Matching and Propensity Scores

The Oxford Handbook of Quantitative Methods: Volume 1: Foundations

Volumn 1, Issue , 2013, Pages 237-259

  Steiner, Peter M ^a   Cook, David ^b  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

^b ABT ASSOCIATES   (United States)

Author keywords

inverse propensity weighting; Matching; observational study; potential outcomes; propensity score regression estimation; propensity score subclassification; propensity scores; Rubin Causal Model; sensitivity analyses

Indexed keywords

EID: 85143958533     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1093/oxfordhb/9780199934874.013.0013     Document Type: Chapter

References (98)

1. Abadie, A., Drukker, D., Herr, J. L., and Imbens, G. W. (2004). Implementing matching estimators for average treatment effects in Stata. The Stata Journal, 4, 290—311.
2. Abadie, A., and Imbens, G. W. (2002). Simple and bias-corrected matching estimators. Technical Report. Department of Economics, University of California, Berkley.
3. Althauser, R., and Rubin, D. B. (1970). The computerized construction of a matched sample. American Journal of Sociology, 76, 325-346.
4. Bang, H., and Robins, J. M. (2005). Doubly robust estimation in missing data and causal inference models. Biometrics, 61, 962-972.
5. Becker, S. O., Ichino, A. (2002). Estimation of average treatment effects based on propensity scores. The Stata Journal, 2, 358-377.
6. Berk, R. A. (2006). An introduction to ensemble methods for data analysis. Sociological Methods and Research, 34, 263-295.
7. Berk, R. A. (2008). Statistical Learning from a Regression Perspective. New York: Springer.
8. Bloom, H. S., Michalopoulos, C., Hill, C. J., and Lei, Y. (2002). Can Non experimental Comparison Group Methods Match the Findings from a Random Assignment Evaluation of Mandatory Welfare-to-Work Programs? Washington, DC: Manpower Demonstration Research Corporation.
9. Cochran, W. G. (1968): The effectiveness of adjustment by subclassification in removing bias in observational studies. Biometrics, 24, 295-313.
10. Cochran, W. G., and Rubin, D. B. (1973). Controlling bias in observational studies: A review. Sankhya: The Indian Journal of Statistics, Series A, 35, 417-446.
11. Cook, T. D., Shadish, W. R., and Wong, V. C. (2008). Three conditions under which experiments and observational studies produce comparable causal estimates: New findings from within-study comparisons. Journal of Policy Analysis and Management, 27(4), 724-750.
12. Cook, T. D., and Steiner, P. M. (2010). Case matching and the reduction of selection bias in quasi-experiments: The relative importance of the pretest as a covariate, unreliable measurement and mode of data analysis. Psychological Methods, 15(1), 56-68.
13. Cook, T. D., Steiner, P. M., and Pohl, S. (2009). Assessing how bias reduction is influenced by covariate choice, unreliability and data analytic mode: An analysis of different kinds of within-study comparisons in different substantive domains. Multivariate Behavioral Research, 44, 828-847.
14. D'Orazio, M., Di Zio, M., and Scanu, M. (2006). Statistical Matching: Theory and Practice. Chichester: Wiley.
15. Dehejia, R., and Wahba, S. (1999). Causal effects in non-experimental studies: Re-evaluating the evaluation oftraining programs. Journal of the American Statistical Association, 94, 1053-1062.
16. Dehejia, R., and Wahba, S. (2002). Propensity score-matching methods for nonexperimental causal studies. The Review of Economics and Statistics, 84(1): 151-161.
17. Gangl, M. (2004). RBOUNDS: Stata module to perform Rosenbaum sensitivity analysis for average treatment effects on the treated. Statistical Software Components S438301, Boston College Department of Economics.
18. Glazerman, S., Levy, D. M., and Myers, D. (2003). Non experimental versus experimental estimates of earnings impacts. The Annals of the American Academy, 589, 63-93.
19. Gu, X., and Rosenbaum, P. R. (1993). Comparison of multivariate matching methods: Structures, distances, and algorithms. Journal of Computational and Graphical Statistics, 2, 405-420.
20. Guo, S., and Fraser, M. W (2010). Propensity score analysis. Statistical Methods and Applications. Thousand Oaks, CA: Sage.
21. Hansen, B. B. (2004). Full matching in an observational study of coaching for the SAT. Journal of the American Statistical Association, 99, 609-618.
