A Partitioning Deletion/Substitution/Addition Algorithm for Creating Survival Risk Groups
Article first published online: 22 APR 2012
© 2012, The International Biometric Society
Volume 68, Issue 4, pages 1146–1156, December 2012
How to Cite
Lostritto, K., Strawderman, R. L. and Molinaro, A. M. (2012), A Partitioning Deletion/Substitution/Addition Algorithm for Creating Survival Risk Groups. Biometrics, 68: 1146–1156. doi: 10.1111/j.1541-0420.2012.01756.x
- Issue published online: 21 DEC 2012
- Article first published online: 22 APR 2012
- Received January 2011. Revised January 2012. Accepted January 2012.
- Brier score;
- Inverse weighting;
- Loss estimation;
- Regression trees;
- Risk stratification;
- Survival analysis
Summary 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 of 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” settings (e.g., uncensored outcomes). 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 partDSA that make use of observed data loss functions constructed using inverse probability of censoring weights. Such loss functions 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. The implementation of partDSA for uncensored and right-censored outcomes is publicly available in the R package, partDSA.