Abstract
In this chapter, we will present one-dimensional universal least favorable parametric submodels for the TMLE of univariate and multivariate target parameters. They guarantee that a single TMLE-update of the initial estimator already solves the efficient influence curve equation. We explain why this type of one-step TMLE is more stable than an iterative TMLE. By the fact that the one-step TMLE for high-dimensional or even infinite-dimensional target parameters is a substitution estimator, it follows that it completely respects the structure of the infinite dimensional parameter. The content of this chapter partly relies on van der Laan and Gruber (2016). As an example, we present a one-step TMLE of a complete treatment-specific survival function.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
K.L. Moore, M.J. van der Laan, Application of time-to-event methods in the assessment of safety in clinical trials, in Design, Summarization, Analysis & Interpretation of Clinical Trials with Time-to-Event Endpoints, ed. by K.E. Peace (Chapman & Hall, Boca Raton, 2009a)
K.L. Moore, M.J. van der Laan, Covariate adjustment in randomized trials with binary outcomes: targeted maximum likelihood estimation. Stat. Med. 28(1), 39–64 (2009b)
K.L. Moore, M.J. van der Laan, Increasing power in randomized trials with right censored outcomes through covariate adjustment. J. Biopharm. Stat. 19(6), 1099–1131 (2009c)
M.J. van der Laan, S. Gruber, One-step targeted minimum loss-based estimation based on universal least favorable one-dimensional submodels. Int. J. Biostat. 12(1), 351–378 (2016)
M.J. van der Laan, M. Petersen, W. Zheng, Estimating the effect of a community-based intervention with two communities. J. Causal Inference 1(1), 83–106 (2013b)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this chapter
Cite this chapter
van der Laan, M.J., Cai, W., Gruber, S. (2018). One-Step TMLE. In: Targeted Learning in Data Science. Springer Series in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-65304-4_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-65304-4_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-65303-7
Online ISBN: 978-3-319-65304-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)