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Bayesian inference for causal effects in randomized experiments with noncompliance. (English) Zbl 0877.62005

Summary: 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. 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.

MSC:

62A01 Foundations and philosophical topics in statistics
62F15 Bayesian inference
62B15 Theory of statistical experiments
62C10 Bayesian problems; characterization of Bayes procedures
62K99 Design of statistical experiments
62P99 Applications of statistics
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[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. · Zbl 1055.91519
[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. JSTOR: · Zbl 0925.62541
[4] Angrist, J. D., Imbens, G. W. and Rubin, D. B. (1996). Identification of causal effects using instrumental variables (with discussion). J. Amer. Statist. Assoc. 91 444-472. · Zbl 0897.62130
[5] 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.
[6] Balke, A. and Pearl, J. (1994). Nonparametric bounds of causal effects from partial compliance data. Technical Report R-199-J, Dept. Computer Science, Univ. California, Los Angeles.
[7] Bloom, H. (1984). Accounting for no-shows in experimental evaluation designs. Evaluation Review 8 225-246.
[8] Bowden, R. J. and Turkington, D. A. (1984). Instrumental Variables. Cambridge Univ. Press. · Zbl 0606.62130
[9] Breslow, N. E. (1982). Clinical trials. In Ency clopedia of Statistical Sciences 2 13-21. Wiley, New York.
[10] Breslow, N. E. (1996). Statistics in epidemiology: the case-control study. J. Amer. Statist. Assoc. 91 14-28. JSTOR: · Zbl 0870.62082
[11] Dempster, A. P., Laird, N. and Rubin, D. B. (1977). Maximum likelihood estimation from incomplete data using the EM algorithm (with discussion). J. Roy. Statist. Soc. Ser. B 39 1-38. JSTOR: · Zbl 0364.62022
[12] Efron, B. and Feldman, D. (1991). Compliance as an explanatory variable in clinical trials (with discussion). J. Amer. Statist. Assoc. 86 9-26.
[13] 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.
[14] Fisher, R. A. (1925). Statistical Methods for Research Workers, 1st ed. Oliver and Boy d, Edinburgh. · JFM 51.0414.08
[15] 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. JSTOR: · Zbl 0702.62020
[16] Gelman, A. and Rubin, D. B. (1992). Inference from iterative simulations using multiple sequences. Statist. Sci. 7 457-511. · Zbl 1386.65060
[17] 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. · Zbl 0573.62030
[18] 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.
[19] 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. · Zbl 0584.62197
[20] Holland, P. (1986). Statistics and causal inference. J. Amer. Statist. Assoc. 81 945-970. JSTOR: · Zbl 0607.62001
[21] Holland, P. (1988). Causal inference, path analysis, and recursive structural equations models. In Sociological Methodology, Chap. 13. American Sociological Association, Washington, DC.
[22] Imbens, G. W. and Angrist, J. D. (1994). Identification and estimation of local average treatment effects. Econometrica 62 467-476. · Zbl 0800.90648
[23] Imbens, G. W. and Rubin, D. B. (1994). Estimating outcome distributions for compliers in instrumental variables models. Working Paper 1545, Harvard Institute of Economic Research. · Zbl 0887.90041
[24] 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.
[25] 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. JSTOR: · Zbl 0812.62028
[26] Manski, C. F. (1990). Non-parametric bounds on treatment effects. American Economic Review, Papers and Proceedings 80 319-323.
[27] 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.
[28] McDonald, C., Hiu, S. and Tierney, W. (1992). Effects of computer reminders for influenza vaccination on morbidity during influenza epidemics. Clinical Computing 9 304-312.
[29] 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.
[30] 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.
[31] Meng, X. and Rubin, D. B. (1993). Maximum likelihood estimation via the ECM algorithm: a general framework. Biometrika 80 267-278. JSTOR: · Zbl 0778.62022
[32] Ney man, J. (1923). On the application of probability theory to agricultural experiments. Essay on principles. Section 9. [Translated in Statist. Sci. 5 (1990) 465-480.] · Zbl 0955.01560
[33] 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. · Zbl 0718.62224
[34] Reiersol, O. (1941). Confluence analysis by means of lag moments and other methods of confluence analysis. Econometrica 9 1-24. JSTOR: · Zbl 0063.06461
[35] 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.).
[36] NCHSR, U.S. Public Health Service, Washington, DC.
[37] Rosenbaum, P. (1995). Observational Studies. Springer, New York. · Zbl 0899.62138
[38] Rosenbaum, P. and Rubin, D. B. (1983). The central role of the propensity score in observational studies for causal effects. Biometrika 70 41-55. JSTOR: · Zbl 0522.62091
[39] Rubin, D. B. (1974). Estimating causal effects of treatments in randomized and non-randomized studies. Journal of Educational Psy chology 66 688-701.
[40] 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.
[41] 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.
[42] Rubin, D. B. (1980). Discussion of ”Randomization analysis of experimental data in the Fisher randomization test” by D. Basu. J. Amer. Statist. Assoc. 75 591-593. Rubin, D. B. (1990a). Comment on ”Ney man (1923) and causal inference in experiments and observational studies.” Statist. Sci. 5 472-480. Rubin, D. B. (1990b). Formal modes of statistical inference for causal effects. J. Statist. Plann. Inference 25 279-292. · Zbl 0444.62089
[43] Salsburg, D. (1994). Intent to treat: the reduction and absurdum that became gospel. Pharmacoepidemiology and Drug Safety 3 329-335.
[44] 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.
[45] Sommer, A. and Zeger, S. (1991). On estimating efficacy from clinical trials. Statistics in Medicine 10 45-52.
[46] Tanner, M. and Wong, W. (1987). The calculation of posterior distributions by data augmentation (with discussion). J. Amer. Statist. Assoc. 82 528-550. JSTOR: · Zbl 0619.62029
[47] Wright, S. (1928). Appendix. In The Tariff on Animal and Vegetable Oils by P. G. Wright. Macmillan, New York.
[48] Wright, S. (1934). The method of path coefficients. Ann. Math. Statist. 5 161-215. · Zbl 0010.31305
[49] Zelen, M. (1979). A new design for randomized clinical trials. New England Journal of Medicine 300 1242-1245.
[50] Zelen, M. (1990). Randomized consent designs for clinical trials: an update. Statistics in Medicine 9 645-656.
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