  The use of cumulative incidence functions for characterizing the risk of one
type of event in the presence of others has become increasingly popular over
the past decade. The problems of modeling, estimation and inference have been
treated using parametric, nonparametric and semi-parametric methods. Efforts to
develop suitable extensions of machine learning methods, such as regression
trees and related ensemble methods, have begun only recently. In this paper, we
develop a novel approach to building regression trees for estimating cumulative
incidence curves in a competing risks setting. The proposed methods employ
augmented estimators of the Brier score risk as the primary basis for building
and pruning trees. The proposed methods are easily implemented using the R
statistical software package. Simulation studies demonstrate the utility of our
approach in the competing risks setting. Data from the Radiation Therapy
Oncology Group (trial 9410) is used to illustrate these new methods.
