HAL-Based Plug-in Estimation with Pointwise Asymptotic Normality of the Causal Dose-Response Curve

TL;DR

This paper introduces a HAL-based plug-in estimator for the causal dose-response curve that achieves pointwise asymptotic normality, providing reliable inference without parametric assumptions, and demonstrates superior empirical performance.

Contribution

The paper develops a novel HAL-based estimator for the causal dose-response curve that ensures asymptotic normality and outperforms existing methods in simulations.

Findings

Achieves pointwise asymptotic normality with valid inference

Outperforms existing estimators in simulation studies

Provides a practical approach bridging theory and empirical application

Abstract

Estimating and obtaining reliable inference for the marginally adjusted causal dose-response curve for continuous treatments without relying on parametric assumptions is a well-known statistical challenge. Parametric models risk introducing significant bias through model misspecification, compromising the accurate representation of the underlying data and dose-response relationship. On the other hand, nonparametric models face difficulties as the dose-response curve is not pathwise differentiable, preventing consistent estimation at standard rates. The Highly Adaptive Lasso (HAL) maximum likelihood estimator offers a promising approach to this issue. In this paper, we introduce a HAL-based plug-in estimator for the causal dose-response curve, bridge theoretical development and empirical application, and assess its empirical performance against other estimators. This work emphasizes not just theoretical proofs, but also demonstrates their application through comprehensive simulations, thereby filling an essential gap between theory and practice. Our comprehensive simulations demonstrate that the HAL-based estimator achieves pointwise asymptotic normality with valid inference and consistently outperforms existing approaches for estimating the causal dose-response curve.