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.
Keywords: 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. doi: 10.1111/j.1541-0420.2005.00377.x. [DOI] [PubMed] [Google Scholar]
- 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. doi: 10.1214/07-STS227. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 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. doi: 10.1002/sim.1903. [DOI] [PubMed] [Google Scholar]
- Robins J. M. Hernán M. Brumback B. Marginal structural models and causal inference in epidemiology. Epidemio. 2000;11:550–60. doi: 10.1097/00001648-200009000-00011. [DOI] [PubMed] [Google Scholar]
- 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. [Google Scholar]
- 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. [Google Scholar]
- Rosenbaum P. R. Model-based direct adjustment. J. Am. Statist. Assoc. 1987;82:387–94. [Google Scholar]
- Rosenbaum P. R. Rubin D. B. The central role of the propensity score in observational studies for causal effects. Biometrika. 1983;70:41–55. [Google Scholar]
- 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. [Google Scholar]
- Rubin D. B. Inference and missing data. Biometrika. 1976;63:581–92. [Google Scholar]
- Rubin D. B. Bayesian inference for causal effects: the role of randomization. Ann. Statist. 1978;6:34–58. [Google Scholar]
- Rubin D. B. Thomas N. Matching using estimated propensity scores: relating theory to practice. Biometrics. 1996;52:249–64. [PubMed] [Google Scholar]
- SAS Institute Inc. SAS Online Documentation 9.1.3. Cary, NC: SAS Institute; 2006. [Google Scholar]
- Stefanski L. A. Boos D. D. The calculus of M-estimation. Am. Statist. 2002;56:29–38. [Google Scholar]
- 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. [Google Scholar]
- Tan Z. A distributional approach for causal inference using propensity scores. J. Am. Statist. Assoc. 2006;101:1619–37. [Google Scholar]
- Tan Z. Understanding OR, PS and DR. Statist. Sci. 2007;22:560–8. [Google Scholar]
- Tsiatis A. A. Semiparametric Theory and Missing Data. New York: Springer; 2006. [Google Scholar]
- 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. doi: 10.1214/07-STS227. [DOI] [PMC free article] [PubMed] [Google Scholar]