Prediction accuracy and variable selection for penalized cause-specific hazards models

We consider modeling competing risks data in high dimensions using a penalized cause-specific hazards (CSHs) approach. CSHs have conceptual advantages that are useful for analyzing molecular data. First, working on hazards level can further understanding of the underlying biological mechanisms that drive transition hazards. Second, CSH models can be used to extend the multistate framework for high-dimensional data. The CSH approach is implemented by fitting separate proportional hazards models for each event type (iCS). In the high-dimensional setting, this might seem too complex and possibly prone to overfitting. Therefore, we consider an extension, namely "linking" the separate models by choosing penalty tuning parameters that in combination yield best prediction of the incidence of the event of interest (penCR). We investigate whether this extension is useful with respect to prediction accuracy and variable selection. The two approaches are compared to the subdistribution hazards (SDH) model, which is an established method that naturally achieves "linking" by working on incidence level, but loses interpretability of the covariate effects. Our simulation studies indicate that in many aspects, iCS is competitive to penCR and the SDH approach. There are some instances that speak in favor of linking the CSH models, for example, in the presence of opposing effects on the CSHs. We conclude that penalized CSH models are a viable solution for competing risks models in high dimensions. Linking the CSHs can be useful in some particular cases; however, simple models using separately penalized CSH are often justified.