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Data-adaptive bias-reduced doubly robust estimation

Karel Vermeulen (UGent) and Stijn Vansteelandt (UGent)
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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 work- ing 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.
Keywords
causal inference, bias-reduced doubly robust estimation, double robustness, missing data, nuisance parameters, super-learning, working models, targeted maximum likelihood estimation (tmle), DEMYSTIFYING DOUBLE ROBUSTNESS, CAUSAL INFERENCE MODELS, INCOMPLETE DATA, MISSING DATA, ALTERNATIVE STRATEGIES, COVARIATE ADJUSTMENT, TRIALS

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Chicago
Vermeulen, Karel, and Stijn Vansteelandt. 2016. “Data-adaptive Bias-reduced Doubly Robust Estimation.” International Journal of Biostatistics 12 (1): 253–282.
APA
Vermeulen, Karel, & Vansteelandt, S. (2016). Data-adaptive bias-reduced doubly robust estimation. INTERNATIONAL JOURNAL OF BIOSTATISTICS, 12(1), 253–282.
Vancouver
1.
Vermeulen K, Vansteelandt S. Data-adaptive bias-reduced doubly robust estimation. INTERNATIONAL JOURNAL OF BIOSTATISTICS. 2016;12(1):253–82.
MLA
Vermeulen, Karel, and Stijn Vansteelandt. “Data-adaptive Bias-reduced Doubly Robust Estimation.” INTERNATIONAL JOURNAL OF BIOSTATISTICS 12.1 (2016): 253–282. Print.
@article{7235060,
  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 work- ing 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.},
  author       = {Vermeulen, Karel and Vansteelandt, Stijn},
  issn         = {2194-573X},
  journal      = {INTERNATIONAL JOURNAL OF BIOSTATISTICS},
  keyword      = {causal inference,bias-reduced doubly robust estimation,double robustness,missing data,nuisance parameters,super-learning,working models,targeted maximum likelihood estimation (tmle),DEMYSTIFYING DOUBLE ROBUSTNESS,CAUSAL INFERENCE MODELS,INCOMPLETE DATA,MISSING DATA,ALTERNATIVE STRATEGIES,COVARIATE ADJUSTMENT,TRIALS},
  language     = {eng},
  number       = {1},
  pages        = {253--282},
  title        = {Data-adaptive bias-reduced doubly robust estimation},
  url          = {http://dx.doi.org/10.1515/ijb-2015-0029},
  volume       = {12},
  year         = {2016},
}

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