The Cox proportional hazards model with a partly linear relative risk function

Area of Science:

• Biostatistics
• Survival Analysis
• Statistical Modeling

Background:

• Conventional Cox models use loglinear relative risk with finite parameters.
• Partly linear Cox models offer a more robust relative risk specification by including infinite dimensional parameters.

Purpose of the Study:

• Develop a likelihood-based inference procedure for finite dimensional parameters in partly linear Cox models.
• Address challenges of infinite dimensional parameters in likelihood approaches.

Main Methods:

• Orthogonal reparameterization of the relative risk function.
• Maximization of the profile partial likelihood using kernel smoothing.
• Establishment of asymptotic distribution theory for the estimates.

Main Results:

• The developed method provides asymptotically efficient estimates for finite dimensional parameters.
• Orthogonal reparameterization allows for standard profile likelihood inference without adjustments.
• Demonstrated methodology with a retrospective cancer analysis.

Conclusions:

• The partly linear Cox model offers a robust alternative to conventional Cox models.
• The proposed inference procedure is statistically sound and efficient.
• This approach is applicable to survival data analysis, particularly in medical research.