Advertisement

Taking Causality Seriously: Propensity Score Methodology Applied to Estimate the Effects of Marketing Interventions

  • Donald B. Rubin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2837)

Abstract

Propensity score methods were proposed by Rosenbaum and Rubin (1983, Biometrika) as central tools to help assess the causal effects of interventions. Since their introduction two decades ago, they have found wide application in a variety of areas, including medical research, economics, epidemiology, and education, especially in those situations where randomized experiments are either difficult to perform, or raise ethical questions, or would require extensive delays before answers could be obtained. Rubin (1997, Annals of Internal Medicine) provides an introduction to some of the essential ideas. In the past few years, the number of published applications using propensity score methods to evaluate medical and epidemiological interventions has increased dramatically. Rubin (2003, Erlbaum) provides a summary, which is already out of date.

Keywords

Propensity Score Bayesian Inference Causal Inference American Statistical Association Tobacco Industry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. (1974).
    Estimating Causal Effects of Treatments in Randomized and Nonrandomized Studies. Journal of Educational Psychology 66(5) (1974)Google Scholar
  2. (1977).
    Assignment to Treatment Group on the Basis of a Covariate. Journal of Educational Statistics 2(1), 1–26. Printer’s correction note 3, p. 384 (1977) Google Scholar
  3. (1977).
    Assignment to Treatment Group on the Basis of a Covariate. Journal of Educational Statistics 2(1), 1–26. Printer’s correction note 3, p. 384 (1977) Google Scholar
  4. (1978).
    Bayesian Inference for Causal Effects: The Role of Randomization. The Annals of Statistics 7(1), 34-58 (1978) Google Scholar
  5. (1983).
    Rosenbaum, P.R.: Assessing Sensitivity to an Unobserved Binary Covariate in an Observational Study with Binary Outcome. The Journal of the Royal Statistical Society, Series B 45(2), 212–218 (1983)Google Scholar
  6. (1983).
    Holland, P.W.: On Lord’s Paradox. In: Wainer, Messick (eds.) Principles of Modern Psychological Measurement: A Festschrift for Frederick Lord, pp. 3–25. Erlbaum, Mahwah (1983)Google Scholar
  7. (1984).
    Rosenbaum, P.R.: Estimating the Effects Caused by Treatments. Discussion of “On the Nature and Discovery of Structure” by Pratt and Schlaifer. Journal of the American Statistical Association 79, 26–28 (1984)CrossRefMathSciNetGoogle Scholar
  8. (1984).
    William G. Cochran’s Contributions to the Design, Analysis, and Evaluation of Observational Studies. In: Rao, Sedransk (eds.) W.G. Cochran’s Impact on Statistics, pp. 37–69. Wiley, New York (1984)Google Scholar
  9. (1986).
    Which Ifs Have Causal Answers? Discussion of Holland’s Statistics and Causal Inference. Journal of the American Statistical Association 81, 961–962 (1986)Google Scholar
  10. (1988).
    Holland, P.W.: Causal Inference in Retrospective Studies. Evaluation Review, 203–231 (1988)Google Scholar
  11. (1990).
    Formal Modes of Statistical Inference for Causal Effects. Journal of Statistical Planning and Inference 25, 279–292 (1990)Google Scholar
  12. (1990).
    Neyman (1923) and Causal Inference in Experiments and Observational Studies. Statistical Science 5(4), 472–480 (1990)Google Scholar
  13. (1991).
    Dose-Response Estimands: A Comment on Efron and Feldman. Journal of the American Statistical Association 86(413), 22–24 (1991)Google Scholar
  14. (1994).
