We prove uniform consistency of Random Survival Forests (RSF), a newly introduced forest ensemble learner for analysis of right-censored survival data. Consistency is proven under general splitting rules, bootstrapping, and random selection of variab
les--that is, under true implementation of the methodology. A key assumption made is that all variables are factors. Although this assumes that the feature space has finite cardinality, in practice the space can be a extremely large--indeed, current computational procedures do not properly deal with this setting. An indirect consequence of this work is the introduction of new computational methodology for dealing with factors with unlimited number of labels.
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 co
nservation-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.
