A DNN-Based Weighted Partial Likelihood for Partially Linear Subdistribution Hazard Model

Deep learning has excelled in the field of statistical learning. In the field of survival analysis, some studies have combined deep learning methods with partially linear structures to propose deep partially linear structures. We extend it to the field of competing risks and propose the deep partially linear subdistribution hazard model (DPLSHM). To evaluate the predictive performance of the model, we further develop a time-dependent AUC method specifically tailored for competing risks data and provide an estimator for AUC. Theoretical results for the proposed model demonstrate the asymptotic normality of the parameter component at a rate of $\sqrt{n}$ and provide the convergence rate of the nonparametric component, which achieves the minimal limit convergence rate (multiplicative logarithmic factors). The theory of consistency and rate of convergence of AUC-related estimates is also developed, while we prove that the regression component of DPLSHM maximizes theoretical AUC asymptotically. Subsequently, the paper validates the excellent performance of DPLSHM in estimation and prediction through numerical simulations and real-world datasets.