Constructing targeted minimum loss/maximum likelihood estimators: a simple illustration to build intuition.

Journal: American journal of epidemiology
Published Date: Jun 3, 2026

Abstract

Machine learning is increasingly used to estimate nuisance functions in causal inference. The efficient influence function (EIF) offers a principled way to construct estimators that can incorporate machine learning with valid inference (eg, estimate valid conference intervals). In this tutorial, we illustrate how to construct targeted maximum likelihood/minimum loss estimators from the EIF, a topic that is well covered in statistical literature but remains less accessible to applied researchers. A companion paper, Renson et al. 2025 (AJE, kwaf169) provides a thorough, but approachable description of the EIF and its derivation for a statistical estimand.

Authors

  • Rachael K Ross
    Department of Epidemiology, Columbia University, New York, NY.
  • Lina M Montoya
    School of Data Science and Society and Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, NC.
  • Dana E Goin
    Division of Epidemiology, School of Public Health, University of California, Berkeley, CA, USA. Electronic address: [email protected].
  • Iván Díaz
    Department of Biostatistics Bloomberg, School of Public Health, Johns Hopkins University, Baltimore, MD 21218, USA. [email protected].
  • Audrey Renson
    Department of Epidemiology, University of North Carolina at Chapel Hill, 135 Dauer Dr., Chapel Hill, NC 27599, USA.

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