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The International Journal of Biostatistics

Ed. by Chambaz, Antoine / Hubbard, Alan E. / van der Laan, Mark J.

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Targeted Minimum Loss Based Estimator that Outperforms a given Estimator

Susan Gruber / Mark J. van der Laan
Published Online: 2012-05-18 | DOI: https://doi.org/10.1515/1557-4679.1332

Targeted minimum loss based estimation (TMLE) provides a template for the construction of semiparametric locally efficient double robust substitution estimators of the target parameter of the data generating distribution in a semiparametric censored data or causal inference model (van der Laan and Rubin (2006), van der Laan (2008), van der Laan and Rose (2011)). In this article we demonstrate how to construct a TMLE that also satisfies the property that it is at least as efficient as a user supplied asymptotically linear estimator. In particular it is shown that this type of TMLE can incorporate empirical efficiency maximization as in Rubin and van der Laan (2008), Tan (2008, 2010), Rotnitzky et al. (2012), and retain double robustness. For the sake of illustration we focus on estimation of the additive average causal effect of a point treatment on an outcome, adjusting for baseline covariates.

Keywords: Asymptotic linearity of an estimator; causal effect; efficient influence curve; empirical efficiency maximization; confounding; G-computation formula; influence curve; loss function; nonparametric structural equation model; positivity assumption; randomization assumption; randomized trial; semiparametric statistical model; targeted maximum likelihood estimation; targeted minimum loss based estimation

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Published Online: 2012-05-18

Citation Information: The International Journal of Biostatistics, Volume 8, Issue 1, ISSN (Online) 1557-4679, DOI: https://doi.org/10.1515/1557-4679.1332.

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