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.

翻译：理解处理效应异质性对于许多科学领域至关重要，因为相同的处理可能对不同个体产生不同影响。分位数回归为建模这种异质性提供了自然框架。我们提出一种新方法，用于在高维协变量存在的情况下对异质性分位数处理效应进行推断。该估计器将 $\ell_1$ 惩罚回归调整与基于秩得分的分位数特定偏差校正方案相结合。我们研究了该估计器的理论性质，包括估计的异质性分位数处理效应过程的弱收敛性和半参数效率。通过模拟和实证案例（涉及英国生物银行研究中参与者的他汀类药物使用对降低低密度脂蛋白胆固醇水平的差异效应）阐明了我们方法的有限样本性能。