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Data-Adaptive Bias-Reduced Doubly Robust Estimation

Author

Listed:
  • Vermeulen Karel
  • Vansteelandt Stijn

    (Department of Applied Mathematics, Computer Science and Statistics, Ghent University, Ghent, Belgium)

Abstract

Doubly robust estimators have now been proposed for a variety of target parameters in the causal inference and missing data literature. These consistently estimate the parameter of interest under a semiparametric model when one of two nuisance working models is correctly specified, regardless of which. The recently proposed bias-reduced doubly robust estimation procedure aims to partially retain this robustness in more realistic settings where both working models are misspecified. These so-called bias-reduced doubly robust estimators make use of special (finite-dimensional) nuisance parameter estimators that are designed to locally minimize the squared asymptotic bias of the doubly robust estimator in certain directions of these finite-dimensional nuisance parameters under misspecification of both parametric working models. In this article, we extend this idea to incorporate the use of data-adaptive estimators (infinite-dimensional nuisance parameters), by exploiting the bias reduction estimation principle in the direction of only one nuisance parameter. We additionally provide an asymptotic linearity theorem which gives the influence function of the proposed doubly robust estimator under correct specification of a parametric nuisance working model for the missingness mechanism/propensity score but a possibly misspecified (finite- or infinite-dimensional) outcome working model. Simulation studies confirm the desirable finite-sample performance of the proposed estimators relative to a variety of other doubly robust estimators.

Suggested Citation

  • 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.
    • Handle: RePEc:bpj:ijbist:v:12:y:2016:i:1:p:253-282:n:12
    DOI: 10.1515/ijb-2015-0029
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Rubin Daniel B & van der Laan Mark J., 2008. "Empirical Efficiency Maximization: Improved Locally Efficient Covariate Adjustment in Randomized Experiments and Survival Analysis," The International Journal of Biostatistics, De Gruyter, vol. 4(1), pages 1-40, May.
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