22. Hansen, B. B, and Klopfer, S. O. (2006). Optimal full matching and related designs via network flows. Journal of Computational and Graphical Statistics, 15, 609-627.
23. Hastie, T., Tibshirani, R., and Friedman, J. (2001). The Elements of Statistical Learning. New York: Springer.
24. Heckman, J. J. (1974). Shadow prices, market wages, and labor supply. Econometrica, 42, 679-694.
25. Heckman, J. J. (1979). Sample selection bias as a specification error. Econometriaca, 47, 153-161.
26. Heckman, J. J. (2005). The scientific model of causality. Sociological Methodology, 35(1), 1-98.
27. Heckman, J. J., Ichimura, H., and Todd, P. E. (1997). Matching as an econometric evaluation estimator: Evidence from evaluating a job training programme. Review ofEconomic Studies, 64, 605-654.
28. Heckman, J. J., Ichimura, H., and Todd, P. E. (1998). Matching as an econometric evaluation estimator. Review of Economic Studies, 65, 261-294.
29. Ho, D. E., Imai, K., King, G., and Stuart, E. A. (2007). Matching as nonparametric preprocessing for reducing model dependence in parametric causal inference. Political Analysis, 15, 199-236.
30. Ho, D. E., Imai, K., King, G., and Stuart, E. A. (in press). Match It: Nonparametric preprocessing for parametric causal inference. Journal of Statistical Software.
31. Holland, P. W. (1986). Statistics and causal inference. Journal of the American Statistical Association, 81, 945—970.
32. Hong, G. (2009). Marginal mean weighting through stratification: Adjustment for selection bias in multi-level data. Unpublished Manuscript.
33. Hong, G., and Raudenbush, S. W. (2006). Evaluating kindergarten retention policy: A case study of causal inference for multilevel observational data. Journal of the American Statistical Association, 101, 901—910.
34. Hong, G., and Raudenbush, S. W. (2008). Causal inference for time-varying instructional treatments. Journal of Educational and Behavioral Statistics, 33(3), 333—362.
35. Horvitz, D. G., and Thompson, D. J. (1952). A generalization of sampling without replacement from a finite universe. Journal of the American Statistical Association, 47, 663—685.
36. Imai, K. and van Dyk, D.A. (2004). Causal inference with general treatment regimes: Generalizing the propensitys core. Journal of the American Statistical Association, 99, 854—866.
37. Imbens, G. W. (2000). The role of the propensity score in estimating dose-response functions. Biometrika, 87, 706—710.
38. Imbens, G. W (2004). Nonparametric estimation of average treatment effects under exogeneity: A review. Review of Economics and Statistics, 86(1), 4—29.
39. Joffe, M. M., and Rosenbaum, P. R. (1999). Propensity scores. American Journal of Epidemiology, 150, 327—333.
40. Kang, J., and Schafer, J. L. (2007). Demystifying double robustness: a comparison of alternative strategies for estimating population means from incomplete data. Statistical Science, 26, 523-539.
41. Kaplan, D. (1999). An extension of the propensity score adjustment method for the analysis of group differences in MIMIC models. Multivariate Behavioral Research, 34(4), 467-492.
42. Kaplan, D. (2009). Causal inference in non-experimental educational policy research. In D. N. Plank, W. E. Schmidt, and G. Sykes (Eds.), AERA Handbook on Education Policy Research. Washington, DC: AERA.
43. Kosanke, J., and Bergstralh, E. (2004). Match cases to controls using variable optimal matching: URL http://mayo-research.mayo.edu/mayo/research/biostat/upload/vmatch.sas and Match 1 or more controls to cases using the GREEDY algorithm: URL http://mayoresearch.mayo.edu/mayo/resea-rch/biostat/upload/gmatch.sas.
44. Keele, L. J. (2009). rbounds: Perform Rosenbaum bounds sensitivity tests for matched data. R package. http://CRAN.R-project.org/package=rbounds.
45. Kolar, A., and Vehovar, V. (2012). Small samples and propensity score methods. Working Paper.
46. Krzanowski, W. J. (2000). Principles of Multivariate Analysis: A User’s Perspective. New York: Oxford University Press.
47. Lee, B., Lessler, J., and Stuart, E. A. (2010). Improving propensity score weighting using machine learning. Statistics in Medicine, 29, 337-346.
48. Leuven, E., and Sianesi, B. (2003). PSMATCH2. Stata module to perform full Mahalanobis and propensity score matching, common support graphing, and covariate imbalance testing. Statistical Software Components S432001, Boston College Department of Economics.
49. Little, R. J. A., and An, H. (2004). Robust likelihood-based analysis of multivariate data with missing values. Statistica Sinica, 14, 949-968.
