A Partitioning Deletion/Substitution/Addition Algorithm for Creating Survival Risk Groups

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.