The relative performance of targeted maximum likelihood estimators

International Journal of Biostatistics

Volumn 7, Issue 1, 2011, Pages

  Porter, Kristin E ^a   Gruber, Susan ^a   Van Der Laan, Mark J ^a   Sekhon, Jasjeet S ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Censored data; collaborative double robustness; collaborative targeted maximum likelihood estimation; double robust; estimator selection; inverse probability of censoring weighting; locally efficient estimation; maximum likelihood estimation; semiparametric model; targeted maximum likelihood estimation; targeted minimum loss based estimation; targeted nuisance parameter estimator selection

Indexed keywords

ARTICLE; MAXIMUM LIKELIHOOD ESTIMATOR; MAXIMUM LIKELIHOOD METHOD; OUTCOME ASSESSMENT; PERFORMANCE; SIMULATION; STATISTICAL ANALYSIS; STATISTICAL PARAMETERS;

LIKELIHOOD FUNCTIONS; STATISTICS AS TOPIC;

DAVIDIA;

EID: 80052507456     PISSN: None     EISSN: 15574679     Source Type: Journal    
DOI: 10.2202/1557-4679.1308     Document Type: Article

References (56)

1. O. Bembom and M.J. Van der Laan. Data-adaptive selection of the truncation level for inverse-probability-of-treatment-weighted estimators. Technical Report 230, Division of Biostatstics, University of California, Berkeley, 2008. URL www.bepress.com/ucbbiostat/paper230/.
2. L. Breiman. Bagging predictors. Machine Learning, 24:123-140, 1996. (Pubitemid 126724382)
3. L. Breiman, J. H. Friedman, R. Olshen, and C. J. Stone. Classification and regression trees. The Wadsworth statistics/probability series. Wadsworth International Group, 1984.
4. W. Cao, A.A. Tsiatis, and M. Davidian. Improving efficiency and robustness of the doubly robust estimator for a population mean with incomplete data. Biometrika, 96,3:723-734, 2009.
5. C.-C. Chang and C.-J. Lin. LIBSVM: a library for support vector machines (version 2.31). Technical report, 2001. http://www.csie.ntu.edu.tw/cjlin/papers/ libsvm2.ps.gz.
6. S.R. Cole and M.A. Hernan. Constructing inverse probability weights for marginal structural models. American Journal of Epidemiology, 168: 656-664, 2008.
7. C. Cortes and V. Vapnik. Support-vector networks. Machine Learning, 20: 273-297, December 1995.
8. E. Dimitriadou, K. Hornik, F. Leisch, D. Meyer, , and A. Weingessel. e1071: Misc Functions of the Department of Statistics (e1071), TU Wien, 2010. URL http://CRAN.R-project.org/package=e1071. R package version 1.5-24.
9. D.A. Freedman and R.A. Berk. Weighting regressions by propensity scores. Evaluation Review, 32,4:392-409, 2008.
10. J. H. Friedman. Multivariate adaptive regression splines. The Annals of Statistics, 19(1):pp. 1-67, 1991. ISSN 00905364. URL http://www. jstor.org/stable/2241837.
11. J. H. Friedman. Fast MARS. Technical report, Department of Statistics, Stanford University, 1993.
12. J. H. Friedman. Flexible metric nearest neighbor classification. Technical report, Department of Statistics, Stanford University, 1994.
13. S. Gruber and M.J. Van der Laan. A targeted maximum likelihood estimator of a causal effect on a bounded continuous outcome. Technical Report 265, UC Berkeley, 2010a.
14. S. Gruber and M.J. Van der Laan. An application of collaborative targeted maximum likelihood estimation in causal inference and genomics. The International Journal of Biostatistics, 6,1(18), 2010b.
15. T.J. Hastie and D. Pregibon. Generalized linear models. In J. M. Chambers and T. J. Hastie, editors, Statistical Models in S, chapter 6. Wadsworth & Brooks/Cole, 1992.
16. A. Rotnitzky J.M. Robins and L.P. Zhao. Estimation of regression coefficients when some regressors are not always observed. J. Am. Statist. Assoc., 89:846-66, 1994.
