ROC-Guided Survival Trees and Forests
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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 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-growing algorithm is guided by decision-theoretic criteria based on ROC, targeting specifically for prediction accuracy. While existing survival trees with time-dependent covariates have practical limitations due to ambiguous prediction, the proposed method provides a consistent prediction of the failure risk. 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.
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