Improving efficiency and robustness of the doubly robust estimator for a population mean with incomplete data

By Weihua Cao, Anastasios A. Tsiatis, Marie Davidian. 2009

352 citations recorded by the source corpus.

Abstract Considerable recent interest has focused on doubly robust estimators for a population mean response in the presence of incomplete data, which involve models for both the propensity score and the regression of outcome on covariates. The usual doubly robust estimator may yield severely biased inferences if neither of these models is correctly specified and can exhibit nonnegligible bias if the estimated propensity score is close to zero for some observations. We propose alternative doubly robust estimators that achieve comparable or improved performance relative to existing methods, even with some estimated propensity scores close to zero.

Subfields: Statistics and Probability

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Citations in the corpus

Intrinsically Efficient, Stable, and Bounded Off-Policy Evaluation for Reinforcement Learning (2019, background): “2, [4, 6, 26] further suggest that to pick τ̂ to minimize an estimate of the asymptotic variance of β̂d({q(x, a; τ)}T−1 t=0 ), leading to the MDR estimator [6] for OPE.”
More Robust Doubly Robust Off-policy Evaluation (2018, background): “This idea has been investigated in statistics in the context of regression when the labels of a subset of samples are randomly missing (Cao et al., 2009).”
Review of inverse probability weighting for dealing with missing data (2013, methodology): “Similarly, Ridgeway and McCaffrey(44) propose using a generalised boosted model, Folsom and Witt(45) propose using constrained logistic regression, and Cao et al.(46) propose an enhanced logistic regression model that contains ordinary logistic regression as a special case.”
Bias-Reduced Doubly Robust Estimation (2015, methodology): “Rubin and van der Laan (2008), Cao et al. (2009) and Tsiatis et al. (2011) developed doubly robust estimators in specific missing data models with desirable efficiency properties when the missingness model is correctly specified. In their development, which generalizes that of Tan (2006), the nuisan”
On model selection and model misspecification in causal inference (2012, neutral): “With a different attainment goal in mind, namely improving the stability of inverse weighting procedures, Cao et al.(60) make a related, although different proposal in a missing data context.”
Multiply Robust Estimation in Regression Analysis With Missing Data (2014, background): “It is worth to mention that the idea of regularizing the weights to improve the numerical performance was also taken by Cao, Tsiatis, and Davidian (2009), who proposed to explicitly impose a constraint∑m i=1 1/π̂ (Xi , Si) = n to drive the near-zero values of π̂ (X, S) away from zero.”
Combining Inverse Probability Weighting and Multiple Imputation to Improve Robustness of Estimation (2016, background): “W Iˇ/ j Zº; for more discussions on AIPW estimators and double robustness, please refer to van der Laan & Robins (2003), Bang & Robins (2005), Tsiatis (2006), Qin & Zhang (2007), Cao et al. (2009), Tan (2010), van der Laan and Gruber (2010) and Rotnitzky et al. (2012).”
A Robust Method for Estimating Optimal Treatment Regimes (2012, methodology): “For example, Gail and Simon (1985) considered data from a trial conducted by the National Surgical Adjuvant Breast and Bowel Project (NSABP) comparing L-phenylalanine mustard and 5fluorouracil (PF) to PF plus tamoxifen (PFT) in patients with primary operable breast cancer and positive nodes (Fisher ”
A GENERAL DOUBLE ROBUSTNESS RESULT FOR ESTIMATING AVERAGE TREATMENT EFFECTS (2014, background): “In particular, Cao, Tsiatis, and Davidian (2009) and Tan (2010) provided new estimators with increased efficiency and improved robustness against very small values of the propensity score.”
Globally efficient non-parametric inference of average treatment effects by empirical balancing calibration weighting (2015, methodology): “…prediction estimators (Oaxaca, 1973; Cheng, 1994; Imbens et al., 2006) have been proposed on the basis of equation (2), and the augmented inverse-probability-weighted estimators (Robins et al., 1994; Bang and Robins, 2005; Cao et al., 2009) have been proposed on the basis of equation (3).”
Multiply robust imputation procedures for the treatment of item nonresponse in surveys (2017, background): “Doubly robust procedures have attracted a lot of attention in recent years; e.g., Robins et al. (1994), Scharfstein et al. (1999), Tan (2006), Bang & Robins (2005), Kang & Schafer (2007), and Cao et al. (2009).”
The Generalized Oaxaca-Blinder Estimator (2020, methodology): “The literature on doubly robust methods (Robins, Rotnitzky, and Zhao 1994a; Kang and Schafer 2007; Cao, Tsiatis, and Davidian 2009; Rosenblum and van der Laan 2011) is full of proposals satisfying 1, 2, and 4, but their theoretical justifications always assume that experimental units are iid…”
Imputation Strategies for the Estimation of Natural Direct and Indirect Effects (2012, background): “…work is required to improve them via the choice of estimators of the nuisance parameters indexing the models for the exposure, mediator and outcome (Cao, Tsiatis, and Davidian, 2009, Vansteelandt, Bekaert, and Claeskens, 2012), or via the choice of index functions (cfr. da,a∗(C) in the Appendix)…”