  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 ensembles, 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 for evaluating the performance of survival trees. The tree-building
algorithm is guided by decision-theoretic criteria based on ROC, targeting
specifically for prediction accuracy. To address the instability issue of a
single tree, we propose a novel ensemble procedure based on averaging
martingale estimating equations, which is different from existing methods that
average the predicted survival or cumulative hazard functions from individual
trees. Extensive simulation studies are conducted to examine the performance of
the proposed methods. We apply the methods to a study on AIDS for illustration.

Methodology