    Sheiner, L.B.: Intention-to-Treat Analysis and the Goals of Clinical Trials. Clinical Pharmacology and Therapeutics 87(1), 6–15 (1994)Google Scholar
  15. (1996).
    Angrist, J.D., Imbens, G.W.: Identification of Causal Effects Using Instrumental Variables. Journal of the American Statistical Association 91(434), 444–472 (1996); as Applications Invited Discussion Article with discussion and rejoinderzbMATHCrossRefGoogle Scholar
  16. (1996).
    Angrist, J.D., Imbens, G.W.: Identification of Causal Effects Using Instrumental Variables. Journal of the American Statistical Association 91(434), 444–472 (1996); as Applications Invited Discussion Article with discussion and rejoinderzbMATHCrossRefMathSciNetGoogle Scholar
  17. (1997).
    Imbens, G.: Estimating Outcome Distributions for Compliers in Instrumental Variables Models. Review of Economic Studies 64, 555–574 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  18. (1998).
    More Powerful Randomization-Based p-values in Double-Blind Trials with Noncompliance. Statistics in Medicine 17, 371–385 (1998) (with discussion by D.R. Cox)Google Scholar
  19. (1999).
    Frangakis, C.: Addressing Complications of Intention-To-Treat Analysis in the Combined Presence of All-or-None Treatment-Noncompliance and Subsequent Missing Outcomes. Biometrika 86(2), 366–379 (1999)CrossRefMathSciNetGoogle Scholar
  20. (1999).
    Frangakis, C.E.: Causal Inquiry in Longitudinal Observational Studies, Discussion of ’Estimation of the Causal Effect of a Time-varying Exposure on the Marginal Mean of a Repeated Binary Outcome’ by J. Robins, S. Greenland and F-C. Hu. Journal of the American Statistical Association 94(447), 702–703 (1999)CrossRefGoogle Scholar
  21. (1999).
    Teaching Causal Inference in Experiments and Observational Studies. In: Proceedings of the Section on Statistical Education of the American Statistical Association, pp. 126–131 (1999)Google Scholar
  22. (2000).
    Statistical Issues in the Estimation of the Causal Effects of Smoking Due to the Conduct of the Tobacco Industry. In: Gastwirth, J. (ed.) Statistical Science in the Courtroom, ch. 16, pp. 321–351. Springer, New York (2000)Google Scholar
  23. (2000).
    The Utility of Counterfactuals for Causal Inference. Comment on A.P. Dawid, Causal Inference Without Counterfactuals. Journal of the American Statistical Association 95(450), 435–438 (2000)Google Scholar
  24. (2000).
    Little, R.J.A.: Causal Inference in Clinical and Epidemiological Studies via Potential Outcomes: Concepts and Analytic Approaches. Annual Review of Public Health 21, 121–145 (2000)CrossRefGoogle Scholar
  25. (2000).
    Statistical Inference for Causal Effects in Epidemiological Studies Via Potential Outcomes. In: Proceedings of the XL Scientific Meeting of the Italian Statistical Society, Florence, Italy, April 26-28, pp. 419–430 (2000)Google Scholar
  26. (2001).
    Estimating The Causal Effects of Smoking. Statistics in Medicine 20, 1395–1414 (2001)Google Scholar
  27. (2001).
    Roberts, S.: Self-Experimentation for Causal Effects. Comment on ‘Surprises From Self-Experimentation: Sleep, Mood, and Weight’ 14(2), 16–17 (2001)Google Scholar
  28. (2001).
    Imbens, G.W., Sacerdote, B.: Estimating the Effect of Unearned Income on Labor Supply, Earnings, Savings and Consumption: Evidence from a Survey of Lottery Players. American Economic Review 19, 778–794 (2001)CrossRefGoogle Scholar
  29. (2000).
    Statistical Assumptions in the Estimation of the Causal Effects of Smoking Due to the Conduct of the Tobacco Industry. In: Blasius, J., Hox, J., de Leeuw, E., Schmidt, P. (eds.) [CD-ROM] In Social Science Methodology in the New Millennium. Proceedings of the Fifth International Conference on Logic and Methodology, Cologne, Germany, October 6 (2000); Opladen, FRG: Leske + Budrich. P023003Google Scholar
