Contrasting survival trees and survival forests with traditional survival models: incorporating time-dependent covariates

Survival data have commonly been analysed using methods that rely on restrictive assumptions such as proportional hazards. With such techniques, identifying non-linear effects or interactions involving multiple variables can be difficult. In contrast, survival trees and survival forests are non-parametric alternatives to these models that may be able to automatically detect certain types of interactions without the need to specify them beforehand. Survival trees emerged with the extension of decision tree-based methods to specifically handle survival data with censoring. Whereas in survival forests, where a survival tree is grown for each bootstrap sample using a random subset of candidate variables at each node, numerous survival trees are combined. Recent advances in these tree-based methods have enabled these non-parametric techniques to handle time-dependent covariates.

In this work, various scenarios of simulated survival data have been generated to enable the comparison of output from survival trees and survival forests to output from traditional survival models. These demonstrate the capabilities of survival trees and forests, while also the useful interpretation capabilities inherent of traditional techniques under certain scenarios. Changes in a patient’s treatment or proportional increases in their exposure are two example scenarios requiring inclusion of time-varying covariates. The capabilities of survival trees and forests in handling a variety of such time-varying covariates is illustrated.