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Propensity Score Matching and Subclassification in Observational Studies with Multi-level Treatments

Author

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  • Yang, Shu

    (Harvard University)

  • Imbens, Guido W.

    (Stanford University)

  • Cui, Zhanglin

    (Eli Lilly and Company)

  • Faries, Douglas E.

    (Eli Lilly and Company)

  • Kadziola, Zbigniew

    (Eli Lilly and Company)

Abstract

In this paper, we develop new methods for estimating average treatment effects in observational studies, focusing on settings with more than two treatment levels under unconfoundedness given pre-treatment variables. We emphasize subclassification and matching methods which have been found to be effective in the binary treatment literature and which are among the most popular methods in that setting. Whereas the literature has suggested that these particular propensity-based methods do not naturally extend to the multi-level treatment case, we show, using the concept of weak unconfoundedness, that adjusting for or matching on a scalar function of the pre-treatment variables removes all biases associated with observed pre-treatment variables. We apply the proposed methods to an analysis of the effect of treatments for fibromyalgia. We also carry out a simulation study to assess the finite sample performance of the methods relative to previously proposed methods.

Suggested Citation

  • Yang, Shu & Imbens, Guido W. & Cui, Zhanglin & Faries, Douglas E. & Kadziola, Zbigniew, 2015. "Propensity Score Matching and Subclassification in Observational Studies with Multi-level Treatments," Research Papers 3381, Stanford University, Graduate School of Business.
    • Handle: RePEc:ecl:stabus:3381
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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.
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    5. 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.
    6. Kosuke Imai & Marc Ratkovic, 2014. "Covariate balancing propensity score," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(1), pages 243-263, January.
    7. Alberto Abadie & Guido W. Imbens, 2012. "A Martingale Representation for Matching Estimators," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 833-843, June.
    8. Huber, Martin & Lechner, Michael & Wunsch, Conny, 2013. "The performance of estimators based on the propensity score," Journal of Econometrics, Elsevier, vol. 175(1), pages 1-21.
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    Cited by:

    1. Sokbae Lee & Bernard Salanié, 2018. "Identifying Effects of Multivalued Treatments," Econometrica, Econometric Society, vol. 86(6), pages 1939-1963, November.
    2. Atila Abdulkadiroğlu & Joshua D. Angrist & Yusuke Narita & Parag A. Pathak, 2017. "Research Design Meets Market Design: Using Centralized Assignment for Impact Evaluation," Econometrica, Econometric Society, vol. 85, pages 1373-1432, September.
    3. Shu Yang & Yunshu Zhang, 2023. "Multiply robust matching estimators of average and quantile treatment effects," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(1), pages 235-265, March.
    4. Rachel C. Nethery & Yue Yang & Anna J. Brown & Francesca Dominici, 2020. "A causal inference framework for cancer cluster investigations using publicly available data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(3), pages 1253-1272, June.
    5. María de los Angeles Resa & José R. Zubizarreta, 2020. "Direct and stable weight adjustment in non‐experimental studies with multivalued treatments: analysis of the effect of an earthquake on post‐traumatic stress," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(4), pages 1387-1410, October.
    6. Issahaku, Gazali & Abdulai, Awudu, 2020. "Household welfare implications of sustainable land management practices among smallholder farmers in Ghana," Land Use Policy, Elsevier, vol. 94(C).
    7. Shu Yang & Jae Kwang Kim, 2020. "Asymptotic theory and inference of predictive mean matching imputation using a superpopulation model framework," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(3), pages 839-861, September.
    8. Lee, Ying-Ying, 2018. "Efficient propensity score regression estimators of multivalued treatment effects for the treated," Journal of Econometrics, Elsevier, vol. 204(2), pages 207-222.
    9. Caloffi, Annalisa & Freo, Marzia & Ghinoi, Stefano & Mariani, Marco & Rossi, Federica, 2022. "Assessing the effects of a deliberate policy mix: The case of technology and innovation advisory services and innovation vouchers," Research Policy, Elsevier, vol. 51(6).
    10. Ao Yuan & Anqi Yin & Ming T. Tan, 2021. "Enhanced Doubly Robust Procedure for Causal Inference," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 13(3), pages 454-478, December.
    11. Zhang, Xiaoke & Xue, Wu & Wang, Qiyue, 2021. "Covariate balancing functional propensity score for functional treatments in cross-sectional observational studies," Computational Statistics & Data Analysis, Elsevier, vol. 163(C).
    12. Zetterqvist, Johan & Waernbaum, Ingeborg, 2020. "Semi-parametric estimation of multi-valued treatment effects for the treated:estimating equations and sandwich estimators," Working Paper Series 2020:4, IFAU - Institute for Evaluation of Labour Market and Education Policy.
    13. Pedro H. C. Sant'Anna & Xiaojun Song, 2020. "Specification tests for generalized propensity scores using double projections," Papers 2003.13803, arXiv.org, revised Apr 2023.
    14. Susan Athey & Guido W. Imbens, 2017. "The State of Applied Econometrics: Causality and Policy Evaluation," Journal of Economic Perspectives, American Economic Association, vol. 31(2), pages 3-32, Spring.
    15. Evan D Peet & Edward N Okeke, 2019. "Utilization and quality: How the quality of care influences demand for obstetric care in Nigeria," PLOS ONE, Public Library of Science, vol. 14(2), pages 1-18, February.
    16. Michael C. Knaus, 2021. "A double machine learning approach to estimate the effects of musical practice on student’s skills," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(1), pages 282-300, January.
    17. Ashesh Rambachan & Neil Shephard, 2019. "Econometric analysis of potential outcomes time series: instruments, shocks, linearity and the causal response function," Papers 1903.01637, arXiv.org, revised Feb 2020.
    18. Cei, Leonardo & Stefani, Gianluca & Defrancesco, Edi, 2020. "The role of group-time treatment effect heterogeneity in long standing European agricultural policies. An application to the European geographical indication policy," Bio-based and Applied Economics Journal, Italian Association of Agricultural and Applied Economics (AIEAA), vol. 9(1), April.
    19. Siying Guo & Jianxuan Liu & Qiu Wang, 2022. "Effective Learning During COVID-19: Multilevel Covariates Matching and Propensity Score Matching," Annals of Data Science, Springer, vol. 9(5), pages 967-982, October.
    20. Hajime Seya & Takahiro Yoshida, 2017. "Propensity score matching for multiple treatment levels: A CODA-based contribution," Papers 1710.08558, arXiv.org.
    21. Yu, Haiyan & Yang, Ching-Chi & Yu, Ping, 2023. "Constrained optimization for stratified treatment rules in reducing hospital readmission rates of diabetic patients," European Journal of Operational Research, Elsevier, vol. 308(3), pages 1355-1364.
    22. Ganesh Karapakula, 2023. "Stable Probability Weighting: Large-Sample and Finite-Sample Estimation and Inference Methods for Heterogeneous Causal Effects of Multivalued Treatments Under Limited Overlap," Papers 2301.05703, arXiv.org, revised Jan 2023.

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