Boosting in Cox regression: a comparison between the likelihood-based and the model-based approaches with focus on the R-packages <Emphasis Type="Italic">CoxBoost</Emphasis> and <Emphasis Type="Italic">mboost</Emphasis>

Despite the limitations imposed by the proportional hazards assumption, the Cox model is probably the most popular statistical tool used to analyze survival data, thanks to its flexibility and ease of interpretation. For this reason, novel statistical/machine learning techniques are usually adapted to fit its requirements, including boosting. Boosting is an iterative technique originally developed in the machine learning community to handle classification problems, and later extended to the statistical field, where it is used in many situations, including regression and survival analysis. The popularity of boosting has been further driven by the availability of user-friendly software such as the R packages mboost and CoxBoost, both of which allow the implementation of boosting in conjunction with the Cox model. Despite the common underlying boosting principles, these two packages use different techniques: the former is an adaptation of model-based boosting, while the latter adapts likelihood-based boosting. Here we contrast these two boosting techniques as implemented in the R packages from an analytic point of view; we further examine solutions adopted within these packages to treat mandatory variables, i.e. variables that—for several reasons—must be included in the model. We explore the possibility of extending solutions currently only implemented in one package to the other. A simulation study and a real data example are added for illustration.