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Variance reduction in the inverse probability weighted estimators for the average treatment effect using the propensity score

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  • Jiangang Liao
  • Charles Rohde

Abstract

The propensity methodology is widely used in medical research to compare different treatments in designs with a nonrandomized treatment allocation. The inverse probability weighted (IPW) estimators are a primary tool for estimating the average treatment effect but the large variance of these estimators is often a significant concern for their reliable use in practice. Inspired by Rao‐Blackwellization, this paper proposes a method to smooth an IPW estimator by replacing the weights in the original estimator by their mean over a distribution of the potential treatment assignment. In our simulation study, the smoothed IPW estimator achieves a substantial variance reduction over its original version with only a small increased bias, for example two‐to‐sevenfold variance reduction for the three IPW estimators in Lunceford and Davidian [Statistics in Medicine, 23(19), 2937–2960]. In addition, our proposed smoothing can also be applied to the locally efficient and doubly robust estimator for added protection against model misspecification. An implementation in R is provided.

Suggested Citation

  • Jiangang Liao & Charles Rohde, 2022. "Variance reduction in the inverse probability weighted estimators for the average treatment effect using the propensity score," Biometrics, The International Biometric Society, vol. 78(2), pages 660-667, June.
    • Handle: RePEc:bla:biomet:v:78:y:2022:i:2:p:660-667
    DOI: 10.1111/biom.13454
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    References listed on IDEAS

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    1. Richard K. Crump & V. Joseph Hotz & Guido W. Imbens & Oscar A. Mitnik, 2009. "Dealing with limited overlap in estimation of average treatment effects," Biometrika, Biometrika Trust, vol. 96(1), pages 187-199.
    2. Matias Busso & John DiNardo & Justin McCrary, 2014. "New Evidence on the Finite Sample Properties of Propensity Score Reweighting and Matching Estimators," The Review of Economics and Statistics, MIT Press, vol. 96(5), pages 885-897, December.
    3. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2003. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometrica, Econometric Society, vol. 71(4), pages 1161-1189, July.
    4. Glynn, Adam N. & Quinn, Kevin M., 2010. "An Introduction to the Augmented Inverse Propensity Weighted Estimator," Political Analysis, Cambridge University Press, vol. 18(1), pages 36-56, January.
    5. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881, September.
    6. Brian K Lee & Justin Lessler & Elizabeth A Stuart, 2011. "Weight Trimming and Propensity Score Weighting," PLOS ONE, Public Library of Science, vol. 6(3), pages 1-6, March.
    7. Fan Li & Kari Lock Morgan & Alan M. Zaslavsky, 2018. "Balancing Covariates via Propensity Score Weighting," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(521), pages 390-400, January.
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