Tree-based methods are very powerful and popular tools for analysing survival data with right-censoring. The existing methods assume that the true time-to-event and the censoring times are independent given the covariates. We propose different ways to build survival forests when dependent censoring is suspected, by using an appropriate estimator of the survival function when aggregating the individual trees and/or by modifying the splitting rule. The appropriate estimator used in this paper is the copula-graphic estimator. We also propose a new method for building survival forests, called p-forest, that may be used not only when dependent censoring is suspected, but also as a new survival forest method in general. The results from a simulation study indicate that these modifications improve greatly the estimation of the survival function in situations of dependent censoring. A real data example illustrates how the proposed methods can be used to perform a sensitivity analysis.
Keywords: Survival data; copula-graphic; dependent-censoring; ensemble methods; random forest; right-censored data; sensitivity analysis; survival forest.