Assessing time-by-covariate interactions in proportional hazards regression models using cubic spline functions

Area of Science:

• Biostatistics
• Survival Analysis
• Statistical Modeling

Background:

• Proportional hazards (Cox) regression is widely used for survival data analysis.
• Investigating time-dependent covariate effects is crucial but often complex.
• Pre-specifying functional forms for covariate-time interactions can be restrictive.

Purpose of the Study:

• To introduce and evaluate the use of cubic spline functions for modeling time-by-covariate interactions in Cox regression.
• To demonstrate how cubic splines can flexibly capture the shape of covariate-time dependencies.
• To show how this method facilitates graphical analysis and formal testing of model assumptions.

Main Methods:

• Utilized cubic spline functions to model time-by-covariate interactions within the Cox regression framework.
• Employed standard maximum likelihood methods for estimating regression coefficients.
• Integrated cubic splines with existing statistical software for practical application.

Main Results:

• Cubic splines allow flexible modeling of covariate-time interactions without assuming a specific functional form.
• This approach enables graphical visualization of complex time-dependent effects.
• Formal tests for proportional hazards assumption and non-linearity of interactions can be conducted.

Conclusions:

• Cubic spline functions offer a powerful and flexible tool for analyzing time-by-covariate interactions in Cox regression.
• This method enhances the investigation of survival data by accommodating non-linear and non-proportional hazards.
• The approach is computationally feasible using standard statistical software and methods.