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Regularized calibrated estimation of propensity scores with model misspecification and high-dimensional data

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  • Z Tan

Abstract

SummaryPropensity scores are widely used with inverse probability weighting to estimate treatment effects in observational studies. We study calibrated estimation as an alternative to maximum likelihood estimation for fitting logistic propensity score models. We show that, with possible model misspecification, minimizing the expected calibration loss underlying the calibrated estimators involves reducing both the expected likelihood loss and a measure of relative errors between the limiting and true propensity scores, which governs the mean squared errors of inverse probability weighted estimators. Furthermore, we derive a regularized calibrated estimator by minimizing the calibration loss with a lasso penalty. We develop a Fisher scoring descent algorithm for computing the proposed estimator and provide a high-dimensional analysis of the resulting inverse probability weighted estimators, leveraging the control of relative errors of propensity scores for calibrated estimation. We present a simulation study and an empirical application to demonstrate the advantages of the proposed methods over maximum likelihood and its regularization. The methods are implemented in the R package RCAL.

Suggested Citation

  • Z Tan, 2020. "Regularized calibrated estimation of propensity scores with model misspecification and high-dimensional data," Biometrika, Biometrika Trust, vol. 107(1), pages 137-158.
    • Handle: RePEc:oup:biomet:v:107:y:2020:i:1:p:137-158.
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    File URL: http://hdl.handle.net/10.1093/biomet/asz059
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    Citations

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    Cited by:

    1. Kuanhao Jiang & Rajarshi Mukherjee & Subhabrata Sen & Pragya Sur, 2022. "A New Central Limit Theorem for the Augmented IPW Estimator: Variance Inflation, Cross-Fit Covariance and Beyond," Papers 2205.10198, arXiv.org, revised Oct 2022.
    2. Lan Wen & Miguel A. Hernán & James M. Robins, 2022. "Multiply robust estimators of causal effects for survival outcomes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(3), pages 1304-1328, September.
    3. Shixiao Zhang & Peisong Han & Changbao Wu, 2023. "Calibration Techniques Encompassing Survey Sampling, Missing Data Analysis and Causal Inference," International Statistical Review, International Statistical Institute, vol. 91(2), pages 165-192, August.
    4. Joseph Antonelli & Georgia Papadogeorgou & Francesca Dominici, 2022. "Causal inference in high dimensions: A marriage between Bayesian modeling and good frequentist properties," Biometrics, The International Biometric Society, vol. 78(1), pages 100-114, March.
    5. Haiyan Yu & Bing Han & Nicholas Rios & Jianbin Chen, 2024. "Missing Data Imputation in Balanced Construction for Incomplete Block Designs," Mathematics, MDPI, vol. 12(21), pages 1-22, October.
    6. 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.
    7. Zhiqiang Tan, 2023. "Consistent and robust inference in hazard probability and odds models with discrete-time survival data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(3), pages 555-584, July.
    8. Y Cui & E J Tchetgen Tchetgen, 2024. "Selective machine learning of doubly robust functionals," Biometrika, Biometrika Trust, vol. 111(2), pages 517-535.
    9. Dasom Lee & Shu Yang & Lin Dong & Xiaofei Wang & Donglin Zeng & Jianwen Cai, 2023. "Improving trial generalizability using observational studies," Biometrics, The International Biometric Society, vol. 79(2), pages 1213-1225, June.
    10. Heejun Shin & Joseph Antonelli, 2023. "Improved inference for doubly robust estimators of heterogeneous treatment effects," Biometrics, The International Biometric Society, vol. 79(4), pages 3140-3152, December.

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