  30. (2002).
    Barnard, J., Frangakis, C., Hill, J.: School Choice in NY City: A Bayesian Analysis of an Imperfect Randomized Experiment. In: Gatsonis, C., Carlin, B., Carriquiry, A. (eds.) With discussion and rejoinder. Case Studies in Bayesian Statistics, vol. V, pp. 3–97. Springer, New York (2002)Google Scholar
  31. (2002).
    Frangakis, C.: Principal Stratification in Causal Inference. Biometrics 58(1), 21–29 (2002)CrossRefMathSciNetzbMATHGoogle Scholar
  32. (2002).
    Frangakis, C.E., Zhou, X.-H.: Clustered Encouragement Designs with Individual Noncompliance: Bayesian Inference with Randomization, and Application to Advance Directive Forms. With discussion and rejoinder, Biostatistics 3(2), 147–177 (2002)zbMATHGoogle Scholar
  33. (2002).
    Mealli, F.: Discussion of ‘Estimation of Intervention Effects with Noncompliance: Alternative Model Specification,’ by Booil Jo. Journal of Educational and Behavioral Statistics 27(4), 411–415 (2002)CrossRefGoogle Scholar
  34. (2003).
    Mealli, F.: Assumptions Allowing the Estimation of Direct Causal Effects: Discussion of Healthy, Wealthy, and Wise? Tests for Direct Causal Paths Between Health and Socioeconomic Status by Adams et al. Journal of Econometrics 112, 79–87 (2003)CrossRefMathSciNetGoogle Scholar
  35. (2003).
    Barnard, J., Frangakis, C., Hill, J.: A Principal Stratification Approach to Broken Randomized Experiments: A Case Study of Vouchers in New York City. Journal of the American Statistical Association 98(462) (2003); with discussion and rejoinderGoogle Scholar
  36. (2003).
    Mealli, F.: Assumptions When Analyzing Randomized Experiments with Noncompliance and Missing Outcomes. To appear in Health Services Outcome Research Methodology (2003)Google Scholar
  37. (2003).
    Peck, C., Sheiner, L.B.: Hypothesis: A Single Clinical Trial Plus Causal Evidence of Effectiveness is Sufficient for Drug Approval. Clinical Pharmacology and Therapeutics 73, 481–490 (2003)CrossRefGoogle Scholar
  38. (2003).
    Teaching Statistical Inference for Causal Effects in Experiments and Observational Studies. To appear in The Journal of Educational and Behavioral Statistics (2003)Google Scholar
  39. (1973).
    Matching to Remove Bias in Observational Studies. Biometrics 29(1), 159–183. Printer’s correction note 30, p. 728 (1973)Google Scholar
  40. (1976).
    Multivariate Matching Methods that are Equal Percent Bias Reducing, I: Some Examples. Biometrics 32(1), 109–120. Printer’s correction note, p. 955 (1976)Google Scholar
  41. (1976).
    Multivariate Matching Methods that are Equal Percent Bias Reducing, II: Maximums on Bias Reduction for Fixed Sample Sizes. Biometrics 32(1), 121–132. Printer’s correction note p. 955 (1976)Google Scholar
  42. (1980).
    Bias Reduction Using Mahalanobis’ Metric Matching. Biometrics 36(2), 295–298. Printer’s Correction, p. 296 ((5,10) = 75%) (1980)Google Scholar
  43. (1983).
    Rosenbaum, P.: The Central Role of the Propensity Score in Observational Studies for Causal Effects. Biometrika 70, 41–55 (1983)zbMATHCrossRefMathSciNetGoogle Scholar
  44. (1984).
    Rosenbaum, P.R.: Reducing Bias in Observational Studies Using Subclassification on the Propensity Score. Journal of the American Statistical Association 79, 516–524 (1984)CrossRefMathSciNetGoogle Scholar
  45. (1985).
    The Use of Propensity Scores in Applied Bayesian Inference. In: Bernardo, De Groot, Lindley, Smith (eds.) Bayesian Statistics, vol. 2, pp. 463–472. North Holland, Amsterdam (1985)Google Scholar
