J, Vytlacil E. Local instrumental variables and latent variable models for identifying and bounding treatment effects. Proc Natl Acad Sci. 1999;96:4730–4.

    Article  PubMed  CAS  PubMed Central  Google Scholar 

  • Hernán M, Robins J. Instruments for causal inference: an epidemiologist’s dream? Epidemiology. 2006;17:360.

    Article  PubMed  Google Scholar 

  • Hernán M, Robins J. Causal inference; 2013.

    Google Scholar 

  • Hirano K, Imbens G, Rubin D, Zhou X. Assessing the effect of an influenza vaccine in an encouragement design. Biostatistics. 2000;1:69–88.

    Article  PubMed  CAS  Google Scholar 

  • Ho V, Hamilton B, Roos L. Multiple approaches to assessing the effects of delays for hip fracture patients in the United States and Canada. Health Serv Res. 2000;34:1499–518.

    PubMed  PubMed Central  CAS  Google Scholar 

  • Ho D, Imai K, King G, Stuart E. Matching as nonparametric preprocessing for reducing model dependence in parametric causal inference. Polit Anal. 2007;15:199–236.

    Article  Google Scholar 

  • Hogan J, Lee J. Marginal structural quantile models for longitudinal observational studies with time-varying treatment. Stat Sin. 2004;14:927–44.

    Google Scholar 

  • Holland P. Causal inference, path analysis, and recursive structural equations models. Sociol Methodol. 1988;18:449–84.

    Article  Google Scholar 

  • Hudgens M, Halloran M. Towards causal inference with interference. J Am Stat Assoc. 2008;103:832–42.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  • Hunink M, Glasziou P, Siegel J, Weeks J, Pliskin J, Elstein A, Weinstein M. Making in health and medicine: integrating evidence and values. Cambridge: Cambridge University Press; 2001.

    Google Scholar 

  • Imbens G. Nonadditive models with endogenous regressors. New York: Cambridge University Press; 2007.

    Google Scholar 

  • Imbens G, Angrist J. Identification and estimation of local average treatment effects. Econometrica. 1994;62:467–75.

    Article  Google Scholar 

  • Imbens G, Rosenbaum P. Robust, accurate confidence intervals with weak instruments: quarter of birth and education. J R Stat Soc Ser A. 2005;168:109–26.

    Article  Google Scholar 

  • Imbens G, Rubin D. Bayesian inference for causal effects in randomized experiments with noncompliance. Ann Stat. 1997a;25:305–27.

    Article  Google Scholar 

  • Imbens G, Rubin D. Estimating outcome distributions for compliers in instrumental variables models. Rev Econ Stud. 1997b;64:555–74.

    Article  Google Scholar 

  • Inoue A, Solon G. Two-sample instrumental variables estimators. Rev Econ Stat. 2010;92:557–61.

    Article  Google Scholar 

  • Joffe M. Administrative and artificial censoring in censored regression models. Stat Med. 2001;20:2287–304.

    Article  PubMed  CAS  Google Scholar 

  • Joffe M. Principal stratification and attribution prohibition: good ideas taken too far. Int J Biostat. 2011;7(1):1–22.

    Article  Google Scholar 

  • Joffe M, Small D, Brunelli S, Ten Have T, Feldman H. Extended instrumental variables estimation for overall effects. Int J Biostat. 2008;4.

    Google Scholar 

  • Johnston S. Combining ecological and individual variables to reduce confounding by indication: case study – subarachnoid hemorrhage treatment. J Clin Epidemiol. 2000;53:1236–41.

    Article  PubMed  CAS  Google Scholar 

  • Kang H, Kreuels B, Adjei O, May J, Small D. The causal effect of malaria on stunting: a Mendelian randomization and matching approach, Working Paper.

    Google Scholar 

  • Karni E. A theory of medical decision making under uncertainty. J Risk Uncertain. 2009;39:1–16.

