Building Cox-type structured hazard regression models with time-varying effects

In recent years, flexible hazard regression models based on penalized splines have been developed that allow us to extend the classical Cox model via the inclusion of time-varying and nonparametric effects. Despite their immediate appeal in terms of flexibility, these models introduce additional difficulties when a subset of covariates and the corresponding modelling alternatives have to be chosen. We present an analysis of data from a specific patient population with 90-day survival as the response variable. The aim is to determine a sensible prognostic model where some variables have to be included due to subject-matter knowledge while other variables are subject to model selection. Motivated by this application, we propose a two-stage stepwise model building strategy to choose both the relevant covariates and the corresponding modelling alternatives within the choice set of possible covariates simultaneously. For categorical covariates, competing modelling approaches are linear effects and time-varying effects, whereas nonparametric modelling provides a further alternative in case of continuous covariates. In our data analysis, we identified a prognostic model containing both smooth and time-varying effects.