50. Luellen, J. K, Shadish, W. R., and Clark, M.H. (2005). Propensity scores: An introduction and experimental test. Evaluation Review, 29, 530-558.
51. Lunceford, J. K., and Davidian, M. (2004). Stratification and weighting via propensity score in estimation of causal treatment effects: A comparative study. Statistical Medicine, 23, 2937-2960.
52. Maddala, G. S. (1983). Limited-dependent and Qualitative Variables in Econometrics. Cambridge: Cambridge University Press.
53. Murphy, S. A., van der Laan, M. J., Robins, J. M., and CPPRG (2001). Marginal mean models for dynamic regimes. Journal ofthe American Statistical Association, 96, 1410-1423.
54. McCaffrey, D. F., Ridgeway, G., and Morral, A. R. (2009). Propensity score estimation with boosted regression for evaluating causal effects in observational studies. Psychological Methods, 9, 403-425.
55. Morgan, S. L., and Winship C. (2007). Counterfactuals and Causal Inference: Methods and Principles for Social Research. Cambridge: Cambridge University Press.
56. Parsons, L. S. (2001). Reducing bias in a propensity score matched-pair sample using greedy matching techniques. SAS Institute Inc., Proceedings of the Twenty-Sixth Annual SAS ®Users Group International Conference, Paper 21426. Cary, NC: SAS Institute Inc., URL http://www2.sas.com/proceedings/sugi26/p214-26.pdf.
57. Pearl, J. (2009). Causality: Models, Reasoning, and Inference (2nd ed.). Cambridge: Cambridge University Press.
58. Pohl, S., Steiner, P. M., Eisermann, J., Soellner, R., and Cook, T. D. (2009). Unbiased causal inference from an observational study: Results of a within-study comparison. Educational Evaluation and Policy Analysis, 31(4), 463-479.
59. Potter, F.J. (1990). A Study of Procedures to Identify and Trim Extreme Sampling Weights. In: Proceedings of the Section on Survey Research Methods of the American Statistical Association, San Francisco, California. (pp. 225-230). Journal of the American Statistical Association.
60. Rässler, S. (2002). Statistical Matching: A Frequentist Theory, Practical Applications and Alternative Bayesian Approaches. New York: Springer.
61. Robins, J. M. (1999). Associations, causation, and marginal structural models. Synthese, 101, 151-179.
62. Robins, J. M., and Rotnitzky, A. (1995). Semi parametric efficiency in multivariate regression models with missing data. Journal of the American Statistical Association, 90, 122-129.
63. Robins, J. M., and Rotnitzky, A. (2001). Comment on ‘Inference for semiparametric models: Some questions and answers’ by Bickel and Kwon. Statistica Sinica, 11, 920-936.
64. Robins, J. M., Rotnitzky, A., and Zhao, L. P. (1995). Analysis of semiparametric regression models for repeated outcomes in the presence of missing data. Journal of the American Statistical Association, 90, 106-121.
65. Rosenbaum, P. R. (1984). From association to causation in observational studies: The role of tests of strongly ignorable treatment assignment. Journal ofthe American Statistical Association, 79, 41-48.
66. Rosenbaum, P. R. (1986). Dropping out high school in the United States: An observational study. Journal of Educational Statistics, 11, 207-224.
67. Rosenbaum, P. R. (2002). Observational Studies (2nd Ed.). New York: Springer-Verlag.
68. Rosenbaum, P. R. (2009). Design Observational Studies. New York: Springer-Verlag.
69. Rosenbaum, P. R., and Rubin, D. B. (1983a). The central role of the propensity score in observational studies for causal effects. Biometrika, 70 (1), 41-55.
70. Rosenbaum, P.R. and. Rubin, D. B. (1983b).Assessing sensitivity to an unobserved binary covariate in an observational study with binary outcome. Journal of the Royal Statistical Society, B, 45, 212-218.
71. Rosenbaum, P. R., and Rubin, D. B. (1984). Reducing bias in observational studies using sub classification on the propensity score. Journal of the American Statistical Association, 79, 516—524.
72. Rosenbaum, P. R., and Rubin, D. B. (1985). Constructing a control group using multivariate matched sampling methods that incorporate the propensity score. The American Statistician, 39, 33—38.
73. Rosenbaum, P. R., and Rubin, D. B. (1985). The bias due to incomplete matching. Biometrics, 41, 103—116.
74. Rubin, D. B. (1974). Estimating causal effects of treatments in randomized and nonrandomized studies. Journal of Educational Psychology, 66, 688—701.