    Article  Google Scholar 

  • Kaushal N. Do food stamps cause obesity? Evidence from immigrant experience. J Health Econ. 2007;26:968–91.

    Article  PubMed  CAS  Google Scholar 

  • Kelejian H. Two-stage least squares and econometric systems linear in parameters but nonlinear in the endogenous variables. J Am Stat Assoc. 1971;66:373–4.

    Article  Google Scholar 

  • Kitcheman J, Adams C, Prevaiz A, Kader I, Mohandas D, Brookes G. Does an encouraging letter encourage attendance at psychiatric outpatient clinics? The Leeds PROMPTS randomized study. Psychol Med. 2008;38:717–23.

    Article  PubMed  CAS  Google Scholar 

  • Korn E, Baumrind S. Clinician preferences and the estimation of causal treatment differences. Stat Sci. 1998;13:209–35.

    Article  Google Scholar 

  • Kramer M, Rooks Y, Pearson H. Growth and development in children with sickle-cell trait. N Engl J Med. 1978;299:686–9.

    Article  PubMed  CAS  Google Scholar 

  • Lawlor D, Harbord R, Sterne J, Timpson N, Smith G. Mendelian randomization: using genes as instruments for making causal inferences in epidemiology. Stat Med. 2008;27:1133–63.

    Article  PubMed  Google Scholar 

  • Little R, Yau L. Statistical techniques for analyzing data from prevention trials: treatment of no-shows using Rubin’s causal model. Psychol Methods. 1998;3:147–59.

    Article  Google Scholar 

  • Loeys T, Goetghebeur E. A causal proportional hazards estimator for the effect of treatment actually received in a randomized trial with all-or-nothing compliance. Biometrics. 2003;59:100–5.

    Article  PubMed  CAS  Google Scholar 

  • Lorch S, Baiocchi M, Ahlberg C, Small D. The differential impact of delivery hospital on the outcomes of premature infants. Pediatrics. 2012a.

    Google Scholar 

  • Lorch S, Kroelinger C, Ahlberg C, Barfield W. Factors that mediate racial/ethnic disparities in us fetal death rates. Am J Public Health. 2012b;102:1902–10.

    Article  PubMed  PubMed Central  Google Scholar 

  • Malkin J, Broder M, Keeler E. Do longer postpartum stays reduce newborn readmissions? Analysis using instrumental variables. Health Serv Res. 2000;35:1071–91.

    PubMed  PubMed Central  CAS  Google Scholar 

  • McClellan M, McNeil B, Newhouse J. Does more intensive treatment of acute myocardial infarction in the elderly reduce mortality? Analysis using instrumental variables. JAMA. 1994;272:859.

    Article  CAS  PubMed  Google Scholar 

  • Moreira M. A conditional likelihood ratio test for structural models. Econometrica. 1990;71:463–80.

    Google Scholar 

  • Muthen B. A structural probit model with latent variables. J Am Stat Assoc. 1979;74:807–11.

    Google Scholar 

  • Newman T, Vittinghoff E, McCulloch C. Efficacy of phototherapy for newborns with hyperbilirubinemia: a cautionary example of an instrumental variable analysis. Med Decis Mak. 2012;32:83–92.

    Article  Google Scholar 

  • Neyman J. On the application of probability theory to agricultural experiments. Stat Sci. 1990;5:463–80.

    Article  Google Scholar 

  • Nie H, Cheng J, Small D. Inference for the effect of treatment on survival probability in randomized trials with noncompliance and administrative censoring. Biometrics. 2011;67:1397–405.

    Article  PubMed  Google Scholar 

  • O’Malley A, Frank R, Normand S. Estimating cost-offsets of new medications: use of new antipsychotics and mental health costs for schizophrenia. Stat Med. 2011;30:1971–88.

    Article  PubMed  PubMed Central  Google Scholar 

  • Okui R, Small D, Tan Z, Robins J. Doubly robust instrumental variables regression. Stat Sin. 2012;22:173–205.

