Deep Learning for Variable Selection in Censored Quantile Regression Models

ABSTRACT Censored quantile regression models have emerged as a powerful tool for addressing heterogeneity in survival outcomes, which is a key challenge in survival analysis. In this paper, we propose a novel deep learning–based approach for variable selection in censored quantile regression, providing a flexible and robust alternative to traditional methods that often depend on restrictive model assumptions. The proposed method is supported by strong theoretical guarantees, including non‐asymptotic upper bounds on the estimator's excess risk and proof of algorithm selection consistency within the framework of the path norm. To ensure practical applicability, we develop an efficient implementation algorithm that is both scalable and computationally feasible. Extensive simulation studies demonstrate the accuracy and effectiveness of the method across diverse settings. Finally, we apply the methodology to a real‐world clinical dataset, highlighting its practical utility and robustness in uncovering complex survival dynamics.