One-Step TMLE

  • Mark J. van der Laan
  • Wilson Cai
  • Susan Gruber
Part of the Springer Series in Statistics book series (SSS)


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.


  1. 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)Google Scholar
  2. 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)Google Scholar
  3. 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)Google Scholar
  4. 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)MathSciNetGoogle Scholar
  5. 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)Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Mark J. van der Laan
    • 1
  • Wilson Cai
    • 2
  • Susan Gruber
    • 3
  1. 1.Division of Biostatistics and Department of StatisticsUniversity of California, BerkeleyBerkeleyUSA
  2. 2.Division of BiostatisticsUniversity of California, BerkeleyBerkeleyUSA
  3. 3.Department of Population MedicineHarvard Medical School, Harvard Pilgrim Health Care InstituteBostonUSA

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