    Article  Google Scholar 

  • Owen A. Empirical likeliood. Boca Raton: Chapman & Hall/CRC; 2002.

    Google Scholar 

  • Pearl J. Causality. Cambridge: Cambridge University Press; 2009.

    Book  Google Scholar 

  • Permutt T, Hebel J. Simultaneous-equation estimation in a clinical trial of the effect of smoking on birth weight. Biometrics. 1989;45:619–22.

    Article  PubMed  CAS  Google Scholar 

  • Phibbs C, Mark D, Luft H, Peltzman-Rennie D, Garnick D, Lichtenberg E, McPhee S. Choice of hospital for delivery: a comparison of high-risk and low-risk women. Health Serv Res. 1993;28:201.

    PubMed  PubMed Central  CAS  Google Scholar 

  • Pliskin J, Shepard D, Weinstein M. Utility functions for life years and health status. Oper Res. 1980;28:206–24.

    Article  Google Scholar 

  • Poulson R, Gadbury G, Allison D. Treatment heterogeneity and individual qualitative interaction. Am Stat. 2012;66:16–24.

    Article  PubMed  PubMed Central  Google Scholar 

  • Qin J, Zhang B. A goodness-of-fit test for logistic regression models based on case–control data. Biometrika. 1997;84:609–18.

    Article  Google Scholar 

  • Rehan N. Growth status of children with and without sickle cell trait. Clin Pediatr. 1981;20:705–9.

    Article  CAS  Google Scholar 

  • Robins J, Greenland S. A comment on Angrist, Imbens and Rubin: Identification of causal effects using instrumental variables. J Am Stat Assoc. 1996;91:456–8.

    Google Scholar 

  • Robins J, Tsiatis A. Correcting for non-compliance in randomized trials using rank preserving structural failure time models. Commun Stat Theory Methods. 1991;20:2609–31.

    Article  Google Scholar 

  • Rosenbaum P. Observational studies. New York: Springer; 2002.

    Book  Google Scholar 

  • Rosenbaum P. Design of observational studies. New York: Springer; 2009.

    Google Scholar 

  • Rosenbaum P, Rubin D. The central role of the propensity score in observational studies for causal effects. Biometrika. 1983;70:41–55.

    Article  Google Scholar 

  • Rubin D. Estimating causal effects of treatments in randomized and non-randomized studies. J Educ Psychol. 1974;66:688–701.

    Article  Google Scholar 

  • Rubin D. Formal modes of statistical inference for causal effects. J Stat Plan Inference. 1990;25:279–92.

    Article  Google Scholar 

  • Saigal S, Stoskopf B, Feeny D, Furlong W, Burrows E, Rosenbaum P, Hoult L. Differences in preferences for neonatal outcomes among health care professionals, parents, and adolescents. J Am Med Assoc. 1999;281:1991–7.

    Article  CAS  Google Scholar 

  • Sargan J. The estimation of economic relationships using instrumental variables. Econometrica. 1958;26:393–415.

    Article  Google Scholar 

  • Sexton M, Hebel J. A clinical trial of change in maternal smoking and its effect on birth weight. J Am Med Assoc. 1984;251:911–5.

    Article  CAS  Google Scholar 

  • Sham P. Statistics in human genetics. London: Arnold; 1998.

    Google Scholar 

  • Shea J. Instrument relevance in multivariate linear models: a simple measure. Rev Econ Stat. 1997;79:348–52.

    Article  Google Scholar 

  • Shetty K, Vogt W, Bhattacharya J. Hormone replacement therapy and cardiovascular health in the United States. Med Care. 2009;47:600–6.

    Article  PubMed  Google Scholar 

  • Siddique Z. Partially identified treatment effects under imperfect compliance: the case of domestic violence. IZA Discussion Paper No. 4565. 2009.

    Google Scholar 

  • Small D. Sensitivity analysis for instrumental variables regression with overidentifying restrictions. J Am Stat Assoc. 2007;102:1049–58.

