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November 2007 Demystifying Double Robustness: A Comparison of Alternative Strategies for Estimating a Population Mean from Incomplete Data
Joseph D. Y. Kang, Joseph L. Schafer
Statist. Sci. 22(4): 523-539 (November 2007). DOI: 10.1214/07-STS227


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.


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Joseph D. Y. Kang. Joseph L. Schafer. "Demystifying Double Robustness: A Comparison of Alternative Strategies for Estimating a Population Mean from Incomplete Data." Statist. Sci. 22 (4) 523 - 539, November 2007.


Published: November 2007
First available in Project Euclid: 7 April 2008

zbMATH: 1246.62073
MathSciNet: MR2420458
Digital Object Identifier: 10.1214/07-STS227

Keywords: Causal inference , missing data , model-assisted survey estimation , propensity score , weighted estimating equations

Rights: Copyright © 2007 Institute of Mathematical Statistics

Vol.22 • No. 4 • November 2007
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