Assessing time-by-covariate interactions in relative survival models using restrictive cubic spline functions

Area of Science:

• Biostatistics
• Survival Analysis
• Epidemiology

Background:

• The Cox proportional hazards model is common for prognostic factors but less suitable for population-based long-term survival.
• Relative survival models are often preferred for unselected populations.
• Evaluating the proportional hazards assumption is crucial for both models.

Purpose of the Study:

• To propose a novel method for relative survival analysis using restricted cubic splines.
• To model time-by-covariate interactions without assuming a specific functional form.
• To formally test the proportional hazards assumption and linearity of interactions.

Main Methods:

• Employed restricted cubic spline functions to model time-by-covariate interactions in relative survival analyses.
• Allowed graphical representation and formal testing of time-by-covariate interactions.
• Facilitated investigation into the shape of covariate effect dependence on time.

Main Results:

• Application to colon cancer mortality data strongly rejected the proportional hazards hypothesis for all prognostic factors.
• Highlighted the importance of modeling non-proportional hazards and using a relative survival approach.
• Demonstrated the advantages of restricted cubic splines for modeling non-proportional hazards, offering new insights into age and diagnosis period impacts.

Conclusions:

• Restricted cubic splines in relative survival models offer a parsimonious way to represent complex relative risk changes over time.
• This approach avoids a priori assumptions about the functional form of these changes.
• Enables more accurate survival analyses in population-based studies.