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On varieties of doubly robust estimators under missingness not at random with a shadow variable

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  • Wang Miao
  • Eric J. Tchetgen Tchetgen

Abstract

Suppose we are interested in the mean of an outcome variable missing not at random. Suppose however that one has available a fully observed shadow variable, which is associated with the outcome but independent of the missingness process conditional on covariates and the possibly unobserved outcome. Such a variable may be a proxy or a mismeasured version of the outcome and is available for all individuals. We have previously established necessary and sufficient conditions for identification of the full data law in such a setting, and have described semiparametric estimators including a doubly robust estimator of the outcome mean. Here, we propose two alternative estimators, which may be viewed as extensions of analogous methods under missingness at random, but enjoy different properties. We assess the correctness of the required working models via straightforward goodness-of-fit tests.

Suggested Citation

  • Wang Miao & Eric J. Tchetgen Tchetgen, 2016. "On varieties of doubly robust estimators under missingness not at random with a shadow variable," Biometrika, Biometrika Trust, vol. 103(2), pages 475-482.
    • Handle: RePEc:oup:biomet:v:103:y:2016:i:2:p:475-482.
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    References listed on IDEAS

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    1. Sheng Wang & Jun Shao & Jae Kwang Kim, "undated". "An Instrumental Variable Approach for Identification and Estimation with Nonignorable Nonresponse," Mathematica Policy Research Reports a9593fac2c9746f486d2162f9, Mathematica Policy Research.
    2. repec:mpr:mprres:8160 is not listed on IDEAS
    3. Joseph G. Ibrahim & Stuart R. Lipsitz & Nick Horton, 2001. "Using auxiliary data for parameter estimation with non‐ignorably missing outcomes," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 50(3), pages 361-373.
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    Cited by:

    1. Tianqing Liu & Xiaohui Yuan, 2020. "Doubly robust augmented-estimating-equations estimation with nonignorable nonresponse data," Statistical Papers, Springer, vol. 61(6), pages 2241-2270, December.
    2. Hairu Wang & Zhiping Lu & Yukun Liu, 2023. "Score test for missing at random or not under logistic missingness models," Biometrics, The International Biometric Society, vol. 79(2), pages 1268-1279, June.
    3. Ao Huang & Kosuke Morikawa & Tim Friede & Satoshi Hattori, 2023. "Adjusting for publication bias in meta‐analysis via inverse probability weighting using clinical trial registries," Biometrics, The International Biometric Society, vol. 79(3), pages 2089-2102, September.
    4. Wang, Lei & Zhao, Puying & Shao, Jun, 2021. "Dimension-reduced semiparametric estimation of distribution functions and quantiles with nonignorable nonresponse," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).
    5. Lei Wang & Wei Ma, 2021. "Improved empirical likelihood inference and variable selection for generalized linear models with longitudinal nonignorable dropouts," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(3), pages 623-647, June.
    6. Rui Duan & C. Jason Liang & Pamela Shaw & Cheng Yong Tang & Yong Chen, 2020. "Missing at Random or Not: A Semiparametric Testing Approach," Papers 2003.11181, arXiv.org.
    7. Liu, Tianqing & Yuan, Xiaohui & Sun, Jianguo, 2021. "Weighted rank estimation for nonparametric transformation models with nonignorable missing data," Computational Statistics & Data Analysis, Elsevier, vol. 153(C).
    8. Andrew Bennett & Nathan Kallus & Xiaojie Mao & Whitney Newey & Vasilis Syrgkanis & Masatoshi Uehara, 2022. "Inference on Strongly Identified Functionals of Weakly Identified Functions," Papers 2208.08291, arXiv.org, revised Jun 2023.
    9. Zhang, Jeffrey & Li, Wei & Miao, Wang & Tchetgen Tchetgen, Eric, 2023. "Proximal causal inference without uniqueness assumptions," Statistics & Probability Letters, Elsevier, vol. 198(C).
    10. Yilin Li & Wang Miao & Ilya Shpitser & Eric J. Tchetgen Tchetgen, 2023. "A self‐censoring model for multivariate nonignorable nonmonotone missing data," Biometrics, The International Biometric Society, vol. 79(4), pages 3203-3214, December.
    11. Shonosuke Sugasawa & Kosuke Morikawa & Keisuke Takahata, 2022. "Bayesian semiparametric modeling of response mechanism for nonignorable missing data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 101-117, March.
    12. Pengfei Li & Jing Qin & Yukun Liu, 2023. "Instability of inverse probability weighting methods and a remedy for nonignorable missing data," Biometrics, The International Biometric Society, vol. 79(4), pages 3215-3226, December.

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