  46. (1985).
    Rosenbaum, P.R.: Constructing a Control Group Using Multivariate Matched Sampling Incorporating the Propensity Score. American Statistician 39, 33–38 (1985)CrossRefMathSciNetGoogle Scholar
  47. (1985).
    Rosenbaum, P.R.: The Bias Due to Incomplete Matching. Biometrics 41, 103–116 (1985)zbMATHCrossRefMathSciNetGoogle Scholar
  48. (1992).
    Czajka, J.C., Hirabayashi, S.M., Little, R.J.A.: Projecting from Advance Data Using Propensity Modelling. The Journal of Business and Economics Statistics 10(2), 117–131 (1992)CrossRefGoogle Scholar
  49. (1992).
    Thomas, N.: Affinely Invariant Matching Methods with Ellipsoidal Distributions. The Annals of Statistics 20(2), 1079–1093 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  50. (1992).
    Thomas, N.: Characterizing the Effect of Matching Using Linear Propensity Score Methods with Normal Covariates. Biometrika 79(4), 797–809 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  51. (1995).
    Reinisch, J., Sanders, S., Mortensen, E.: In Utero Exposure to Phenobarbital and Intelligence Deficits in Adult Men. The Journal of the American Medical Association 274(19), 1518–1525 (1995)CrossRefGoogle Scholar
  52. (1996).
    Thomas, N.: Matching Using Estimated Propensity Scores: Relating Theory to Practice. Biometrics 52, 249–264 (1996)zbMATHCrossRefGoogle Scholar
  53. (1999).
    McIntosh, M.: On Estimating the Causal Effects of Do Not Resuscitate Orders. Medical Care 37(8), 722–726 (1999)CrossRefGoogle Scholar
  54. (1999).
    Hill, J., Thomas, N.: The Design of the New York School Choice Scholarship Program Evaluation. In: Bickman, L. (ed.) Research Designs: Inspired by the Work of Donald Campbell, vol. ch. 7, pp. 155–180. Sage, Thousand Oaks (1999)Google Scholar
  55. (2000).
    D’Agostino Jr., R.: Estimation and Use of Propensity Scores with Incomplete Data. Journal of the American Statistical Association 95(451), 749–759 (2000)CrossRefGoogle Scholar
  56. (2001).
    Using Propensity Scores to Help Design Observational Studies: Application to the Tobacco Litigation. Health Services & Outcomes Research Methodology 2, 169–188 (2001)Google Scholar
  57. (1973).
    The Use of Matched Sampling and Regression Adjustment to Remove Bias in Observational Studies. Biometrics 29(1), 184–203 (1973)Google Scholar
  58. (1973).
    Cochran, W.G.: Controlling Bias in Observational Studies: A Review. Sankhya - A 35(4), 417–446 (1973)zbMATHMathSciNetGoogle Scholar
  59. (1979).
    Using Multivariate Matched Sampling and Regression Adjustment to Control Bias in Observational Studies. The Journal of the American Statistical Association 74(366), 318–328 (1979)Google Scholar
  60. (2000).
    Thomas, N.: Combining Propensity Score Matching with Additional Adjustments for Prognostic Covariates. Journal of the American Statistical Association 95(450), 573–585 (2000)CrossRefGoogle Scholar
  61. (1997).
    Estimating Causal Effects From Large Data Sets Using Propensity Scores. Annals of Internal Medicine 127, 8(II), 757–763 (1997)Google Scholar
  62. (1998).
    Estimation from Nonrandomized Treatment Comparisons Using Subclassification on Propensity Scores. In: Abel, U., Koch, A. (eds.) Nonrandomized Comparative Clinical Studies, pp. 85–100. Symposion Publishing, Dusseldorf (1998)Google Scholar
  63. (2003).
    Estimating Treatment Effects From Nonrandomized Studies Using Subclassification on Propensity Scores. To appear in Festschrift for Ralph Rosnow. Erlbaum publishers (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Donald B. Rubin
    • 1
  1. 1.Department of StatisticsHarvard UniversityCambridge

Personalised recommendations