Comparing measures of model selection for penalized splines in Cox models

This article presents an application and a simulation study of model fit criteria for selecting the optimal degree of smoothness for penalized splines in Cox models. The criteria considered were the Akaike information criterion, the corrected AIC, two formulations of the Bayesian information criterion, and a generalized cross-validation method. The estimated curves selected by the five methods were compared to each other in a study of rectal cancer mortality in autoworkers. In the stimulation study, we estimated the fit of the penalized spline models in six exposure-response scenarios, using the five model fit criteria. The methods were compared on the basis of a mean squared error score and the power and size of hypothesis tests for any effect and for detecting nonlinearity. All comparisons were made across a range in the total sample size and number of cases.