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Covariate association eliminating weights: a unified weighting framework for causal effect estimation

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  • Sean Yiu
  • Li Su

Abstract

SummaryWeighting methods offer an approach to estimating causal treatment effects in observational studies. However, if weights are estimated by maximum likelihood, misspecification of the treatment assignment model can lead to weighted estimators with substantial bias and variance. In this paper, we propose a unified framework for constructing weights such that a set of measured pretreatment covariates is unassociated with treatment assignment after weighting. We derive conditions for weight estimation by eliminating the associations between these covariates and treatment assignment characterized in a chosen treatment assignment model after weighting. The moment conditions in covariate balancing weight methods for binary, categorical and continuous treatments in cross-sectional settings are special cases of the conditions in our framework, which extends to longitudinal settings. Simulation shows that our method gives treatment effect estimates with smaller biases and variances than the maximum likelihood approach under treatment assignment model misspecification. We illustrate our method with an application to systemic lupus erythematosus data.

Suggested Citation

  • Sean Yiu & Li Su, 2018. "Covariate association eliminating weights: a unified weighting framework for causal effect estimation," Biometrika, Biometrika Trust, vol. 105(3), pages 709-722.
    • Handle: RePEc:oup:biomet:v:105:y:2018:i:3:p:709-722.
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    File URL: http://hdl.handle.net/10.1093/biomet/asy015
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    References listed on IDEAS

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    Cited by:

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    2. Tübbicke Stefan, 2022. "Entropy Balancing for Continuous Treatments," Journal of Econometric Methods, De Gruyter, vol. 11(1), pages 71-89, January.
    3. Chunrong Ai & Lukang Huang & Zheng Zhang, 2018. "A Simple and Efficient Estimation of the Average Treatment Effect in the Presence of Unmeasured Confounders," Papers 1807.05678, arXiv.org.
    4. Chunrong Ai & Oliver Linton & Kaiji Motegi & Zheng Zhang, 2021. "A unified framework for efficient estimation of general treatment models," Quantitative Economics, Econometric Society, vol. 12(3), pages 779-816, July.
    5. Cerqua Augusto & Di Stefano Roberta & Mattera Raffaele, 2024. "The Clustered Dose-Response Function Estimator for continuous treatment with heterogeneous treatment effects," Papers 2409.08773, arXiv.org.
    6. Yukitoshi Matsushita & Taisuke Otsu & Keisuke Takahata, 2022. "Estimating density ratio of marginals to joint: Applications to causal inference," STICERD - Econometrics Paper Series 619, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    7. Vahe Avagyan & Stijn Vansteelandt, 2021. "Stable inverse probability weighting estimation for longitudinal studies," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(3), pages 1046-1067, September.
    8. Sean Yiu & Li Su, 2022. "Joint calibrated estimation of inverse probability of treatment and censoring weights for marginal structural models," Biometrics, The International Biometric Society, vol. 78(1), pages 115-127, March.
    9. Hamori, Shigeyuki & Motegi, Kaiji & Zhang, Zheng, 2019. "Calibration estimation of semiparametric copula models with data missing at random," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 85-109.
    10. Davide Viviano & Jelena Bradic, 2021. "Dynamic covariate balancing: estimating treatment effects over time with potential local projections," Papers 2103.01280, arXiv.org, revised Jan 2024.
    11. Yuqian Zhang & Weijie Ji & Jelena Bradic, 2021. "Dynamic treatment effects: high-dimensional inference under model misspecification," Papers 2111.06818, arXiv.org, revised Jun 2023.
    12. 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).
    13. Cousineau, Martin & Verter, Vedat & Murphy, Susan A. & Pineau, Joelle, 2023. "Estimating causal effects with optimization-based methods: A review and empirical comparison," European Journal of Operational Research, Elsevier, vol. 304(2), pages 367-380.

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