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Part of the book series: ICSA Book Series in Statistics ((ICSABSS))

Abstract

In causal inference for binary treatments, the propensity score is defined as the probability of receiving the treatment given covariates. Under the ignorability assumption, causal treatment effects can be estimated by conditioning on/adjusting for the propensity scores. However, in observational studies, propensity scores are unknown and need to be estimated from the observed data. Estimation of propensity scores is essential in making reliable causal inference. In this chapter, we first briefly discuss the modeling of propensity scores for a binary treatment; then we will focus on the estimation of the generalized propensity scores for categorical treatment variables with more than two levels and continuous treatment variables. We will review both parametric and nonparametric approaches for estimating the generalized propensity scores. In the end, we discuss how to evaluate the performance of different propensity score models and how to choose an optimal one among several candidate models.

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References

  1. Breiman, L.: Random forests. Mach. Learn. 45 (1), 5–32 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  2. Breiman, L., Friedman, J.H., Olshen, R.A., Stone C.J.: Classification and Regression Trees Chapman & Hall/CRC, Boca Raton, FL (1984)

    MATH  Google Scholar 

  3. Brookhart, M.A., van der Laan, M.J.: A semiparametric model selection criterion with applications to the marginal structural model. Comput. Stat. Data Anal. 50 (2), 475–498 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  4. Hall, P., Wolff, R.C.L., Yao, Q.: Methods for estimating a conditional distribution function. J. Am. Stat. Assoc. 94 (445), 154–163 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  5. Hansen, L.P.: Large sample properties of generalized method of moments estimators. Econometrica 50 (4), 1029–1054 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  6. Hirano, K., Imbens, G.W.: Estimation of causal effects using propensity score weighting: an application to data on right heart catheterization. Health Serv. Outcome Res. Methodol. 2 (3), 259–278 (2001)

    Article  Google Scholar 

  7. Hirano, K., Imbens, G.W., Ridder, G.: Efficient estimation of average treatment effects using the estimated propensity score. Econometrica 71 (4), 1161–1189 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  8. Imai, K., Ratkovic, M.: Covariate balancing propensity score. J. R. Stat. Soc. Ser. B (Stat Methodol.) 76 (1), 243–263 (2014)

    Google Scholar 

  9. Imai, K., Van Dyk, D.A.: Causal inference with general treatment regimes. J. Am. Stat. Assoc. 99 (467), 854–866 (2004)

    Article  MATH  Google Scholar 

  10. Imbens, G.W.: The role of the propensity score in estimating dose-response functions. Biometrika 87 (3), 706–710 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  11. Kang, J.D.Y., Schafer, J.L.: Demystifying double robustness: a comparison of alternative strategies for estimating a population mean from incomplete data. Stat. Sci. 22 (4), 523–539 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  12. Lechner, M.: Program heterogeneity and propensity score matching: an application to the evaluation of active labor market policies. Rev. Econ. Stat. 84 (2), 205–220 (2002)

    Article  MathSciNet  Google Scholar 

  13. Lee, B.K., Lessler, J., Stuart, E.A.: Improving propensity score weighting using machine learning. Stat. Med. 29 (3), 337–346 (2010)

    MathSciNet  Google Scholar 

  14. Lee, B.K., Lessler, J., Stuart, E.A.: Weight trimming and propensity score weighting. PLoS ONE 6 (3), e18174 (2011)

    Article  Google Scholar 

  15. Lunceford, J.K., Davidian, M.: Stratification and weighting via the propensity score in estimation of causal treatment effects: a comparative study. Stat. Med. 23 (19), 2937–2960 (2004)

    Article  Google Scholar 

  16. McCaffrey, D.F., Ridgeway, G., Morral, A.R.: Propensity score estimation with boosted regression for evaluating causal effects in observational studies. Psychol. Methods 9 (4), 403–425 (2004)

    Article  Google Scholar 

  17. McCaffrey, D.F., Griffin, B.A., Almirall, D., Slaughter, M.E., Ramchand, R., Burgette, L.F.: A tutorial on propensity score estimation for multiple treatments using generalized boosted models. Stat. Med. 32 (19), 3388–3414 (2013)

    Article  MathSciNet  Google Scholar 

  18. Pregibon, D.: Resistant fits for some commonly used logistic models with medical applications. Biometrics 38 (2), 485–498 (1982)

    Article  Google Scholar 

  19. Ridgeway, G., McCaffrey, D., Morral, A., Burgette, L., Griffin, B.A.: Toolkit for weighting and analysis of nonequivalent groups: a tutorial for the twang package. R vignette. RAND, 2015.

