ROC-Guided Survival Trees and Forests

Tree-based methods are popular nonparametric tools in studying time-to-event outcomes. In this article, we introduce a novel framework for survival trees and forests, where the trees partition the dynamic survivor population and can handle time-dependent covariates. Using the idea of randomized tests, we develop generalized time-dependent Receiver Operating Characteristic (ROC) curves to evaluate the performance of survival trees and establish the optimality of the target hazard function with respect to the ROC curve. The tree-building algorithm is guided by decision-theoretic criteria based on ROC, targeting specifically for prediction accuracy. We further extend the survival trees to random forests, where the ensemble is based on martingale estimating equations, in contrast with many existing survival forest algorithms that average the predicted survival or cumulative hazard functions. Simulations studies demonstrate strong performances of the proposed methods. We apply the methods to a study on AIDS for illustration.