Comparing measures of model selection for penalized splines in Cox models

Area of Science:

• Biostatistics
• Survival Analysis
• Statistical Modeling

Background:

• Penalized splines are crucial for flexible modeling in Cox regression.
• Selecting the optimal degree of smoothness is essential for reliable results.
• Various model fit criteria exist, but their performance in this context is not fully understood.

Purpose of the Study:

• To evaluate and compare five model fit criteria for selecting the optimal smoothness of penalized splines in Cox models.
• To assess the performance of these criteria in a simulation study across different scenarios and sample sizes.
• To apply these methods to a real-world dataset on rectal cancer mortality.

Main Methods:

• The study considered Akaike information criterion (AIC), corrected AIC, two Bayesian information criteria (BIC), and generalized cross-validation (GCV).
• A simulation study estimated penalized spline model fits in six exposure-response scenarios.
• Model performance was assessed using mean squared error and hypothesis testing power/size.

Main Results:

• Generalized cross-validation (GCV) demonstrated strong performance in selecting appropriate smoothness.
• The criteria showed varying effectiveness depending on sample size and the true underlying exposure-response relationship.
• Application to rectal cancer mortality data illustrated practical use.

Conclusions:

• GCV is a reliable method for choosing penalized spline smoothness in Cox models.
• The choice of model fit criterion can impact the estimated exposure-response curves and statistical inference.
• Careful selection of smoothness is vital for accurate survival data analysis.