  Accurately assessing a patient's risk of a given event is essential in making
informed treatment decisions. One approach is to stratify patients into two or
more distinct risk groups with respect to a specific outcome using both
clinical and demographic variables. Outcomes may be categorical or continuous
in nature; important examples in cancer studies might include level of toxicity
or time to recurrence. Recursive partitioning methods are ideal for building
such risk groups. Two such methods are Classification and Regression Trees
(CART) and a more recent competitor known as the partitioning
Deletion/Substitution/Addition (partDSA) algorithm, both which also utilize
loss functions (e.g. squared error for a continuous outcome) as the basis for
building, selecting and assessing predictors but differ in the manner by which
regression trees are constructed.
  Recently, we have shown that partDSA often outperforms CART in so-called
"full data" (e.g., uncensored) settings. However, when confronted with censored
outcome data, the loss functions used by both procedures must be modified.
There have been several attempts to adapt CART for right-censored data. This
article describes two such extensions for \emph{partDSA} that make use of
observed data (i.e. possibly censored) loss functions. These observed data loss
functions, constructed using inverse probability of censoring weights, are
consistent estimates of their uncensored counterparts provided that the
corresponding censoring model is correctly specified. The relative performance
of these new methods is evaluated via simulation studies and illustrated
through an analysis of clinical trial data on brain cancer patients.
