Skip Navigation


Biometrika Advance Access originally published online on August 7, 2009
Biometrika 2009 96(3):723-734; doi:10.1093/biomet/asp033
This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Cao, W.
Right arrow Articles by Davidian, M.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© 2009 Biometrika Trust

Article

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

Weihua Cao, Anastasios A. Tsiatis and Marie Davidian

Department of Statistics, North Carolina State University, Raleigh, North Carolina 27695-8203, U.S.A. wcao5{at}ncsu.edu tsiatis{at}stat.ncsu.edu davidian{at}stat.ncsu.edu

Received for publication 1 June 2008. Revision received 1 December 2008.

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.

Key Words: Causal inference • Enhanced propensity score model • Missing at random • No unmeasured confounders • Outcome regression



References

    Bang H., Robins J. M. Doubly robust estimation in missing data and causal inference models. Biometrics (2005) 61:962–72.[CrossRef][Web of Science][Medline]

    Kang D. Y. J., Schafer J. L. Demystifying double robustness: a comparison of alternative strategies for estimating a population mean from incomplete data (with discussion and rejoinder). Statist. Sci. (2007) 22:523–80.[CrossRef]

    Lunceford J. K., Davidian M. Stratification and weighting via the propensity score in estimation of causal treatment effects: a comparative study. Statist. Med. (2004) 23:2937–60.[CrossRef]

    Robins J. M., Hernán M., Brumback B. Marginal structural models and causal inference in epidemiology. Epidemio. (2000) 11:550–60.[CrossRef]

    Robins J. M., Rotnitzky A., Zhao L. P. Estimation of regression coefficients when some regressors are not always observed. J. Am. Statist. Assoc. (1994) 89:846–66.[CrossRef][Web of Science]

    Robins J. M., Sued M., Lei-Gomez Q., Rotnitzky A. Performance of double-robust estimators when inverse probability weights are highly variable. Statist. Sci. (2007) 22:544–59.[CrossRef]

    Rosenbaum P. R. Model-based direct adjustment. J. Am. Statist. Assoc. (1987) 82:387–94.[CrossRef][Web of Science]

    Rosenbaum P. R., Rubin D. B. The central role of the propensity score in observational studies for causal effects. Biometrika (1983) 70:41–55.[Abstract/Free Full Text]

    Rosenbaum P. R., Rubin D. B. Reducing bias in observational studies using subclassification on the propensity score. J. Am. Statist. Assoc. (1984) 79:516–24.[CrossRef][Web of Science]

    Rubin D. B. Inference and missing data. Biometrika (1976) 63:581–92.[Abstract/Free Full Text]

    Rubin D. B. Bayesian inference for causal effects: the role of randomization. Ann. Statist. (1978) 6:34–58.[CrossRef]

    Rubin D. B., Thomas N. Matching using estimated propensity scores: relating theory to practice. Biometrics (1996) 52:249–64.[CrossRef][Web of Science][Medline]

    SAS Institute Inc. SAS Online Documentation 9.1.3 (2006) Cary, NC: SAS Institute.

    Stefanski L. A., Boos D. D. The calculus of M-estimation. Am. Statist. (2002) 56:29–38.[CrossRef]

    Scharfstein D. O., Rotnitzky A., Robins J. M. Adjusting for nonignorable drop-out using semiparametric nonresponse models (with discussion and rejoinder). J. Am. Statist. Assoc. (1999) 94:1096–146.[CrossRef][Web of Science]

    Tan Z. A distributional approach for causal inference using propensity scores. J. Am. Statist. Assoc. (2006) 101:1619–37.[CrossRef][Web of Science]

    Tan Z. Understanding OR, PS and DR. Statist. Sci. (2007) 22:560–8.[CrossRef]

    Tsiatis A. A. Semiparametric Theory and Missing Data. (2006) New York: Springer.

    Tsiatis A. A., Davidian M. Comment on `Demystifying Double Robustness: A Comparison of Alternative Strategies for Estimating a Population Mean from Incomplete Data. Statist. Sci. (2007) 22:569–73.[CrossRef]


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?



This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Cao, W.
Right arrow Articles by Davidian, M.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?