Demystifying a class of multiply robust estimators

Biometrika ◽  
2020 ◽  
Vol 107 (4) ◽  
pp. 919-933
Author(s):  
Wei Li ◽  
Yuwen Gu ◽  
Lan Liu
Keyword(s):  
Propensity Score ◽  
Parametric Models ◽  
Robust Estimator ◽  
Robust Estimators ◽  
Improve Model ◽  
Special Cases ◽  
Model Mixing ◽  
Doubly Robust ◽  
Multiple Robustness ◽  
Robust Procedures

Summary For estimating the population mean of a response variable subject to ignorable missingness, a new class of methods, called multiply robust procedures, has been proposed. The advantage of multiply robust procedures over the traditional doubly robust methods is that they permit the use of multiple candidate models for both the propensity score and the outcome regression, and they are consistent if any one of the multiple models is correctly specified, a property termed multiple robustness. This paper shows that, somewhat surprisingly, multiply robust estimators are special cases of doubly robust estimators, where the final propensity score and outcome regression models are certain combinations of the candidate models. To further improve model specifications in the doubly robust estimators, we adapt a model mixing procedure as an alternative method for combining multiple candidate models. We show that multiple robustness and asymptotic normality can also be achieved by our mixing-based doubly robust estimator. Moreover, our estimator and its theoretical properties are not confined to parametric models. Numerical examples demonstrate that the proposed estimator is comparable to and can even outperform existing multiply robust estimators.

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

Biometrika ◽  
2009 ◽  
Vol 96 (3) ◽  
pp. 723-734 ◽  
Author(s):  
Weihua Cao ◽  
Anastasios A. Tsiatis ◽  
Marie Davidian
Keyword(s):  
Propensity Score ◽  
Incomplete Data ◽  
Propensity Scores ◽  
Robust Estimator ◽  
Robust Estimators ◽  
Population Mean ◽  
Recent Interest ◽  
Improved Performance ◽  
Doubly Robust

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.

scholarly journals Doubly Robust Estimation of Causal Effect

2020 ◽  
Vol 13 (1) ◽  
Author(s):  
Xiaochun Li ◽  
Changyu Shen
Keyword(s):  
Propensity Score ◽  
Causal Effect ◽  
Model Specification ◽  
Robust Estimator ◽  
Data Set ◽  
Multiple Regressions ◽  
Doubly Robust Estimation ◽  
Doubly Robust ◽  
Confounding Adjustment ◽  
The Relationship

Propensity score–based methods or multiple regressions of the outcome are often used for confounding adjustment in analysis of observational studies. In either approach, a model is needed: A model describing the relationship between the treatment assignment and covariates in the propensity score–based method or a model for the outcome and covariates in the multiple regressions. The 2 models are usually unknown to the investigators and must be estimated. The correct model specification, therefore, is essential for the validity of the final causal estimate. We describe in this article a doubly robust estimator which combines both models propitiously to offer analysts 2 chances for obtaining a valid causal estimate and demonstrate its use through a data set from the Lindner Center Study.

scholarly journals “Robust-Squared” Imputation Models Using Bart

2019 ◽  
Vol 7 (4) ◽  
pp. 465-497
Author(s):  
Yaoyuan V Tan ◽  
Carol A C Flannagan ◽  
Michael R Elliott
Keyword(s):  
Model Misspecification ◽  
Blood Alcohol Concentration ◽  
Alcohol Concentration ◽  
Penalized Splines ◽  
Robust Estimator ◽  
Robust Estimators ◽  
Sampling System ◽  
Additive Regression ◽  
Doubly Robust ◽  
Augmented Inverse Probability Weighting

Abstract Examples of “doubly robust” estimators for missing data include augmented inverse probability weighting (AIPWT) and penalized splines of propensity prediction (PSPP). Doubly robust estimators have the property that, if either the response propensity or the mean is modeled correctly, a consistent estimator of the population mean is obtained. However, doubly robust estimators can perform poorly when modest misspecification is present in both models. Here we consider extensions of the AIPWT and PSPP that use Bayesian additive regression trees (BART) to provide highly robust propensity and mean model estimation. We term these “robust-squared” in the sense that the propensity score, the means, or both can be estimated with minimal model misspecification, and applied to the doubly robust estimator. We consider their behavior via simulations where propensities and/or mean models are misspecified. We apply our proposed method to impute missing instantaneous velocity (delta-v) values from the 2014 National Automotive Sampling System Crashworthiness Data System dataset and missing Blood Alcohol Concentration values from the 2015 Fatality Analysis Reporting System dataset. We found that BART, applied to PSPP and AIPWT, provides a more robust estimate compared with PSPP and AIPWT.

