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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 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. [ABSTRACT FROM AUTHOR]

There has been a rising interest in better exploiting auxiliary summary information from large databases in the analysis of smaller‐scale studies that collect more comprehensive patient‐level information. The purpose of this paper is twofold: first, we propose a novel approach to synthesize information from both the aggregate summary statistics and the individual‐level data in censored linear regression. We show that the auxiliary information amounts to a system of nonsmooth estimating equations and thus can be combined with the conventional weighted log‐rank estimating equations by using the generalized method of moments (GMM) approach. The proposed methodology can be further extended to account for the potential inconsistency in information from different sources. Second, in the absence of auxiliary information, we propose to improve estimation efficiency by combining the overidentified weighted log‐rank estimating equations with different weight functions via the GMM framework. To deal with the nonsmooth GMM‐type objective functions, we develop an asymptotics‐guided algorithm for parameter and variance estimation. We establish the asymptotic normality of the proposed GMM‐type estimators. Simulation studies show that the proposed estimators can yield substantial efficiency gain over the conventional weighted log‐rank estimators. The proposed methods are applied to a pancreatic cancer study for illustration. [ABSTRACT FROM AUTHOR]