Robust functional Cox regression model

Area of Science:

• Statistics
• Biostatistics
• Survival Analysis

Background:

• Classical Cox proportional hazards models with functional covariates are sensitive to outliers.
• Existing functional Cox models lack robustness, impacting time-to-event outcome assessments.

Purpose of the Study:

• To develop a robust functional Cox regression model resistant to outliers.
• To enhance the reliability of survival analysis when functional data contains aberrant observations.

Main Methods:

• Combines projection-pursuit robust functional principal component analysis (RPCA) for dimension reduction.
• Utilizes a robust partial likelihood approach for parameter estimation in a finite-dimensional subspace.
• Incorporates robust functional principal components and scalar covariates.

Main Results:

• The proposed robust functional Cox model demonstrates superior performance compared to classical and penalized methods, especially with outlier-prone data.
• Asymptotic properties including consistency and normality were established.
• Influence function analysis confirmed robustness characteristics.

Conclusions:

• The robust functional Cox regression model offers a reliable alternative for survival analysis with functional data containing outliers.
• The method is effective in real-world applications, as shown with National Health and Nutrition Examination Survey accelerometry data.