A comparative study of doubly robust estimators of the mean with missing data

Journal of Statistical Computation and Simulation

Volumn 81, Issue 12, 2011, Pages 2039-2058

  Zhang, Guangyu ^a   Little, Roderick ^b  

^a UNIVERSITY OF MARYLAND   (United States)

^b UNIVERSITY OF MICHIGAN   (United States)

Author keywords

calibration; non response; propensity; robust models; simulation study; weighting

Indexed keywords

EID: 84863229165     PISSN: 00949655     EISSN: 15635163     Source Type: Journal    
DOI: 10.1080/00949655.2010.516750     Document Type: Article

References (36)

1. Little, R. J.A. and Rubin, D. B. 2002. Statistical Analysis with Missing Data, New York: Wiley.
2. Horvitz, D. G. and Thompson, D. J. 1952. A generalization of sampling without replacement from a finite universe. J. Am. Statist. Assoc., 47: 663-685.
3. Cochran, W. G. 1965. The planning of observational studies of human populations. J. R. Statist. Soc. Ser. A, 128: 234-256.
4. Cochran, W. G. 1968. The effectiveness of adjustment by subclassification in removing bias in observational studies. Biometrics, 24: 205-213.
5. Rosenbaum, P. R. and Rubin, D. B. 1983. The central role of the propensity score in observational studies for causal effects. Biometrika, 70: 41-55.
6. Rosenbaum, P. R. and Rubin, D. B. 1984. Reducing bias in observational studies using subclassification on the propensity score. J. Am. Statist. Assoc., 79: 516-524.
7. Rubin, D. B. Multiple imputations in sample surveys - a phenomenological Bayesian approach to nonresponse. Proceedings of Survey Research Methods Section, the American Statistical Association. pp.20-34.
8. Rubin, D. B. 1987. Multiple Imputation for Non-response in Surveys, New York: John Wiley.
9. Rubin, D. B. 1996. Multiple imputation after 18+ years. J. Am. Statist. Assoc., 91: 473-489.
10. Rubin, D. B. and Schenker, N. 1986. Multiple imputation for interval estimation from simple random samples with ignorable nonresponse. J. Am. Statist. Assoc., 81: 366-374.
11. Barnard, J. and Rubin, D. B. 1999. Small-sample degrees of freedom with multiple imputation. Biometrika, 86: 948-955.
12. Robins, J. M., Rotnitzky, A. and Zhao, L. P. 1994. Estimation of regression coefficients when some regressors are not always observed. J. Am. Statist. Assoc., 89: 846-866.
13. Rotnitzky, A., Robins, J. M. and Scharfstein, D. O. 1998. Semiparametric regression for repeated measures outcomes with non-ignorable non-response. J. Am. Statist. Assoc., 93: 1321-1339.
14. Little, R. J.A. and An, H. 2004. Robust likelihood-based analysis of multivariate data with missing values. Statist. Sin., 14: 949-968.
15. Bang, H. and Robins, J. M. 2005. Doubly robust estimation in missing data and causal inference models. Biometrics, 61: 962-972.
16. Zhang, G. and Little, R. J. 2008. Extensions of the penalized spline propensity prediction method of imputation. Biometrics, 65(3): 911-918.
17. Firth, D. and Bennett, K. E. 1998. Robust models in probability sampling. J. R. Statist. Soc. Ser. B., 60: 3-21.
18. Scharfstein, D. O., Rotnitzky, A. and Robins, J. M. 1999. Adjusting for nonignorable drop-out using semiparametric nonresponse models (with discussion). J. Am. Statist. Assoc., 94: 1096-1146.
19. Eilers, P. H.C. and Marx, B. D. 1996. Flexible smoothing with B-Splines and penalties. Statist. Sci., 11: 89-121.
20. Ruppert, D., Wand, M. P. and Carroll, R. J. 2003. Semiparametric Regression, Cambridge: Cambridge University Press.
21. Ngo, L. and Wand, M. P. 2004. Smoothing with mixed model software. J. Statist. Softw., 9(1): 1-54.
22. Eubank, R. L. 1988. Spline Smoothing and Nonparametric Regression, New York: Marcel Dekker.
23. Wahba, G. 1990. Spline Models for Observational Data, Philadelphia: SIAM.
24. SAS, The mixed procedure. Chapter 16 in SAS/STAT Software: Changes and Enhancements, Release 6.07, Tech. Rep. P-229, SAS Institute, Inc., Cary, NC
25. Littell, R. C., Milliken, G. A., Stroup, W. W. and Wolnger, R. D. 1996. SAS System for Mixed Models, Cary, NC: SAS Institute, Inc.
26. Ruppert, D. 2002. Selecting the number of knots for penalized splines. J. Comput. Graph. Stat., 11: 735-757.
27. Pinheiro, J. C. and Bates, D. M. 2000. Mixed-Effects Models in S and S-PLUS, New York: Springer-Verlag.
28. Sarndal, C.-E., Swensson, B. and Wretman, J. 2003. Model Assisted Survey Sampling, New York: Springer.
29. Robins, J. M. and Rotnitzky, A. 2001. Comment on 'inference for semiparametric models: Some questions and an answer' by Bickel and Kwon. Statist. Sin., 11: 920-936.
30. Lunceford, J. K. and Davidian, M. 2004. Stratification and weighting via the propensity score in estimation of causal treatment effects: A comparative study. Statist. Med., 23: 2937-2960.
31. Yu, M. and Nan, B. 2006. A revisit of semiparametric regression models with missing data. Statist. Sin., 16: 1193-1212.
32. Little, R. J.A. 1983. Estimating a finite population mean from unequal probability samples. J. Am. Statist. Assoc., 78: 596-604.
33. Little, R. J.A. 1986. Survey nonresponse adjustments for estimates of means. Int. Statist. Rev., 54: 139-157.
34. Little, R. J.A. 1991. Inference with survey weights. J. Off. Stat., 7: 405-424.
35. Kang, J. D.Y. and Schafer, J. L. 2007. Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data. Statist. Sci., 22(4): 523-539.
36. Couper, M. P., Peytchev, A., Little, R. J.A., Strecher, V. J. and Rothert, K. Combining information from multiple modes to reduce nonresponse bias, Contributed Paper. Joint Statistical Meetings.