IDEAS home Printed from https://ideas.repec.org/a/bpj/causin/v8y2020i1p300-314n12.html
   My bibliography  Save this article

Improved Doubly Robust Estimation in Marginal Mean Models for Dynamic Regimes

Author

Listed:
  • Sun Hao

    (Uber Technologies Inc, San Francisco, 94103, California, United States of America)

  • Ertefaie Ashkan

    (Department of Biostatistics and Computational Biology, University of Rochester, Rochester, 14642, New York, United States of America)

  • Lu Xin

    (Department of Biostatistics and Programming, Sanofi, Bridgewater, 07657, New Jersey, United States of America)

  • Johnson Brent A.

    (Department of Biostatistics and Computational Biology, University of Rochester, Rochester, 14642, New York, United States of America)

Abstract

Doubly robust (DR) estimators are an important class of statistics derived from a theory of semiparametric efficiency. They have become a popular tool in causal inference, including applications to dynamic treatment regimes. The doubly robust estimators for the mean response to a dynamic treatment regime may be conceived through the augmented inverse probability weighted (AIPW) estimating function, defined as the sum of the inverse probability weighted (IPW) estimating function and an augmentation term. The IPW estimating function of the causal estimand via marginal structural model is defined as the complete-case score function for those subjects whose treatment sequence is consistent with the dynamic regime in question divided by the probability of observing the treatment sequence given the subject's treatment and covariate histories. The augmentation term is derived by projecting the IPW estimating function onto the nuisance tangent space and has mean-zero under the truth. The IPW estimator of the causal estimand is consistent if (i) the treatment assignment mechanism is correctly modeled and the AIPW estimator is consistent if either (i) is true or (ii) nested functions of intermediate and final outcomes are correctly modeled.Hence, the AIPW estimator is doubly robust and, moreover, the AIPW is semiparametric efficient if both (i) and (ii) are true simultaneously. Unfortunately, DR estimators can be inferior when either (i) or (ii) is true and the other false. In this case, the misspecified parts of the model can have a detrimental effect on the variance of the DR estimator. We propose an improved DR estimator of causal estimand in dynamic treatment regimes through a technique originally developed by [4] which aims to mitigate the ill-effects of model misspecification through a constrained optimization.In addition to solving a doubly robust system of equations, the improved DR estimator simultaneously minimizes the asymptotic variance of the estimator under a correctly specified treatment assignment mechanism but misspecification of intermediate and final outcome models. We illustrate the desirable operating characteristics of the estimator through Monte Carlo studies and apply the methods to data from a randomized study of integrilin therapy for patients undergoing coronary stent implantation. The methods proposed here are new and may be used to further improve personalized medicine, in general.