75. Rubin, D. B. (1997). Estimating causal effects from large data sets using propensity scores. Annals of Internal Medicine, 127, 757—763.
76. Rubin, D.B. (1978). Bayesian inference for causal effects: The role of randomization. Annals of Statistics, 6, 34—58.
77. Rubin, D. B. (1979). Using multivariate matched sampling and regression adjustment to control bias in observational studies. Journal of the American Statistical Association, 74, 318—328.
78. Rubin, D. B. (2001). Using propensity scores to help design observational studies: Application to the tobacco litigation. Health Services and Outcomes Research Methodology, 2, 169—188.
79. Rubin, D. B. (2006). Matched Sampling for Causal Effects. Cambridge: Cambridge University Press.
80. Rubin, D. B., and Thomas, N. (1996). Matching using estimated propensity scores: Relating theory to practice. Biometrics, 52, 249—264.
81. Rubin, D. B., and Thomas, N. (2000). Combining propensity score matching with additional adjustments for prognostic covariates. Journal of the American Statistical Association, 95, 573—585.
82. Schafer, J. L., and Kang, J. (2008). Average causal effects from non-randomized studies: A practical guide and simulated example. Psychological Methods, 13(4), 279—313.
83. Sekhon, J. S. (2011). Multivariate and propensity score matching software with automated balance optimization: the matching package for R. Journal of Statistical Software, 42(7), 1—52.
84. Setoguchi, S., Schneeweiss, S., Brookhart, M. A., Glynn, R. J., and Cook, E. F. (2008). Evaluating uses of data mining techniques in propensity score estimation: A simulation study. Pharmacoepidemiology and Drug Safety, 17, 546—555.
85. Shadish, W.R. (in press). Campbell and Rubin: A primer and comparison of their approaches to causal inference in field settings. Psychological Methods.
86. Shadish, W. R., Clark, M. H., and Steiner, P. M. (2008). Can nonrandomized experiments yield accurate answers? A randomized experiment comparing random to nonrandom assignment. Journal of the American Statistical Association, 103, 1334—1343.
87. Shadish, W. R., Cook, T. D., and Campbell, D. T. (2002). Experimental and Quasi-Experimental Designs for Generalized Causal Inference. Boston: Houghton-Mifflin.
88. Shadish, W. R., and Steiner, P. M. (2010). A primer on propensity score analysis. Newborn and Infant Nursing Reviews, 10(1), 19—26.
89. Shah, B. R., Laupacis, A., Hux, J. E., and Austin, P. C. (2005). Propensity score methods gave similar results to traditional regression modeling in observational studies: a systematic review. Journal of Clinical Epidemiology, 58, 550—559.
90. Steiner, P. M., Cook, T. D., and Shadish, W. R. (2011). On the importance of reliable covariate measurement in selection bias adjustments using propensity scores. Journal of Educational and Behavioral Statistics, 36(2), 213—236.
91. Steiner, P. M., Cook, T. D., Shadish, W. R., and Clark, M. H. (2010). The importance of covariate selection in controlling for selection bias in observational studies. Psychological Methods, 15(3), 250—267.
92. Steyer, R. (2005). Analyzing individual and average causal effects via structural equation models. Methodology, 1, 39—64.
93. Steyer, R., Gabler, S., von Davier, A. A., Nachtigall, C., and Buhl, T. (2000). Causal regression models I: Individual and average causal effects. Methods of Psychological Research Online, 5(2), 39—71.
94. Steyer, R., Gabler, S., von Davier, A. A. and Nachtigall, C. (2000). Causal regression models II: Unconfoundedness and causal unbiasedness. Methods of Psychological Research Online, 5(3), 55—87.
95. Stuart, E. A. (2010). Matching methods for causal inference: A review and a look forward. Statistical Sciences, 25(1), 1—21.
96. Stuart, E. A., and Rubin, D. B. (2007). Best practices in quasi-experimental designs: matching methods for causal inference. In: Best Practices in Quantitative Methods, Chapter 11, Osborne J (Ed.). (pp. 155—176), Thousand Oaks, CA: Sage Publications.
97. Stürmer, T., Joshi, M., Glynn, R. J., Avorn, J., Rothman, K. J., and Schneeweiss, S. (2006). A review of the application of propensity score methods yielded increasing use, advantages in specific settings, but not substantially different estimates compared with conventional multivariable methods. Journal of Clinical Epidemiology, 59, 437-447.
98. Wood, S.N. (2006). Generalized Additive Models. An Introduction with R. Boca Raton: Chapman and Hall/CRC.