IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v135y2015icp59-70.html
   My bibliography  Save this article

Achieving semiparametric efficiency bound in longitudinal data analysis with dropouts

Author

Listed:
  • Han, Peisong
  • Song, Peter X.-K.
  • Wang, Lu

Abstract

In longitudinal data analysis with dropouts, despite its local efficiency in theory, the augmented inverse probability weighted (AIPW) estimator hardly achieves the semiparametric efficiency bound in practice, even if the variance–covariance of the longitudinal outcomes is correctly modeled. In this paper, we propose a method based on conditional empirical likelihood. Assuming missing at random (MAR) mechanism, our estimator is doubly robust and locally efficient. Unlike the AIPW estimator, our estimator does not require to model any second moments, including the variance–covariance of the longitudinal outcomes, in order to achieve the semiparametric efficiency bound.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:135:y:2015:i:c:p:59-70
    DOI: 10.1016/j.jmva.2014.12.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X14002711
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2014.12.006?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Jian Zhang & Irène Gijbels, 2003. "Sieve Empirical Likelihood and Extensions of the Generalized Least Squares," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(1), pages 1-24, March.
    2. 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.
    3. Zhiqiang Tan, 2010. "Bounded, efficient and doubly robust estimation with inverse weighting," Biometrika, Biometrika Trust, vol. 97(3), pages 661-682.
    4. J. Chen, 2002. "Using empirical likelihood methods to obtain range restricted weights in regression estimators for surveys," Biometrika, Biometrika Trust, vol. 89(1), pages 230-237, March.
    5. 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.
    6. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
    7. Yuichi Kitamura & Gautam Tripathi & Hyungtaik Ahn, 2004. "Empirical Likelihood-Based Inference in Conditional Moment Restriction Models," Econometrica, Econometric Society, vol. 72(6), pages 1667-1714, November.
    8. Jing Qin & Biao Zhang, 2007. "Empirical‐likelihood‐based inference in missing response problems and its application in observational studies," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(1), pages 101-122, February.
    9. Peisong Han & Lu Wang, 2013. "Estimation with missing data: beyond double robustness," Biometrika, Biometrika Trust, vol. 100(2), pages 417-430.
    10. Qin, Jing & Shao, Jun & Zhang, Biao, 2008. "Efficient and Doubly Robust Imputation for Covariate-Dependent Missing Responses," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 797-810, June.
    11. 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.
    12. Heejung Bang & James M. Robins, 2005. "Doubly Robust Estimation in Missing Data and Causal Inference Models," Biometrics, The International Biometric Society, vol. 61(4), pages 962-973, December.
    13. 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.
    14. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    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. 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.
    2. 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.
    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. Wang, Qihua & Su, Miaomiao & Wang, Ruoyu, 2021. "A beyond multiple robust approach for missing response problem," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    5. Peisong Han & Linglong Kong & Jiwei Zhao & Xingcai Zhou, 2019. "A general framework for quantile estimation with incomplete data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(2), pages 305-333, April.
    6. 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.
    7. Y Cui & E J Tchetgen Tchetgen, 2024. "Selective machine learning of doubly robust functionals," Biometrika, Biometrika Trust, vol. 111(2), pages 517-535.
    8. 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.
    9. Satoshi Hattori & Masayuki Henmi, 2014. "Stratified doubly robust estimators for the average causal effect," Biometrics, The International Biometric Society, vol. 70(2), pages 270-277, June.
    10. 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.
    11. Difang Huang & Jiti Gao & Tatsushi Oka, 2022. "Semiparametric Single-Index Estimation for Average Treatment Effects," Papers 2206.08503, arXiv.org, revised Apr 2024.
    12. 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.
    13. 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.
    14. Kwun Chuen Gary Chan & Sheung Chi Phillip Yam & Zheng Zhang, 2016. "Globally efficient non-parametric inference of average treatment effects by empirical balancing calibration weighting," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(3), pages 673-700, June.
    15. Chen, Sixia & Haziza, David, 2018. "Jackknife empirical likelihood method for multiply robust estimation with missing data," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 258-268.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. Lucia Babino & Andrea Rotnitzky & James Robins, 2019. "Multiple robust estimation of marginal structural mean models for unconstrained outcomes," Biometrics, The International Biometric Society, vol. 75(1), pages 90-99, March.

    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:eee:jmvana:v:135:y:2015:i:c:p:59-70. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.