    Google Scholar 

  20. Robins, J.M.: Association, causation, and marginal structural models. Synthese 121 (1), 151–179 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  21. Robins, J.M., Hernán, M.Á., Brumback, B.: Marginal structural models and causal inference in epidemiology. Epidemiology. 11 (5), 550–560 (2000)

    Article  Google Scholar 

  22. Rosenbaum, P.R., Rubin, D.B.: The central role of the propensity score in observational studies for causal effects. Biometrika 70 (1), 41–55 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  23. Rubin, D.B.: Estimating causal effects of treatments in randomized and nonrandomized studies. J. Educ. Psychol. 66 (5), 688–701 (1974)

    Article  Google Scholar 

  24. Setoguchi, S., Schneeweiss, S., Brookhart, M.A., Glynn, R.J., Cook, E.F.: Evaluating uses of data mining techniques in propensity score estimation: a simulation study. Pharmacoepidemiol. Drug Saf. 17 (6), 546–555 (2008)

    Article  Google Scholar 

  25. Stuart, E.A., Lee, B.K., Leacy, F.P.: Prognostic score–based balance measures can be a useful diagnostic for propensity score methods in comparative effectiveness research. J. Clin. Epidemiol. 66 (8), S84–S90 (2013)

    Article  Google Scholar 

  26. Székely, G.J., Rizzo, M.L.: Brownian distance covariance. Ann. Appl. Stat. 32 (8), 1236–1265 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  27. Székely, G.J., Rizzo, M.L., Bakirov, N.K.: Measuring and testing dependence by correlation of distances. Ann. Stat. 35 (6), 2769–2794 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  28. Tchernis, R., Horvitz-Lennon, M., Normand, S.L.T.: On the use of discrete choice models for causal inference. Stat. Med. 24 (14), 2197–2212 (2005)

    Article  MathSciNet  Google Scholar 

  29. Venables, W.N., Ripley, B.D.: Modern Applied Statistics with S, 4th edn. Springer, New York (2002). ISBN 0-387-95457-0

    Book  MATH  Google Scholar 

  30. Zhu, Y., Coffman, D.L., Ghosh, D.: A boosting algorithm for estimating generalized propensity scores with continuous treatments. J. Causal Inference 3 (1), 25–40 (2015)

    Article  Google Scholar 

  31. Zhu, Y., Ghosh, D., Mitra, N., Mukherjee, B.: A data-adaptive strategy for inverse weighted estimation of causal effect. Health Serv. Outcome Res. Methodol. 14 (3), 69–91 (2014)

    Article  Google Scholar 

  32. Zhu, Y., Schonbach, M., Coffman, D.L., Williams, J.S.: Variable selection for propensity score estimation via balancing covariates. Epidemiology 26 (2), e14–e15 (2015)

    Article  Google Scholar 

  33. Zhu, Y., Ghosh, D., Coffman, D.L., Savage, J.S.: Estimating controlled direct effects of restrictive feeding practices in the ‘early dieting in girls’ study. J. R. Stat. Soc.: Ser. C: Appl. Stat. 65 (1), 115–130 (2016)

    Google Scholar 

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Correspondence to Yeying Zhu .

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Zhu, Y., (Laura) Lin, L. (2016). Propensity Score Modeling and Evaluation. In: He, H., Wu, P., Chen, DG. (eds) Statistical Causal Inferences and Their Applications in Public Health Research. ICSA Book Series in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-41259-7_6

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