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

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 and making the construction of confidence intervals challenging. 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 between recent theoretical developments and empirical applications, and assess its empirical performance against other estimators. This work emphasizes the translation of existing HAL asymptotic theory to the causal dose-response setting and demonstrates its practical implications through comprehensive simulations, thereby filling an essential gap between theory and practice. Our comprehensive simulations demonstrate that the HAL-based estimator approaches pointwise asymptotic normality under the assumed smoothness conditions and yields confidence intervals that are consistently closer to nominal coverage than those of competing methods. While undercoverage can persist in more complex settings at moderate sample sizes, the HAL estimator consistently outperforms existing approaches for estimating the causal dose-response curve.