    Article  CAS  Google Scholar 

  • Small D, Rosenbaum P. War and wages: the strength of instrumental variables and their sensitivity to unobserved biases. J Am Stat Assoc. 2008;103:924–33.

    Article  CAS  Google Scholar 

  • Sobel M. What do randomized studies of housing mobility demonstrate? Causal inference in the face of interference. J Am Stat Assoc. 2006;101:1398–407.

    Article  CAS  Google Scholar 

  • Sommers BD, Beard CJ, Dahl D, D’Amico AV, Kaplan IP, Richie JP, Zeckhauser RJ. Decision analysis using individual patient preferences to determine optimal treatment for localized prostate cancer. Cancer. 2007;110:2210–7.

    Article  PubMed  Google Scholar 

  • Stock J, Wright J, Yogo M. A survey of weak instruments and weak identification in generalized method of moments. J Bus Econ Stat. 2002;20:518–29.

    Article  Google Scholar 

  • Tan Z. Regression and weighting methods for causal inference using instrumental variables. J Am Stat Assoc. 2006;101:1607–18.

    Article  CAS  Google Scholar 

  • Tan Z. Marginal and nested structural models using instrumental variables. J Am Stat Assoc. 2010;105:157–69.

    Article  CAS  Google Scholar 

  • Ten Have T, Elliott M, Joffe M, Zanutto E, Datto C. Causal models for randomized physician encouragement trials in treating primary care depression. J Am Stat Assoc. 2004;99:16–25.

    Article  Google Scholar 

  • Terza J, Basu A, Rathouz P. Two-stage residual inclusion estimation: addressing endogeneity in health econometric modeling. Health Econ. 2008;27:527–43.

    Google Scholar 

  • Vansteelandt S, Bowden J, Babnezhad M, Goetghebeur E. On instrumental variables estimation of causal odds ratios. Stat Sci. 2011;26:403–22.

    Article  Google Scholar 

  • Voight B, Peloso G, Orho-Melander M, Frikke-Schmidt R, Barbalic M, Jensen M, Hindy G, Hólm H, Ding E, Johnson T, et al. Plasma HDL cholesterol and risk of myocardial infarction: a Mendelian randomisation study. Lancet. 2012;380:572–80.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  • Vytlacil E. Independence, monotonicity, and latent index models: an equivalence result. Econometrica. 2002;70:331–41.

    Article  Google Scholar 

  • Wehby G, Jugessur A, Moreno L, Murray J, Wilcox A, Lie R. Genetic instrumental variable studies of the impacts of risk behaviors: an application to maternal smoking and orofacial clefts. Health Serv Outcome Res Methodol. 2011;11:54–78.

    Article  Google Scholar 

  • White H. Asymptotic theory for econometricians. 1984.

    Google Scholar 

  • Wooldridge J. On two stage least squares estimation of the average treatment effect in a random coefficient model. Econ Lett. 1997;56:129–33.

    Article  Google Scholar 

  • Zelen M. A new design for randomized clinical trials. N Engl J Med. 1979;300:1242–5.

    Article  PubMed  CAS  Google Scholar 

Download references

Acknowledgments

Jing Cheng and Dylan Small were supported by grant RC4MH092722 from the National Institute of Mental Health. The authors thank Scott Lorch for the use of the data from the NICU study.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Michael Baiocchi .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Science+Business Media, LLC, part of Springer Nature

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Baiocchi, M., Cheng, J., Small, D.S. (2019). Instrumental Variable Analysis. In: Levy, A., Goring, S., Gatsonis, C., Sobolev, B., van Ginneken, E., Busse, R. (eds) Health Services Evaluation. Health Services Research. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-8715-3_32

Download citation

  • DOI: https://doi.org/10.1007/978-1-4939-8715-3_32

  • Published:

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4939-8714-6

  • Online ISBN: 978-1-4939-8715-3

  • eBook Packages: MedicineReference Module Medicine

Publish with us

Policies and ethics