SpringerLink
Log in

An Alternative Doubly Robust Estimation in Causal Inference Model

  • Published:
Communications in Mathematics and Statistics Aims and scope Submit manuscript

Abstract

Doubly robust (DR) methods that employ both the propensity score and outcome models are widely used to estimate the causal effect of a treatment and generally outperform those methods only using the propensity score or the outcome model. However, without appropriately chosen the working models, DR estimators may substantially lose efficiency. In this paper, based on the augmented inverse probability weighting procedure, we derive a new estimating equation for the causal effect by the strategy of combining estimating equations. The resulting estimator by solving the new estimating equation retains doubly robust and can improve the efficiency under the misspecification of conditional mean working model. We further show the large sample properties of the proposed estimator under some regularity conditions. Through simulation experiments and a real data analysis, we illustrate that the proposed method is competitive with its competitors, which is in line with those implied by the asymptotic theory.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Austin, P.C.: The performance of different propensity score methods for estimating marginal hazard ratios. Stat. Med. 32, 2837–2849 (2013)

    Article  MathSciNet  Google Scholar 

  2. Bang, H., Robins, J.M.: Doubly robust estimation in missing data and causal inference models. Biometrics 61, 962–973 (2005)

    Article  MathSciNet  Google Scholar 

  3. Benkeser, D., Carone, M., Laan, M.J.V.D., Gilbert, P.B.: Doubly robust nonparametric inference on the average treatment effect. Biometrika 104, 863–880 (2017)

    Article  MathSciNet  Google Scholar 

  4. Cao, W., Tsiatis, A.A., Davidian, M.: Improving efficiency and robustness of the doubly robust estimator for a population mean with incomplete data. Biometrika 96, 723–734 (2009)

    Article  MathSciNet  Google Scholar 

  5. Cattaneo, M.D.: Efficient semiparametric estimation of multi-valued treatment effects under ignorability. J. Econom. 155, 138–154 (2010)

    Article  MathSciNet  Google Scholar 

  6. Dehejia, R.H., Wahba, S.: Causal effects in nonexperimental studies: Reevaluating the evaluation of training programs. J. Am. Stat. Assoc. 94, 1053–1062 (1999)

    Article  Google Scholar 

  7. Firpo, S.: Efficient semiparametric estimation of quantile treatment effects. Econometrica 75, 259–276 (2007)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  11. LaLonde, R.J.: Evaluating the econometric evaluations of training programs with experimental data. Am. Econ. Rev. 76, 604–620 (1986)

    Google Scholar 

  12. Linden, A., Adams, J.L.: Using propensity score-based weighting in the evaluation of health management programme effectiveness. J. Eval. Clin. Pract. 16, 175–179 (2010)

    Article  Google Scholar 

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

    Article  Google Scholar 

  14. Newey, W.K., McFadden, D.: Large sample estimation and hypothesis testing. In: Engle, R., McFadden, D. (eds.) Handbook of Econometrics, pp. 2111–2245. Elsevier, Amsterdam (1994)

    Google Scholar 

  15. Neyman, J.: On the application of probability theory to agricultural experiments. Essay on principles, section 9. translation of original 1923 paper, which appeared in roczniki nauk rolniczych. Stat. Sci. 5, 465–472 (1990)

    Google Scholar 

  16. Qin, J., Zhang, B., Leung, D.H.: Efficient augmented inverse probability weighted estimation in missing data problems. J. Bus. Econ. Stat. 35, 86–97 (2017)

    Article  MathSciNet  Google Scholar 

  17. Ridgeway, G., McCaffrey, D.F.: Comment: Demystifying double robustness: a comparison of alternative strategies for estimating a population mean from incomplete data. Stat. Sci. 22, 540–543 (2007)

    Article  Google Scholar 

  18. Robins, J., Rotnitzky, A., Zhao, L.: Estimation of regression coefficients when some regressors are not always observed. J. Am. Stat. Assoc. 89, 846–866 (1994)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  20. Robins, J.M., Hernan, M.A., Brumback, B.: Marginal structural models and causal inference in epidemiology. Epidemiology 11, 550–560 (2000)

