The Relative Performance of Targeted Maximum Likelihood Estimators

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

The International Journal of Biostatistics, 2011, vol. 7, issue 1, 1-34

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.

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 (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (25)

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DOI: 10.2202/1557-4679.1308

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