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Numerous practical applications within engineering disciplines, such as telecommunications, necessitate optimizing power delivery to a connected load. This pursuit, however, entails inherent internal losses, which can either equal or exceed the power supplied to the load. The Thevenin equivalent circuit is helpful in finding the maximum power a linear circuit can deliver to a load. It is assumed in this context that the load resistance can be adjusted.
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Related Experiment Video

Updated: Feb 11, 2026

Author Spotlight: A Computational Pipeline for Analyzing Chimeric Noncoding RNA-Target RNA Interactions in High-Throughput Sequencing Data
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Targeted maximum likelihood estimation for a binary treatment: A tutorial.

Miguel Angel Luque-Fernandez1,2,3, Michael Schomaker4, Bernard Rachet1

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|April 25, 2018
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Summary
This summary is machine-generated.

Targeted Maximum Likelihood Estimation (TMLE) offers a robust approach for estimating treatment effects, outperforming traditional methods by requiring fewer assumptions. This tutorial provides a practical guide to implementing TMLE for binary outcomes and exposures.

Keywords:
causal inferenceensemble Learningmachine learningobservational studiestargeted maximum likelihood estimation

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Area of Science:

  • Epidemiology
  • Biostatistics
  • Machine Learning

Background:

  • Traditional regression methods for estimating average treatment effects can be biased if outcome models are misspecified.
  • Propensity score methods require correct exposure model specification.
  • Double-robust methods offer improved accuracy by requiring only one model (outcome or exposure) to be correctly specified.

Purpose of the Study:

  • To provide a step-by-step educational introduction to Targeted Maximum Likelihood Estimation (TMLE) for binary outcomes and exposures.
  • To illustrate TMLE implementation in a realistic cancer epidemiology scenario with near-violations of positivity and correct model specification assumptions.
  • To enable readers to apply TMLE in practice through reproducible examples and provided code.

Main Methods:

  • Targeted Maximum Likelihood Estimation (TMLE) as a semiparametric, double-robust method.
  • Utilizing machine learning for flexible, nonparametric estimation.
  • Step-by-step guided implementation with extensive R-code for replicability.

Main Results:

  • TMLE demonstrates robustness even when assumptions of correct model specification and positivity are nearly violated.
  • The method offers a more flexible and assumption-lean alternative to traditional approaches.
  • Reproducible code facilitates practical application and further research.

Conclusions:

  • TMLE is a powerful and flexible method for estimating causal effects, particularly in complex epidemiological settings.
  • The provided tutorial and code empower researchers to confidently apply TMLE.
  • TMLE's weaker assumptions enhance the reliability of causal inference in observational studies.