HAL-based Plugin Estimation of the Causal Dose-Response Curve

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 and assess its empirical performance against other estimators. Through comprehensive simulations, we evaluate the accuracy of the estimation and the quality of the inference, particularly in terms of coverage, using robust standard error estimators. Our results demonstrate the finite-sample effectiveness of the HAL-based estimator, utilizing an undersmoothed and smoothness-adaptive fit for the conditional outcome model. Additionally, the simulations reveal that the HAL-based estimator consistently outperforms existing methods for estimating the causal dose-response curve.