Heterogeneous Quantile Treatment Effect Estimation for Longitudinal Data with High-Dimensional Confounding

Causal inference plays a fundamental role in various real-world applications. However, in the motivating non-small cell lung cancer (NSCLC) study, it is challenging to estimate the treatment effect of chemotherapy on circulating tumor DNA (ctDNA). First, the heterogeneous treatment effects vary across patient subgroups defined by baseline characteristics. Second, there exists a broad set of demographic, clinical and molecular variables act as potential confounders. Third, ctDNA trajectories over time show heavy-tailed non-Gaussian behavior. Finally, repeated measurements within subjects introduce unknown correlation. Combining convolution-smoothed quantile regression and orthogonal random forest, we propose a framework to estimate heterogeneous quantile treatment effects in the presence of high-dimensional confounding, which not only captures effect heterogeneity across covariates, but also behaves robustly to nuisance parameter estimation error. We establish the theoretical properties of the proposed estimator and demonstrate its finite-sample performance through comprehensive simulations. We illustrate its practical utility in the motivated NSCLC study.