Debiased Inference on Heterogeneous Quantile Treatment Effects with Regression Rank-Scores

TL;DR

This paper introduces a novel method for inference on heterogeneous quantile treatment effects using high-dimensional covariates, combining penalized regression and rank-score bias correction, with theoretical guarantees and empirical validation.

Contribution

It develops a new estimator that integrates $$-penalized regression adjustment with a rank-score bias correction for quantile treatment effects in high-dimensional settings.

Findings

The estimator is weakly convergent and semiparametrically efficient.

Simulation studies demonstrate good finite-sample performance.

Empirical analysis reveals differential effects of statin use on LDL cholesterol in Alzheimer's patients.

Abstract

Understanding treatment effect heterogeneity is vital to many scientific fields because the same treatment may affect different individuals differently. Quantile regression provides a natural framework for modeling such heterogeneity. We propose a new method for inference on heterogeneous quantile treatment effects in the presence of high-dimensional covariates. Our estimator combines an $\ell_1$-penalized regression adjustment with a quantile-specific bias correction scheme based on rank scores. We study the theoretical properties of this estimator, including weak convergence and semiparametric efficiency of the estimated heterogeneous quantile treatment effect process. We illustrate the finite-sample performance of our approach through simulations and an empirical example, dealing with the differential effect of statin usage for lowering low-density lipoprotein cholesterol levels for the Alzheimer's disease patients who participated in the UK Biobank study.