    Article  Google Scholar 

  21. Robins, J.M., Rotnitzky, A., Zhao, L.P.: Analysis of semiparametric regression models for repeated outcomes in the presence of missing data. J. Am. Stat. Assoc. 90, 106–121 (1995)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  24. Rubin, D.B.: Randomization analysis of experimental data: the fisher randomization test comment. J. Am. Stat. Assoc. 75, 591–593 (1980)

    Google Scholar 

  25. Rubin, D.B., van der Laan, M.J.: Empirical efficiency maximization: improved locally efficient covariate adjustment in randomized experiments and survival analysis. Int. J. Biostat. 4, 1–40 (2008)

    MathSciNet  Google Scholar 

  26. Scharfstein, D.O., Rotnitzky, A., Robins, J.M.: Adjusting for nonignorable drop-out using semiparametric nonresponse models. J. Am. Stat. Assoc. 94, 1096–1120 (1999)

    Article  MathSciNet  Google Scholar 

  27. Smith, J.A., Todd, P.E.: Does matching overcome LaLondes critique of nonexperimental estimators? J. Econom. 125, 305–353 (2005)

    Article  MathSciNet  Google Scholar 

  28. Tan, Z.: Comment: Understanding OR. PS and DR. Stat. Sci. 22, 560–568 (2007)

    MATH  Google Scholar 

  29. Tan, Z.: Bounded, efficient and doubly robust estimation with inverse weighting. Biometrika 97, 661–682 (2010)

    Article  MathSciNet  Google Scholar 

  30. Tsiatis, A.: Semiparametric Theory and Missing Data. Springer, New York (2006)

    MATH  Google Scholar 

  31. Uysal, S.D.: Doubly robust estimation of causal effects with multivalued treatments: an application to the returns to schooling. J. Appl. Econom. 30, 763–786 (2015)

    Article  MathSciNet  Google Scholar 

  32. van der Laan, M.J., Rose, S.: Targeted Learning: Causal Inference for Observational and Experimental Data. Springer, Berlin (2011)

    Book  Google Scholar 

  33. Vansteelandt, S., Bekaert, M., Claeskens, G.: On model selection and model misspecification in causal inference. Stat. Methods Med. Res. 21, 7–30 (2012)

    Article  MathSciNet  Google Scholar 

  34. Vermeulen, K., Vansteelandt, S.: Bias-reduced doubly robust estimation. J. Am. Stat. Assoc. 110, 1024–1036 (2015)

    Article  MathSciNet  Google Scholar 

  35. Vermeulen, K., Vansteelandt, S.: Data-adaptive bias-reduced doubly robust estimation. Int. J. Biostat. 12, 253–282 (2016)

    Article  MathSciNet  Google Scholar 

  36. Wooldridge, J.M.: Inverse probability weighted estimation for general missing data problems. J. Econom. 141, 1281–1301 (2007)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The authors are grateful to the editor, the field editor and the two anonymous referees for the constructive comments and suggestions that led to significant improvement of an early manuscript. The researches of Shaojie Wei and Zhongzhan Zhang were partly supported by the National Natural Science Foundation of China (No. 11771032 and No.11971045) and Natural Science Foundation of Bei**g (No. 1202001). Gaorong Li’s research was supported by the National Natural Science Foundation of China (No. 11871001, No. 12131006 and No. 11971001) and the Fundamental Research Funds for the Central Universities (2019NTSS18).

Author information

Authors and Affiliations

  1. Faculty of Science, Bei**g University of Technology, Bei**g, 100124, People’s Republic of China

    Shaojie Wei & Zhongzhan Zhang

  2. School of Statistics, Bei**g Normal University, Bei**g, 100875, People’s Republic of China

    Gaorong Li

Authors
  1. Shaojie Wei
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gaorong Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhongzhan Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhongzhan Zhang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wei, S., Li, G. & Zhang, Z. An Alternative Doubly Robust Estimation in Causal Inference Model. Commun. Math. Stat. (2022). https://doi.org/10.1007/s40304-022-00308-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40304-022-00308-4

Keywords

Mathematics Subject Classification

Search

Navigation