Deep partially linear cox model for current status data.

Area of Science:

• Statistics
• Machine Learning
• Biostatistics

Background:

• Deep learning has shown success in various fields, but its application to survival data analysis is underexplored.
• Current methods for survival data analysis, especially with high-dimensional covariates, face challenges like the curse of dimensionality.

Purpose of the Study:

• To propose a deep partially linear Cox model for analyzing current status survival data.
• To address the curse of dimensionality and model nonlinear covariate effects in survival analysis.

Main Methods:

• Utilizing deep neural networks (DNNs) to capture nonlinear covariate effects.
• Employing monotone splines to approximate the baseline cumulative hazard function.
• Developing maximum likelihood estimators and analyzing their convergence properties.

Main Results:

• The proposed model circumvents the curse of dimensionality for survival data analysis.
• The finite-dimensional estimator for treatment covariate effects is proven to be $\sqrt{n}$-consistent, asymptotically normal, and semiparametric efficient.
• The model demonstrates strong performance in simulation studies and real-world data applications.

Conclusions:

• The deep partially linear Cox model offers a flexible and efficient approach for survival data analysis, particularly in high-dimensional settings.
• This method enhances the application of deep learning techniques to survival analysis, opening avenues for further research.