A Time-varying Subdistribution Hazard Model with Neural Network

The subdistribution hazard model has gained popularity for analyzing competing risks data. However, existing subdistribution-based methods either require assumptions about the model structure or lack theoretical results. This paper introduces a sufficiently flexible time-varying nonparametric subdistribution hazard model and employs neural networks as an estimator to circumvent the curse of dimensionality. Theoretical results demonstrate that the estimator achieves the minimax optimal rate of convergence, up to a polylogarithmic factor. We introduce a novel time-dependent AUC and a new generalized C-index to evaluate the predictive performance of time-varying models, and propose two tests: a structure test to select a more suitable model and a significance test to identify covariates that have a significant effect on the outcome. Numerical simulations illustrate the strong performance of the proposed model and the effectiveness of the tests. Finally, we integrate these methods into the Python package “TimeSub” and applied the methods to a real dataset, providing a corresponding analysis.