Demystifying Double Robustness: A Comparison of Alternative Strategies for Estimating a Population Mean from Incomplete Data

Abstract

When outcomes are missing for reasons beyond an investigator's control, there are two different ways to adjust a parameter estimate for covariates that may be related both to the outcome and to missingness. One approach is to model the relationships between the covariates and the outcome and use those relationships to predict the missing values. Another is to model the probabilities of missingness given the covariates and incorporate them into a weighted or stratified estimate. Doubly robust (DR) procedures apply both types of model simultaneously and produce a consistent estimate of the parameter if either of the two models has been correctly specified. In this article, we show that DR estimates can be constructed in many ways. We compare the performance of various DR and non-DR estimates of a population mean in a simulated example where both models are incorrect but neither is grossly misspecified. Methods that use inverse-probabilities as weights, whether they are DR or not, are sensitive to misspecification of the propensity model when some estimated propensities are small. Many DR methods perform better than simple inverse-probability weighting. None of the DR methods we tried, however, improved upon the performance of simple regression-based prediction of the missing values. This study does not represent every missing-data problem that will arise in practice. But it does demonstrate that, in at least some settings, two wrong models are not better than one.

This paper commented in: [arXiv:0804.2962], [arXiv:0804.2965], [arXiv:0804.2969], [arXiv:0804.2970]. Rejoinder in [arXiv:0804.2973]. Published in at http://dx.doi.org/10.1214/07-STS227 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Cited by in corpus (38)

• Matching Methods for Causal Inference: A Review and a Look Forward
• A quantile-based g-computation approach to addressing the effects of exposure mixtures
• Semiparametric theory for causal mediation analysis: Efficiency bounds, multiple robustness and sensitivity analysis
• A Comparison of Different Methods to Adjust Survival Curves for Confounders
• Estimation of causal effects with multiple treatments: a review and new ideas
• Doubly Robust Policy Evaluation and Optimization
• Propensity score weighting under limited overlap and model misspecification
• Identifying the consequences of dynamic treatment strategies: A decision-theoretic overview
• Minimal Dispersion Approximately Balancing Weights: Asymptotic Properties and Practical Considerations
• On the estimation of average treatment effects with right-censored time to event outcome and competing risks
• Calibrated Bayes, for Statistics in General, and Missing Data in Particular
• Efficient augmentation and relaxation learning for individualized treatment rules using observational data
• Oracle, Multiple Robust and Multipurpose Calibration in a Missing Response Problem
• Effect of breastfeeding on gastrointestinal infection in infants: A targeted maximum likelihood approach for clustered longitudinal data
• Parametric G-computation for Compatible Indirect Treatment Comparisons with Limited Individual Patient Data
• Inverse probability of treatment weighting with generalized linear outcome models for doubly robust estimation
• Independence weights for causal inference with continuous treatments
• Doubly-Robust Estimation for Correcting Position-Bias in Click Feedback for Unbiased Learning to Rank
• G-computation and doubly robust standardisation for continuous-time data: a comparison with inverse probability weighting
• Fractional Imputation in Survey Sampling: A Comparative Review
• A Calibration Approach to Transportability and Data-Fusion with Observational Data
• Estimating a Causal Exposure Response Function with a Continuous Error-Prone Exposure: A Study of Fine Particulate Matter and All-Cause Mortality
• Rebar: Reinforcing a Matching Estimator with Predictions from High-Dimensional Covariates
• Causal mediation analysis: From simple to more robust strategies for estimation of marginal natural (in)direct effects
• Semiparametric regression and risk prediction with competing risks data under missing cause of failure
• "Robust-squared" Imputation Models Using BART
• Analysing the causal effect of London cycle superhighways on traffic congestion
• A Framework for Covariate Balance using Bregman Distances
• Confounding Adjustment Methods for Multi-level Treatment Comparisons Under Lack of Positivity and Unknown Model Specification
• Estimation of Policy-Relevant Causal Effects in the Presence of Interference with an Application to the Philadelphia Beverage Tax
• Approximated Doubly Robust Search Relevance Estimation
• Peer Recommendation Interventions for Health-related Social Support: a Feasibility Assessment
• Propensity score matching for estimating a marginal hazard ratio
• Classification using Ensemble Learning under Weighted Misclassification Loss
• Estimating the average treatment effects of nutritional label use using subclassification with regression adjustment
• The Effect of Alcohol intake on Brain White Matter Microstructural Integrity: A New Causal Inference Framework for Incomplete Phenomic Data
• Rejoinder
• Discussion of "Impact of Frequentist and Bayesian Methods on Survey Sampling Practice: A Selective Appraisal" by J. N. K. Rao