  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.
