We introduce random survival forests, a random forests method for the analysis of right-censored survival data. New survival splitting rules for growing survival trees are introduced, as is a new missing data algorithm for imputing missing data. A conservation-of-events principle for survival forests is introduced and used to define ensemble mortality, a simple interpretable measure of mortality that can be used as a predicted outcome. Several illustrative examples are given, including a case study of the prognostic implications of body mass for individuals with coronary artery disease. Computations for all examples were implemented using the freely available R-software package, randomSurvivalForest.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS169 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

We introduce a new approach to competing risks using random forests. Our method is fully non-parametric and can be used for selecting event-specific variables and for estimating the cumulative incidence function. We show that the method is highly effective for both prediction and variable selection in high-dimensional problems and in settings such as HIV/AIDS that involve many competing risks.

The minimal depth of a maximal subtree is a dimensionless order statistic measuring the predictiveness of a variable in a survival tree. We derive the distribution of the minimal depth and use it for high-dimensional variable selection using random survival forests. In big p and small n problems (where p is the dimension and n is the sample size), the distribution of the minimal depth reveals a "ceiling effect" in which a tree simply cannot be grown deep enough to properly identify predictive variables. Motivated by this limitation, we develop a new regularized algorithm, termed RSF-Variable Hunting. This algorithm exploits maximal subtrees for effective variable selection under such scenarios. Several applications are presented demonstrating the methodology, including the problem of gene selection using microarray data. In this work we focus only on survival settings, although our methodology also applies to other random forests applications, including regression and classification settings. All examples presented here use the R-software package randomSurvivalForest.