Structured Nonlinear Cure Model With Deep Neural Networks for High-Dimensional Survival Analysis

Accurate prognosis and effective variable selection are essential in high-dimensional survival analysis, particularly for understanding long-term survival outcomes. The mixture cure rate model has been commonly adopted for subjects with exceptionally long survival times. However, traditional models usually assume log-linear effects of covariates, which may not capture the complex and nonlinear relationships in real-world data. Additionally, clinical observations reveal structural similarity between covariates that influence both patient cure rates and survival times. Existing methods typically estimate the two components of the mixture cure model independently, neglecting their inherent connections. To address these limitations, in this study, we enhance the conventional cure rate model by incorporating deep neural networks with a selection layer, while preserving the similarity structure between the cured and susceptible fractions. By integrating regularization constraints on the selection parameters and weight matrices within the neural network, the proposed approach simultaneously achieves effective variable selection and handles a series of complex nonlinear relationships within the data. To further enhance consistency in variable selection across both components of the cure model, a novel penalty is introduced, enabling the proposed model to identify key variables and enhance overall performance and interpretability in high-dimensional datasets. Through extensive simulation studies and real-world data analysis, the superior performance and robustness of the proposed approach are evident.