A hybrid Newton-type method for censored survival data using double weights in linear models

Area of Science:

• Statistics
• Biostatistics
• Survival Analysis

Background:

• The Cox model is a standard for survival data analysis.
• Rank-based estimating methods offer an alternative but face numerical challenges due to discontinuous estimating functions.
• Existing methods by Tsiatis (1990) and Nan et al. (2006) address randomly observed and case-cohort data, respectively.

Purpose of the Study:

• To address the computational challenges of rank-based estimating functions for censored survival data.
• To propose an efficient computational method for a family of doubly weighted rank-based estimating functions.
• To extend these methods to handle biased sampling problems like case-cohort data.

Main Methods:

• Investigated a family of doubly weighted rank-based estimating functions, encompassing existing methods.
• Demonstrated the monotonicity of these discontinuous estimating functions using generalized Gehan-type weights.
• Developed a Newton-type iterative method as an alternative to linear programming for solving the estimating equations, especially for large datasets.

Main Results:

• The proposed doubly weighted rank-based estimating functions exhibit monotonicity under generalized Gehan-type weights.
• The Newton-type iterative method provides an efficient approach to find approximate solutions for the estimating equations.
• Simulation studies validated the effectiveness of the proposed computational method.
• The method was successfully applied to a real-world survival data example.

Conclusions:

• The proposed Newton-type method offers a computationally feasible solution for complex rank-based survival data analysis.
• This approach enhances the applicability of rank-based methods, particularly for biased sampling scenarios.
• The findings contribute to more robust statistical inference in survival analysis.