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Nonparametric inverse-probability-weighted estimators based on the highly adaptive lasso.

Ashkan Ertefaie1, Nima S Hejazi2, Mark J van der Laan3

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|July 15, 2022
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Summary

This study introduces novel nonparametric inverse-probability-weighted estimators for causal effects, improving efficiency and overcoming the curse of dimensionality. The new method enhances causal effect estimation in large statistical models without complex model specification.

Keywords:
adaptive estimationcausal inferenceefficient influence functionsemiparametric efficiency

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Area of Science:

  • Statistics
  • Causal Inference
  • Epidemiology

Background:

  • Inverse-probability-weighted (IPW) estimators are widely used for causal effect estimation.
  • Traditional IPW methods suffer from inefficiency and the curse of dimensionality.
  • Correct specification of the weighting mechanism model is crucial but challenging.

Purpose of the Study:

  • To propose a new class of nonparametric IPW estimators.
  • To enhance the efficiency and robustness of causal effect estimation.
  • To address limitations of existing IPW and doubly robust estimators.

Main Methods:

  • Estimated the weighting mechanism using undersmoothing of the highly adaptive lasso.
  • Demonstrated asymptotic linearity of the proposed estimators.
  • Showcased variance convergence to the nonparametric efficiency bound.

Main Results:

  • The proposed nonparametric IPW estimators achieve asymptotic linearity.
  • The variance of the estimators converges to the nonparametric efficiency bound.
  • The methodology avoids the need for efficient influence function derivation or conditional outcome model specification.

Conclusions:

  • The novel estimators offer a more efficient and practical approach to causal effect estimation.
  • This method has broad implications for large statistical models and diverse problem settings.
  • The approach was validated through simulations and an epidemiologic study.