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Cited by 538Advanced Causal Inference TechniquesStatistical Methods and Bayesian InferenceStatistical Methods in Clinical Trials

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Bayesian inference for causal effects in randomized experiments with noncompliance

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Imbens, Guido W., Rubin, Donald B.·1997·The Annals of Statistics
DOI 10.1214/aos/1034276631
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Abstract

For most of this century, randomization has been a cornerstone of scientific experimentation, especially when dealing with humans as experimental units. In practice, however, noncompliance is relatively common with human subjects, complicating traditional theories of inference that require adherence to the random treatment assignment. In this paper we present Bayesian inferential methods for causal estimands in the presence of noncompliance, when the binary treatment assignment is random and hence ignorable, but the binary treatment received is not ignorable. We assume that both the treatment assigned and the treatment received are observed. We describe posterior estimation using EM and data augmentation algorithms. Also, we investigate the role of two assumptions often made in econometric instrumental variables analyses, the exclusion restriction and the monotonicity assumption, without which the likelihood functions generally have substantial regions of maxima. We apply our procedures to real and artificial data, thereby demonstrating the technology and showing that our new methods can yield valid inferences that differ in practically important ways from those based on previous methods for analysis in the presence of noncompliance, including intention-to-treat analyses and analyses based on econometric instrumental variables techniques. Finally, we perform a simulation to investigate the operating characteristics of the competing procedures in a simple setting, which indicates relatively dramatic improvements in frequency operating characteristics attainable using our Bayesian procedures.

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Research works printed but not linked: 36

