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The Relative Performance of Targeted Maximum Likelihood Estimators

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  • Porter Kristin E.
  • Gruber Susan
  • van der Laan Mark J.
  • Sekhon Jasjeet S.

Abstract

There is an active debate in the literature on censored data about the relative performance of model based maximum likelihood estimators, IPCW-estimators, and a variety of double robust semiparametric efficient estimators. Kang and Schafer (2007) demonstrate the fragility of double robust and IPCW-estimators in a simulation study with positivity violations. They focus on a simple missing data problem with covariates where one desires to estimate the mean of an outcome that is subject to missingness. Responses by Robins, et al. (2007), Tsiatis and Davidian (2007), Tan (2007) and Ridgeway and McCaffrey (2007) further explore the challenges faced by double robust estimators and offer suggestions for improving their stability. In this article, we join the debate by presenting targeted maximum likelihood estimators (TMLEs). We demonstrate that TMLEs that guarantee that the parametric submodel employed by the TMLE procedure respects the global bounds on the continuous outcomes, are especially suitable for dealing with positivity violations because in addition to being double robust and semiparametric efficient, they are substitution estimators. We demonstrate the practical performance of TMLEs relative to other estimators in the simulations designed by Kang and Schafer (2007) and in modified simulations with even greater estimation challenges.

Suggested Citation

  • Porter Kristin E. & Gruber Susan & van der Laan Mark J. & Sekhon Jasjeet S., 2011. "The Relative Performance of Targeted Maximum Likelihood Estimators," The International Journal of Biostatistics, De Gruyter, vol. 7(1), pages 1-34, August.
    • Handle: RePEc:bpj:ijbist:v:7:y:2011:i:1:n:31
    DOI: 10.2202/1557-4679.1308
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    References listed on IDEAS

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    1. Mark van der Laan & Sandrine Dudoit & Aad van der Vaart, 2004. "The Cross-Validated Adaptive Epsilon-Net Estimator," U.C. Berkeley Division of Biostatistics Working Paper Series 1141, Berkeley Electronic Press.
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    5. Rubin Daniel B & van der Laan Mark J., 2008. "Empirical Efficiency Maximization: Improved Locally Efficient Covariate Adjustment in Randomized Experiments and Survival Analysis," The International Journal of Biostatistics, De Gruyter, vol. 4(1), pages 1-42, May.
    6. Gruber Susan & van der Laan Mark J., 2010. "A Targeted Maximum Likelihood Estimator of a Causal Effect on a Bounded Continuous Outcome," The International Journal of Biostatistics, De Gruyter, vol. 6(1), pages 1-18, August.
    7. Rosenblum Michael & van der Laan Mark J., 2010. "Targeted Maximum Likelihood Estimation of the Parameter of a Marginal Structural Model," The International Journal of Biostatistics, De Gruyter, vol. 6(2), pages 1-30, April.
    8. James Robins & Andrea Rotnitzky & Stijn Vansteelandt, 2007. "Discussions," Biometrics, The International Biometric Society, vol. 63(3), pages 650-653, September.
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    Cited by:

