A stable and more efficient doubly robust estimator

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.

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“Robust-Squared” Imputation Models Using Bart

Journal of Survey Statistics and Methodology ◽

10.1093/jssam/smz002 ◽

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.

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Doubly robust estimator of risk in the presence of censoring dependent on time-varying covariates: application to a primary prevention trial for coronary events with pravastatin

10.21203/rs.3.rs-11458/v2 ◽

2020 ◽

Author(s):

Takuya Kawahara ◽

Tomohiro Shinozaki ◽

Yutaka Matsuyama

Keyword(s):

Model Misspecification ◽

Clinical Trial Data ◽

Dependent Censoring ◽

Model Specification ◽

Robust Estimator ◽

Time Varying ◽

Simulation Studies ◽

Kaplan Meier ◽

Doubly Robust ◽

Time Varying Covariates

Abstract Background: In the presence of dependent censoring even after stratification of baseline covariates, the Kaplan–Meier estimator provides an inconsistent estimate of risk. To account for dependent censoring, time-varying covariates can be used along with two statistical methods: the inverse probability of censoring weighted (IPCW) Kaplan–Meier estimator and the parametric g-formula estimator. The consistency of the IPCW Kaplan–Meier estimator depends on the correctness of the model specification of censoring hazard, whereas that of the parametric g-formula estimator depends on the correctness of the models for event hazard and time-varying covariates. Methods: We combined the IPCW Kaplan–Meier estimator and the parametric g-formula estimator into a doubly robust estimator that can adjust for dependent censoring. The estimator is theoretically more robust to model misspecification than the IPCW Kaplan–Meier estimator and the parametric g-formula estimator. We conducted simulation studies with a time-varying covariate that affected both time-to-event and censoring under correct and incorrect models for censoring, event, and time-varying covariates. We applied our proposed estimator to a large clinical trial data with censoring before the end of follow-up. Results: Simulation studies demonstrated that our proposed estimator is doubly robust, namely it is consistent if either the model for the IPCW Kaplan–Meier estimator or the models for the parametric g-formula estimator, but not necessarily both, is correctly specified. Simulation studies and data application demonstrated that our estimator can be more efficient than the IPCW Kaplan–Meier estimator. Conclusions: The proposed estimator is useful for estimation of risk if censoring is affected by time-varying risk factors.

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Data-Adaptive Bias-Reduced Doubly Robust Estimation

The International Journal of Biostatistics ◽

10.1515/ijb-2015-0029 ◽

2016 ◽

Vol 12 (1) ◽

pp. 253-282 ◽

Cited By ~ 5

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.

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Doubly robust estimator of risk in the presence of censoring dependent on time-varying covariates: application to a primary prevention trial for coronary events with pravastatin

BMC Medical Research Methodology ◽

10.1186/s12874-020-01087-8 ◽

2020 ◽

Vol 20 (1) ◽

Author(s):

Takuya Kawahara ◽

Tomohiro Shinozaki ◽

Yutaka Matsuyama

Keyword(s):

Primary Prevention ◽

Prevention Trial ◽

Robust Estimator ◽

Time Varying ◽

Primary Prevention Trial ◽

Coronary Events ◽

Doubly Robust ◽

Time Varying Covariates

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Doubly robust estimation of attributable fractions in survival analysis

Statistical Methods in Medical Research ◽

10.1177/0962280214564003 ◽

2014 ◽

Vol 26 (2) ◽

pp. 948-969 ◽

Cited By ~ 16

Author(s):

Arvid Sjölander ◽

Stijn Vansteelandt

Keyword(s):

Public Health ◽

Health Impact ◽

Attributable Fraction ◽

Binary Outcomes ◽

Robust Estimator ◽

Likelihood Estimator ◽

The Public ◽

Attributable Fractions ◽

Doubly Robust Estimation ◽

Doubly Robust

The attributable fraction is a commonly used measure that quantifies the public health impact of an exposure on an outcome. It was originally defined for binary outcomes, but an extension has recently been proposed for right-censored survival time outcomes; the so-called attributable fraction function. A maximum likelihood estimator of the attributable fraction function has been developed, which requires a model for the outcome. In this paper, we derive a doubly robust estimator of the attributable fraction function. This estimator requires one model for the outcome, and one joint model for the exposure and censoring. The estimator is consistent if either model is correct, not necessarily both.

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Policy Learning With Observational Data

Econometrica ◽

10.3982/ecta15732 ◽

2021 ◽

Vol 89 (1) ◽

pp. 133-161 ◽

Cited By ~ 1

Author(s):

Susan Athey ◽

Stefan Wager

Keyword(s):

Observational Data ◽

Functional Form ◽

Causal Effect ◽

Individual Characteristics ◽

Efficient Estimation ◽

Causal Effects ◽

Robust Estimator ◽

New Approach ◽

Doubly Robust ◽

Application Specific

In many areas, practitioners seek to use observational data to learn a treatment assignment policy that satisfies application‐specific constraints, such as budget, fairness, simplicity, or other functional form constraints. For example, policies may be restricted to take the form of decision trees based on a limited set of easily observable individual characteristics. We propose a new approach to this problem motivated by the theory of semiparametrically efficient estimation. Our method can be used to optimize either binary treatments or infinitesimal nudges to continuous treatments, and can leverage observational data where causal effects are identified using a variety of strategies, including selection on observables and instrumental variables. Given a doubly robust estimator of the causal effect of assigning everyone to treatment, we develop an algorithm for choosing whom to treat, and establish strong guarantees for the asymptotic utilitarian regret of the resulting policy.

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A general GEE framework for the analysis of longitudinal ordinal missing data and related issues

Statistical Modelling ◽

10.1177/1471082x17752753 ◽

2018 ◽

Vol 19 (2) ◽

pp. 174-193 ◽

Cited By ~ 1

Author(s):

José LP da Silva ◽

Enrico A Colosimo ◽

Fábio N Demarqui

Keyword(s):

Missing Data ◽

Longitudinal Data ◽

Missing At Random ◽

Robust Estimator ◽

Parameter Estimates ◽

Missing Responses ◽

Robust Property ◽

Computational Simplicity ◽

Association Structure ◽

Doubly Robust

Generalized estimating equations (GEEs) are a well-known method for the analysis of categorical longitudinal data. This method presents computational simplicity and provides consistent parameter estimates that have a population-averaged interpretation. However, with missing data, the resulting parameter estimates are consistent only under the strong assumption of missing completely at random (MCAR). Some corrections can be done when the missing data mechanism is missing at random (MAR): inverse probability weighting GEE (WGEE) and multiple imputation GEE (MIGEE). A recent method combining ideas of these two approaches has a doubly robust property in the sense that one only needs to correctly specify the weight or the imputation model in order to obtain consistent estimates for the parameters. In this work, a proportional odds model is assumed and a doubly robust estimator is proposed for the analysis of ordinal longitudinal data with intermittently missing responses and covariates under the MAR mechanism. In addition, the association structure is modelled by means of either the correlation coefficient or local odds ratio. The performance of the proposed method is compared to both WGEE and MIGEE through a simulation study. The method is applied to a dataset related to rheumatic mitral stenosis.

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