17. J. Kang and J. Schafer. Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data (with discussion). Statistical Science, 22:523-39, 2007.
18. L. Kish. Weighting for unequal pi. Journal of Official Statistics, 8:183-200, 1992.
19. S Milborrow. earth: Multivariate Adaptive Regression Spline Models, 2009. URL http://CRAN.R-project.org/package=earth. R package version 2.4-0.
20. K.L. Moore, R.S. Neugebauer, M.J. Van der Laan, and I.B. Tager. Causal inference in epidemiological studies with strong confounding. Technical Report 255, Division of Biostatistics, University of California, Berkeley, 2009. URL www.bepress.com/ucbbiostat/paper255/.
21. R. Neugebauer and J. Bullard. DSA: Deletion/Substitution/Addition algorithm, 2010. URL http://www.stat.berkeley.edu/~laan/Software/. R package version 3.1.4.
22. R. Neugebauer and M.J. Van der Laan. Why prefer double robust estimators in causal inference? Journal of Statistical Planning and Inference, 129, Issues 1-2:405-426, 2005. (Pubitemid 39631036)
23. A Peters and T Hothorn. ipred: Improved Predictors, 2009. URL http://CRAN.R-project.org/package=ipred. R package version 0.8-8.
24. M.L. Petersen, K. Porter, S. Gruber, Y. Wang, and M.J. Van der Laan. Diagnosing and responding to violations in the positivity assumption. Statistical Methods in Medical Research, 2010.
25. G. Ridgeway and D. McCaffrey. Comment: Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data (with discussion). Statistical Science, 22: 540-43, 2007.
26. B. D. Ripley. Pattern recognition and neural networks. Cambridge University Press, Cambridge, New York, 1996.
27. J. M. Robins, M. Sued, Q. Lei-Gomez, and A. Rotnitzky. Comment: Performance of double-robust estimators when "inverse probability" weights are highly variable. Statistical Science, 22:544-559, 2007.
28. J.M. Robins. A new approach to causal inference in mortality studies with sustained exposure periods-application to control of the healthy worker survivor effect. Mathematical Modelling, 7:1393-1512, 1986.
29. J.M. Robins. Addendum to: "A new approach to causal inference in mortality studies with a sustained exposure period-application to control of the healthy worker survivor effect" [Math. Modelling 7 (1986), no. 9-12, 1393-1512; MR 87m:92078]. Comput. Math. Appl., 14(9-12):923-945, 1987. ISSN 0097-4943. (Pubitemid 18561978)
30. J.M. Robins. Robust estimation in sequentially ignorable missing data and causal inference models. In Proceedings of the American Statistical Association: Section on Bayesian Statistical Science, pages 6-10, 1999.
31. J.M. Robins. Commentary on using inverse weighting and predictive inference to estimate the effecs of time-varying treatments on the discrete-time hazard. Statistics in Medicine, (21):1663-1680, 1999. (Pubitemid 34678899)
32. J.M. Robins, A. Rotnitzky, and L.P. Zhao. Estimation of regression coefficients when some regressors are not always observed. Journal of the American Statistical Association, 89(427):846-66, September 1994.
33. M. Rosenblum and M. J. Van der Laan. Targeted maximum likelihood estimation of the parameter of a marginal structural model. The International Journal of Biostatistics, 6(19), 2010.
34. A. Rotnitzky, L. Li, and X. Li. A note on overadjustment in inverse probability weighted estimation. Biometrika, 97(4):997-1001, 2010.
35. D.B. Rubin and M.J. Van der Laan. Empirical efficiency maximization: Improved locally efficient covariate adjustment in randomized experiments and survival analysis. The International Journal of Biostatis-tics, Vol. 4, Iss. 1, Article 5, 2008.