scholarly journals Data-Adaptive Bias-Reduced Doubly Robust Estimation

2016 ◽  
Vol 12 (1) ◽  
pp. 253-282 ◽  
Author(s):  
Karel Vermeulen ◽  
Stijn Vansteelandt
Keyword(s):  
Nuisance Parameter ◽  
Nuisance Parameters ◽  
Robust Estimator ◽  
Robust Estimators ◽  
Infinite Dimensional ◽  
Working Models ◽  
Finite Dimensional ◽  
Doubly Robust Estimation ◽  
Data Adaptive ◽  
Doubly Robust

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.

scholarly journals Doubly robust pseudo-likelihood for incomplete hierarchical binary data

2018 ◽  
Vol 20 (1) ◽  
pp. 42-57
Author(s):  
Lisa Hermans ◽  
Anna Ivanova ◽  
Cristina Sotto ◽  
Geert Molenberghs ◽  
Geert Verbeke ◽  
...  
Keyword(s):  
Missing Data ◽  
Binary Data ◽  
Standard Form ◽  
Missing At Random ◽  
Correlated Data ◽  
Marginal Model ◽  
Robust Estimator ◽  
Robust Estimators ◽  
Pseudo Likelihood ◽  
Doubly Robust

Missing data is almost inevitable in correlated-data studies. For non-Gaussian outcomes with moderate to large sequences, direct-likelihood methods can involve complex, hard-to-manipulate likelihoods. Popular alternative approaches, like generalized estimating equations, that are frequently used to circumvent the computational complexity of full likelihood, are less suitable when scientific interest, at least in part, is placed on the association structure; pseudo-likelihood (PL) methods are then a viable alternative. When the missing data are missing at random, Molenberghs et al. (2011, Statistica Sinica, 21,187–206) proposed a suite of corrections to the standard form of PL, taking the form of singly and doubly robust estimators. They provided the basis and exemplified it in insightful yet primarily illustrative examples. We here consider the important case of marginal models for hierarchical binary data, provide an effective implementation and illustrate it using data from an analgesic trial. Our doubly robust estimator is more convenient than the classical doubly robust estimators. The ideas are illustrated using a marginal model for a binary response, more specifically a Bahadur model.

scholarly journals Causal Subclassification Tree Algorithm and Robust Causal Effect Estimation via Subclassification

2020 ◽  
Vol 10 (1) ◽  
pp. 40
Author(s):  
Tomoshige Nakamura ◽  
Mihoko Minami
Keyword(s):  
Propensity Score ◽  
Propensity Scores ◽  
Causal Effect ◽  
Model Misspecification ◽  
Robust Estimator ◽  
Propensity Score Model ◽  
Confounding Variables ◽  
Score Model ◽  
Effect Estimation ◽  
Weighting Methods

In observational studies, the existence of confounding variables should be attended to, and propensity score weighting methods are often used to eliminate their e ects. Although many causal estimators have been proposed based on propensity scores, these estimators generally assume that the propensity scores are properly estimated. However, researchers have found that even a slight misspecification of the propensity score model can result in a bias of estimated treatment effects. Model misspecification problems may occur in practice, and hence, using a robust estimator for causal effect is recommended. One such estimator is a subclassification estimator. Wang, Zhang, Richardson, & Zhou (2020) presented the conditions necessary for subclassification estimators to have $\sqrt{N}$-consistency and to be asymptotically well-defined and suggested an idea how to construct subclasses.

scholarly journals Entropy Balancing is Doubly Robust

2016 ◽  
Vol 5 (1) ◽  
Author(s):  
Qingyuan Zhao ◽  
Daniel Percival
Keyword(s):  
Propensity Score ◽  
Observational Studies ◽  
Optimization Problem ◽  
Entropy Maximization ◽  
Entropy Balancing ◽  
Covariate Balance ◽  
Original Proposal ◽  
Variance Bound ◽  
Doubly Robust ◽  
Theoretical Results

AbstractCovariate balance is a conventional key diagnostic for methods estimating causal effects from observational studies. Recently, there is an emerging interest in directly incorporating covariate balance in the estimation. We study a recently proposed entropy maximization method called Entropy Balancing (EB), which exactly matches the covariate moments for the different experimental groups in its optimization problem. We show EB is doubly robust with respect to linear outcome regression and logistic propensity score regression, and it reaches the asymptotic semiparametric variance bound when both regressions are correctly specified. This is surprising to us because there is no attempt to model the outcome or the treatment assignment in the original proposal of EB. Our theoretical results and simulations suggest that EB is a very appealing alternative to the conventional weighting estimators that estimate the propensity score by maximum likelihood.

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