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    6. van der Laan Mark J., 2014. "Targeted Estimation of Nuisance Parameters to Obtain Valid Statistical Inference," The International Journal of Biostatistics, De Gruyter, vol. 10(1), pages 29-57, May.
    7. Youmi Suk, 2024. "A Within-Group Approach to Ensemble Machine Learning Methods for Causal Inference in Multilevel Studies," Journal of Educational and Behavioral Statistics, , vol. 49(1), pages 61-91, February.
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    9. Stitelman Ori M & Wester C. William & De Gruttola Victor & van der Laan Mark J., 2011. "Targeted Maximum Likelihood Estimation of Effect Modification Parameters in Survival Analysis," The International Journal of Biostatistics, De Gruyter, vol. 7(1), pages 1-34, March.
    10. van der Laan Mark J. & Gruber Susan, 2012. "Targeted Minimum Loss Based Estimation of Causal Effects of Multiple Time Point Interventions," The International Journal of Biostatistics, De Gruyter, vol. 8(1), pages 1-41, May.
    11. Brooks Jordan & van der Laan Mark J. & Go Alan S., 2012. "Targeted Maximum Likelihood Estimation for Prediction Calibration," The International Journal of Biostatistics, De Gruyter, vol. 8(1), pages 1-35, October.
    12. Kreif, N. & Grieve, R. & Díaz, I. & Harrison, D., 2014. "Health econometric evaluation of the effects of a continuous treatment: a machine learning approach," Health, Econometrics and Data Group (HEDG) Working Papers 14/19, HEDG, c/o Department of Economics, University of York.
    13. Díaz Iván & Carone Marco & van der Laan Mark J., 2016. "Second-Order Inference for the Mean of a Variable Missing at Random," The International Journal of Biostatistics, De Gruyter, vol. 12(1), pages 333-349, May.
    14. Sherri Rose & Sharon‐Lise Normand, 2019. "Double robust estimation for multiple unordered treatments and clustered observations: Evaluating drug‐eluting coronary artery stents," Biometrics, The International Biometric Society, vol. 75(1), pages 289-296, March.
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    16. Chaffee Paul H. & van der Laan Mark J., 2012. "Targeted Maximum Likelihood Estimation for Dynamic Treatment Regimes in Sequentially Randomized Controlled Trials," The International Journal of Biostatistics, De Gruyter, vol. 8(1), pages 1-32, June.
    17. Youmi Suk & Kyung T. Han, 2024. "A Psychometric Framework for Evaluating Fairness in Algorithmic Decision Making: Differential Algorithmic Functioning," Journal of Educational and Behavioral Statistics, , vol. 49(2), pages 151-172, April.
    18. Schnitzer Mireille E. & Lok Judith J. & Gruber Susan, 2016. "Variable Selection for Confounder Control, Flexible Modeling and Collaborative Targeted Minimum Loss-Based Estimation in Causal Inference," The International Journal of Biostatistics, De Gruyter, vol. 12(1), pages 97-115, May.
    19. Díaz Iván & Rosenblum Michael, 2015. "Targeted Maximum Likelihood Estimation using Exponential Families," The International Journal of Biostatistics, De Gruyter, vol. 11(2), pages 233-251, November.
    20. Nima S. Hejazi & Mark J. van der Laan & Holly E. Janes & Peter B. Gilbert & David C. Benkeser, 2021. "Efficient nonparametric inference on the effects of stochastic interventions under two‐phase sampling, with applications to vaccine efficacy trials," Biometrics, The International Biometric Society, vol. 77(4), pages 1241-1253, December.
    21. Gilbert Peter B. & Blette Bryan S. & Shepherd Bryan E. & Hudgens Michael G., 2020. "Post-randomization Biomarker Effect Modification Analysis in an HIV Vaccine Clinical Trial," Journal of Causal Inference, De Gruyter, vol. 8(1), pages 54-69, January.
    22. Sherri Rose & Julie Shi & Thomas G. McGuire & Sharon-Lise T. Normand, 2017. "Matching and Imputation Methods for Risk Adjustment in the Health Insurance Marketplaces," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 9(2), pages 525-542, December.
    23. van der Laan Mark, 2017. "A Generally Efficient Targeted Minimum Loss Based Estimator based on the Highly Adaptive Lasso," The International Journal of Biostatistics, De Gruyter, vol. 13(2), pages 1-35, November.
    24. Gilbert Peter B. & Blette Bryan S. & Hudgens Michael G. & Shepherd Bryan E., 2020. "Post-randomization Biomarker Effect Modification Analysis in an HIV Vaccine Clinical Trial," Journal of Causal Inference, De Gruyter, vol. 8(1), pages 54-69, January.
    25. Mariela Sued & Marina Valdora & Víctor Yohai, 2020. "Robust doubly protected estimators for quantiles with missing data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 819-843, September.

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