36. D.O. Scharfstein, A. Rotnitzky, and J.M. Robins. Adjusting for non-ignorable drop-out using semiparametric nonresponse models, (with discussion and rejoinder). Journal of the American Statistical Association, (94): 1096-1120 (1121-1146), 1999.
37. J.S. Sekhon, S. Gruber, K. Porter, and M.J. Van der Laan. Propensity-score-based estimators and C-TMLE. In M.J. Van der Laan and S. Rose, Targeted Learning: Prediction and Causal Inference for Observational and Experimental Data, chapter 21. Springer, New York, 2011.
38. S. Sinisi and M.J. Van der Laan. The Deletion/Substitution/Addition algorithm in loss function based estimation: Applications in genomics. Journal of Statistical Methods in Molecular Biology, 3(1), 2004.
39. Z. Tan. A distributional approach for causal inference using propensity scores. J. Am. Statist. Assoc., 101:1619-37, 2006.
40. Z. Tan. Comment: Understanding OR, PS and DR. Statistical Science, 22: 560-568, 2007.
41. Zhiqiang Tan. Bounded, efficient and doubly robust estimation with inverse weighting. Biometrika, 97,3:661-682, 2010.
42. R Development Core Team. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria, 2010.
43. A. Tsiatis and M. Davidian. Comment: Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data (with discussion). Statistical Science, 22:569-73, 2007.
44. M.J. Van der Laan and S. Dudoit. Unified cross-validation methodology for selection among estimators and a general cross-validated adaptive epsilon-net estimator: Finite sample oracle inequalities and examples. Technical report, Division of Biostatistics, University of California, Berkeley, November 2003.
45. M.J. Van der Laan and S. Gruber. Collaborative double robust penalized targeted maximum likelihood estimation. The International Journal of Biostatistics, 2009.
46. M.J. Van der Laan and J.M. Robins. Unified methods for censored longitudinal data and causality. Springer, New York, 2003.
47. M.J. Van der Laan and D. Rubin. Targeted maximum likelihood learning. The International Journal of Biostatistics, 2(1), 2006.
48. M.J. Van der Laan, S. Dudoit, and A.W. Van der Vaart. The cross-validated adaptive epsilon-net estimator. Technical report 142, Division of Bio-statistics, University of California, Berkeley, February 2004.
49. M.J. Van der Laan, E. Polley, and A. Hubbard. Super learner. Statistical Applications in Genetics and Molecular Biology, 6(25), 2007. ISSN 1.
50. M.J. Van der Laan, S. Rose, and S. Gruber. Readings on targeted maximum likelihood estimation. Technical report, working paper series http://www.bepress.com/ucbbiostat/paper254, 2009.
51. R. Varadhan. alabama: Constrained nonlinear optimization, 2010. URL http://CRAN.R-project.org/package=alabama. R package version 2010.10-1.
52. W. N. Venables and B. D. Ripley. Modern applied statistics with S. Springer, New York, 4th edition, 2002.
53. E. Grosse W. S. Cleveland and W. M. Shyu. Local regression models. In J. M. Chambers and T. J. Hastie, editors, Statistical Models in S, chapter 6. Wadsworth & Brooks/Cole, 1992.
54. Y. Wang, M. Petersen, D. Bangsberg, and M.J. Van der Laan. Diagnosing bias in the inverse probability of treatment weighted estimator resulting from violation of experimental treatment assignment. Technical Report 211, Division of Biostatistics, University of California, Berkeley, 2006a.
55. Y. Wang, M. Petersen, and M.J. Van der Laan. A statistical method for diagnosing ETA bias in IPTW estimators. Technical report, Division of Biostatistics, University of California, Berkeley, 2006b.
56. R.W.M. Wedderburn. Quasi-likelihood functions, generalized linear models, and the Gauss-Newton method. Biometrika, 61, 1974.