Comment: Understanding OR, PS and DR

By Zhiqiang Tan. 2007

121 citations recorded by the source corpus.

We congratulate Kang and Schafer (KS) on their ex cellent article comparing various estimators of a popu lation mean in the presence of missing data, and thank the Editor for organizing the discussion. In this com munication, we systematically examine the propen sity score (PS) and the outcome regression (OR) ap proaches and doubly robust (DR) estimation, which are all discussed by KS. The aim is to clarify and better our understanding of the three interrelated subjects. Sections 1 and 2 contain the following main points, respectively.

Subfields: Cognitive Neuroscience, Family Practice, Radiology, Nuclear Medicine and Imaging

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Citations in the corpus

Efficiently Breaking the Curse of Horizon in Off-Policy Evaluation with Double Reinforcement Learning (2019, methodology): “This result is well-known in the bandit setting when we use a binary deterministic policy (Tan 2007).”
Doubly Robust Inference With Nonprobability Survey Samples (2018, background): “See, for instance, Tan (2007) for further discussion.”
Improving efficiency and robustness of the doubly robust estimator for a population mean with incomplete data (2009, methodology): “When both models are incorrectly specified, μ̂USUAL shows nonnegligible bias, as observed by Kang & Schafer (2007) and Tan (2007); however, the use of the enhanced propensity model in μ̂enUSUAL eliminates this behaviour.”
Multiply Robust Estimation in Regression Analysis With Missing Data (2014, background): “However, if one had such information available, one would estimate β0 by directly solving (1) with Y substituted by the fitted value based on the correct model, due to the high efficiency of this estimator (e.g., Tan 2007).”
Bias-Reduced Doubly Robust Estimation (2015, background): “The discussions of that article (Ridgeway and McCaffrey 2007; Robins et al. 2007; Tan 2007; Tsiatis and Davidian 2007; Kang and Schafer 2007b) reveal that many different DR estimators may exist for a given target parameter, all with potentially very different behavior and properties under…”
Bounded, efficient and doubly robust estimation with inverse weighting (2010, unknown): “…intrinsically efficient: if the propensity score model is correctly specified, then each such estimator is asymptotically efficient among a class of augmented inverse-probability-weighted estimators that use the same fitted outcome regression function as the estimator itself does (Tan, 2006, 2007).”
Regularized calibrated estimation of propensity scores with model misspecification and high-dimensional data (2017, background): “There are two broad approaches to estimating (μ0,μ1), depending on additional modelling assumptions on the outcome regression function m∗(t, X ) = E(Y | T = t, X ) or the propensity score (Rosenbaum & Rubin, 1983) π∗(X ) = pr(T = 1 | X ); see Tan (2007) for further discussion.”
Model-assisted inference for treatment effects using regularized calibrated estimation with high-dimensional data (2018, background): “In particular, as the main problem to be tackled in the paper, estimation of average treatment effects typically requires building and fitting outcome regression or propensity score models (e.g., Tan (2007)).”
A GENERAL DOUBLE ROBUSTNESS RESULT FOR ESTIMATING AVERAGE TREATMENT EFFECTS (2014, background): “Tan (2006a) developed an alternative AIPW estimator, which might provide either an efficiency gain—if the propensity score is correctly specified—or bias reduction— if the propensity score is misspecified, but the conditional mean is correctly”