Suggested Citation

  • Sun Hao & Ertefaie Ashkan & Lu Xin & Johnson Brent A., 2020. "Improved Doubly Robust Estimation in Marginal Mean Models for Dynamic Regimes," Journal of Causal Inference, De Gruyter, vol. 8(1), pages 300-314, January.
    • Handle: RePEc:bpj:causin:v:8:y:2020:i:1:p:300-314:n:12
    DOI: 10.1515/jci-2020-0015
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/jci-2020-0015
    Download Restriction: no
    File URL: https://libkey.io/10.1515/jci-2020-0015?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. repec:bla:biomet:v:71:y:2015:i:4:p:867-874 is not listed on IDEAS
    2. D Benkeser & M Carone & M J Van Der Laan & P B Gilbert, 2017. "Doubly robust nonparametric inference on the average treatment effect," Biometrika, Biometrika Trust, vol. 104(4), pages 863-880.
    3. Anastasios A. Tsiatis & Marie Davidian & Weihua Cao, 2011. "Improved Doubly Robust Estimation When Data Are Monotonely Coarsened, with Application to Longitudinal Studies with Dropout," Biometrics, The International Biometric Society, vol. 67(2), pages 536-545, June.
    4. Zhiqiang Tan, 2010. "Bounded, efficient and doubly robust estimation with inverse weighting," Biometrika, Biometrika Trust, vol. 97(3), pages 661-682.
    5. Murphy S.A. & van der Laan M.J. & Robins J.M., 2001. "Marginal Mean Models for Dynamic Regimes," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1410-1423, December.
    6. Tan, Zhiqiang, 2006. "A Distributional Approach for Causal Inference Using Propensity Scores," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1619-1637, December.
    7. Jing Qin & Biao Zhang & Denis H.Y. Leung, 2017. "Efficient Augmented Inverse Probability Weighted Estimation in Missing Data Problems," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(1), pages 86-97, January.
    8. Weihua Cao & Anastasios A. Tsiatis & Marie Davidian, 2009. "Improving efficiency and robustness of the doubly robust estimator for a population mean with incomplete data," Biometrika, Biometrika Trust, vol. 96(3), pages 723-734.
    9. van der Laan Mark J. & Rubin Daniel, 2006. "Targeted Maximum Likelihood Learning," The International Journal of Biostatistics, De Gruyter, vol. 2(1), pages 1-40, December.
    10. Brent A. Johnson & Anastasios A. Tsiatis, 2004. "Estimating Mean Response as a Function of Treatment Duration in an Observational Study, Where Duration May Be Informatively Censored," Biometrics, The International Biometric Society, vol. 60(2), pages 315-323, June.
    11. repec:bla:biomet:v:71:y:2015:i:4:p:881-883 is not listed on IDEAS
    12. Andrea Rotnitzky & Quanhong Lei & Mariela Sued & James M. Robins, 2012. "Improved double-robust estimation in missing data and causal inference models," Biometrika, Biometrika Trust, vol. 99(2), pages 439-456.
    13. Xin Lu & Brent A. Johnson, 2015. "Direct estimation of the mean outcome on treatment when treatment assignment and discontinuation compete," Biometrika, Biometrika Trust, vol. 102(4), pages 797-807.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Iván Díaz & Elizabeth Colantuoni & Daniel F. Hanley & Michael Rosenblum, 2019. "Improved precision in the analysis of randomized trials with survival outcomes, without assuming proportional hazards," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(3), pages 439-468, July.
    2. Jianxuan Liu & Yanyuan Ma & Lan Wang, 2018. "An alternative robust estimator of average treatment effect in causal inference," Biometrics, The International Biometric Society, vol. 74(3), pages 910-923, September.
    3. Zhiwei Zhang & Zhen Chen & James F. Troendle & Jun Zhang, 2012. "Causal Inference on Quantiles with an Obstetric Application," Biometrics, The International Biometric Society, vol. 68(3), pages 697-706, September.
    4. Karel Vermeulen & Stijn Vansteelandt, 2015. "Bias-Reduced Doubly Robust Estimation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1024-1036, September.
    5. Słoczyński, Tymon & Wooldridge, Jeffrey M., 2018. "A General Double Robustness Result For Estimating Average Treatment Effects," Econometric Theory, Cambridge University Press, vol. 34(1), pages 112-133, February.
    6. repec:bla:istatr:v:83:y:2015:i:3:p:449-471 is not listed on IDEAS
    7. Peisong Han, 2014. "Multiply Robust Estimation in Regression Analysis With Missing Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1159-1173, September.
    8. Han, Peisong & Song, Peter X.-K. & Wang, Lu, 2015. "Achieving semiparametric efficiency bound in longitudinal data analysis with dropouts," Journal of Multivariate Analysis, Elsevier, vol. 135(C), pages 59-70.
    9. 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.
    10. Y Cui & E J Tchetgen Tchetgen, 2024. "Selective machine learning of doubly robust functionals," Biometrika, Biometrika Trust, vol. 111(2), pages 517-535.
    11. Hao Cheng & Ying Wei, 2018. "A fast imputation algorithm in quantile regression," Computational Statistics, Springer, vol. 33(4), pages 1589-1603, December.
    12. Xiaogang Duan & Guosheng Yin, 2017. "Ensemble Approaches to Estimating the Population Mean with Missing Response," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(4), pages 899-917, December.
    13. Weibin Mo & Yufeng Liu, 2022. "Efficient learning of optimal individualized treatment rules for heteroscedastic or misspecified treatment‐free effect models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(2), pages 440-472, April.
    14. Difang Huang & Jiti Gao & Tatsushi Oka, 2022. "Semiparametric Single-Index Estimation for Average Treatment Effects," Papers 2206.08503, arXiv.org, revised Apr 2024.
    15. Wang, Qihua & Su, Miaomiao & Wang, Ruoyu, 2021. "A beyond multiple robust approach for missing response problem," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    16. Han, Peisong, 2012. "A note on improving the efficiency of inverse probability weighted estimator using the augmentation term," Statistics & Probability Letters, Elsevier, vol. 82(12), pages 2221-2228.
    17. David Cheng & Ashwin N. Ananthakrishnan & Tianxi Cai, 2021. "Robust and efficient semi‐supervised estimation of average treatment effects with application to electronic health records data," Biometrics, The International Biometric Society, vol. 77(2), pages 413-423, June.
    18. Peisong Han, 2016. "Combining Inverse Probability Weighting and Multiple Imputation to Improve Robustness of Estimation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 246-260, March.
    19. Huiming Lin & Bo Fu & Guoyou Qin & Zhongyi Zhu, 2017. "Doubly robust estimation of generalized partial linear models for longitudinal data with dropouts," Biometrics, The International Biometric Society, vol. 73(4), pages 1132-1139, December.
    20. AmirEmad Ghassami & Andrew Ying & Ilya Shpitser & Eric Tchetgen Tchetgen, 2021. "Minimax Kernel Machine Learning for a Class of Doubly Robust Functionals with Application to Proximal Causal Inference," Papers 2104.02929, arXiv.org, revised Mar 2022.
    21. Vermeulen Karel & Vansteelandt Stijn, 2016. "Data-Adaptive Bias-Reduced Doubly Robust Estimation," The International Journal of Biostatistics, De Gruyter, vol. 12(1), pages 253-282, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bpj:causin:v:8:y:2020:i:1:p:300-314:n:12. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.