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Targeted maximum likelihood estimation of natural direct effects.

Wenjing Zheng1, Mark J van der Laan

  • 1University of California, Berkeley, Berkeley, CA, USA.

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This study introduces a new method for estimating direct causal effects, reducing reliance on mediator density estimation. The novel approach offers improved robustness in causal inference for understanding exposure-outcome relationships.

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Area of Science:

  • Causal Inference
  • Biostatistics
  • Epidemiology

Background:

  • Estimating direct causal effects, unmediated by intermediate variables, is crucial in causal inference.
  • Formal definitions of natural and controlled direct effects exist within the counterfactual framework.
  • Prior work established efficient scores and estimators for natural effects under nonparametric models.

Purpose of the Study:

  • To develop a semiparametric efficient, multiply robust, substitution estimator for the natural direct effect.
  • To apply the targeted maximum likelihood framework to causal effect estimation.
  • To weaken existing robustness conditions and reduce reliance on mediator density estimation.

Main Methods:

  • Application of the targeted maximum likelihood (TML) framework.
  • Construction of a substitution estimator satisfying a specific efficient score equation.
  • Relaxation of robustness conditions compared to previous methods.

Main Results:

  • The proposed estimator is asymptotically unbiased under three distinct sets of conditions, involving estimation of outcome, exposure, and mediator densities.
  • The estimator achieves asymptotic efficiency when all three sets of conditions are met.
  • The robustness conditions are shown to be weaker than previously established.

Conclusions:

  • The targeted maximum likelihood framework provides a robust and efficient method for estimating natural direct effects.
  • The new estimator offers flexibility by relaxing assumptions on mediator density estimation.
  • The methodology can be extended to investigate natural indirect effects.