  1. Angrist, J. D. (1990). Lifetime earnings and the Vietnam era draft lottery: evidence from social security administrative records. American Economic Review 80 313-335.
  2. Angrist, J. D., Graddy, K. and Imbens, G. W. (1995). Non-parametric demand analysis with an application to the demand for fish. Technical Report 178, National Bureau of Economic Research, Cambridge, MA. · DOI
  3. Angrist, J. D. and Imbens, G. W. (1995). Two-stage least squares estimation of average causal effects in models with variable treatment intensity. J. Amer. Statist. Assoc. 90 431-442. · DOI
  4. Baker, S. G. and Lindeman, K. (1994). The paired availability design: a proposal for evaluating epidural analgesia during labor. Statistics in Medicine 13 2269-2278. · DOI
  5. Bowden, R. J. and Turkington, D. A. (1984). Instrumental Variables. Cambridge Univ. Press. · DOI
  6. Breslow, N. E. (1982). Clinical trials. In Ency clopedia of Statistical Sciences 2 13-21. Wiley, New York.
  7. Efron, B. and Feldman, D. (1991). Compliance as an explanatory variable in clinical trials (with discussion). J. Amer. Statist. Assoc. 86 9-26. · DOI
  8. Fisher, L., Dixon, D., Herson, J., Frankowski, R., Hearron, M. and Peace, K. (1990). Intention to treat in clinical trials. In Statistical Issues in Drug Research and Development (K. Peace, ed.) 331-350. Dekker, New York. · DOI
  9. Gelfand, A., Hills, S., Racine-Poon, A. and Smith, A. (1990). Illustration of Bayesian inference in normal data models using Gibbs sampling. J. Amer. Statist. Assoc. 85 398-405. · DOI
  10. Gelman, A. and Rubin, D. B. (1992). Inference from iterative simulations using multiple sequences. Statist. Sci. 7 457-511. · DOI · Paper page
  11. Geman, S. and Geman, D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Trans. Pattern Analy sis and Machine Intelligence 6 721- 741. · DOI · Paper page
  12. Hearst, N., Newman, T. and Hulley, S. (1986). Delay ed effects of the military draft on mortality: a randomized natural experiment. New England Journal of Medicine 314 620-624. · DOI
  13. Heckman, J. and Robb, R. (1985). Alternative methods for evaluating the impact of interventions. In Longitudinal Analy sis of Labor Market Data (J. Heckman and B. Singer, eds.). Cambridge Univ. Press. · DOI
  14. Holland, P. (1988). Causal inference, path analysis, and recursive structural equations models. In Sociological Methodology, Chap. 13. American Sociological Association, Washington, DC. · DOI
  15. Lee, Y., Ellenberg, J., Hirtz, D. and Nelson, K. (1991). Analy sis of clinical trials by treatment actually received: is it really an option? Statistics in Medicine 10 1595-1605. · DOI
  16. Liu, C. and Rubin, D. B. (1994). The ECME algorithm: a simple extension of EM and ECM with faster monotone convergence. Biometrica 81 633-648. · DOI
  17. Manski, C. F. (1990). Non-parametric bounds on treatment effects. American Economic Review, Papers and Proceedings 80 319-323.
  18. McClellan, M. and Newhouse, J. P. (1994). Does more intensive treatment of acute my ocardial infarction in the elderly reduce mortality? Journal of the American Medical Association 272 859-866. · DOI
  19. Meier, P. (1991). Comment on "Compliance as an explanatory variable in clinical trials" by B. Efron and D. Feldman. J. Amer. Statist. Assoc. 86 19-22. · DOI
  20. Meng, X. and Rubin, D. B. (1991). Using EM to obtain asy mptotic variance-covariance matrices: the SEM algorithm. J. Amer. Statist. Assoc. 86 899-909. · DOI
  21. Permutt, T. and Hebel, J. (1989). Simultaneous-equation estimation in a clinical trial of the effect of smoking on birth weight. Biometrics 45 619-622. · DOI
  22. Reiersol, O. (1941). Confluence analysis by means of lag moments and other methods of confluence analysis. Econometrica 9 1-24. · DOI
  23. Robins, J. M. (1989). The analysis of randomized and non-randomized 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. Bailey, eds.).
  24. Rosenbaum, P. (1995). Observational Studies. Springer, New York. · DOI
  25. Rosenbaum, P. and Rubin, D. B. (1983). The central role of the propensity score in observational studies for causal effects. Biometrika 70 41-55. · DOI · Paper page
  26. Rubin, D. B. (1975). Bayesian inference for causality: the importance of randomization. In Proceedings of the Social Statistics Section of the American Statistical Association 233-239. Amer. Statist. Assoc.
  27. Rubin, D. B. (1977). Assignment to treatment on the basis of a covariate. Journal of Education Statistics 2 1-26. Rubin, D. B. (1978a). Bayesian inference for causal effects: the role of randomization. Ann. Statist. 6 34-58. Rubin, D. B. (1978b). The phenomenological Bayesian perspective in sample survey s from finite populations: foundations. In Imputation and the Editing of Faulty or Missing Survey Data 10-18. U.S. Department of Commerce, Washington, DC. · DOI · Paper page
  28. Salsburg, D. (1994). Intent to treat: the reduction and absurdum that became gospel. Pharmacoepidemiology and Drug Safety 3 329-335. · DOI
  29. Sheiner, L. B. and Rubin, D. B. (1995). Intention-to-treat analysis and the goals of clinical trials. Clinical Pharmacology and Therapy 57 6-10. · DOI
  30. Sommer, A. and Zeger, S. (1991). On estimating efficacy from clinical trials. Statistics in Medicine 10 45-52. · DOI
  31. Tanner, M. and Wong, W. (1987). The calculation of posterior distributions by data augmentation (with discussion). J. Amer. Statist. Assoc. 82 528-550. · DOI
  32. Zelen, M. (1979). A new design for randomized clinical trials. New England Journal of Medicine 300 1242-1245. · DOI
  33. Breslow, N. E. (1996). Statistics in epidemiology: the case-control study. J. Amer. Statist. Assoc. 91 14-28. · DOI
  34. Meng, X. and Rubin, D. B. (1993). Maximum likelihood estimation via the ECM algorithm: a general framework. Biometrika 80 267-278. · DOI
  35. Wright, S. (1934). The method of path coefficients. Ann. Math. Statist. 5 161-215. · DOI
  36. Zelen, M. (1990). Randomized consent designs for clinical trials: an update. Statistics in Medicine 9 645-656. · DOI

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Metadata

Authors
Imbens, G. W., & Rubin, D. B.
Affiliations
Harvard University (US)
ORCID
Venue
The Annals of Statistics
Publisher
Institute of Mathematical Statistics
Published
1997-02-01
Volume
25
Issue
1
Pages
305-327
ISSN
  • 0090-5364 (ISSN-L)
  • 2168-8966
DOI
10.1214/aos/1034276631
OpenAlex
W2016729144
Cited by
538
References
7
Citations by year
2026: 12 · 2025: 17 · 2024: 20 · 2023: 22 · 2022: 17 · 2021: 25 · 2020: 20 · 2019: 25 · 2018: 12 · 2017: 16 · 2016: 12 · 2015: 37 · 2014: 27 · 2013: 28 · 2012: 26
FWCI
13.37
Type
journal article
Language
en
Open access
Locations
  • The Annals of Statistics (publishedVersion)
  • Project Euclid (Cornell University) (submittedVersion)
Funders
National Science Foundation
Topics
  • Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
Keywords
non-compliance, causal inference, Bayesian inference, randomized experiments, treatment allocation, treatment effect estimation, exclusion restriction, monotonicity assumption, instrumental variables, expectation-maximization algorithm, data augmentation, intention-to-treat analysis, operating characteristics

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