Piecewise exponential survival trees with time-dependent covariates

Survival trees methods are nonparametric alternatives to the semiparametric Cox regression in survival analysis. In this paper, a tree-based method fo r censored survival data with time-dependent covariates is proposed. The pr oposed method assumes a very general model for the hazard function and is f ully nonparametric. The recursive partitioning algorithm uses the likelihoo d estimation procedure to grow trees under a piecewise exponential structur e that handles time-dependent covariates in a parallel way to time-independ ent covariates. In general, the estimated hazard at a node gives the risk f or a group of individuals during a specific time period. Both cross-validat ion and bootstrap resampling techniques are implemented in the tree selecti on procedure. The performance of the proposed survival trees method is show n to be good through simulation and application to real data.