A Regression Tree Approach to Subgroup Identification for Censored Data

• Activity Number: 60
• Type: Topic Contributed
• Date/Time: Sunday, August 4, 2013 : 4:00 PM to 5:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Wei-Yin Loh*+ and Michael Man and Xu He
• Companies: University of Wisconsin and Eli Lilly and Chinese Academy of Sciences
• Keywords: recursive partitioning ; proportional hazards ; missing values ; selection bias ; survival analysis ; Poisson regression

Abstract

In the search for new drugs to fight diseases, it is often difficult to find one that has a uniformly positive effect on all subjects. A more realistic and practical goal is to identify subgroups of the subject population where the drug has a strong effect. Because a regression tree model partitions the data into subgroups, it would seem to be the ideal solution to this problem. No practically successful algorithm, however, has been found previously, due to conceptual and computational difficulties that are compounded when the response variable is censored. We discuss the problem and propose three solutions derived from the GUIDE algorithm for piecewise linear regression. Our solutions employ two key ideas: (i) extension of GUIDE to proportional hazards regression via Poisson regression and (ii) use of the treatment variable as a linear predictor in the node models. Each solution yields an importance ranking of the variables as well. Simulation experiments show that our solutions are more effective in identifying the important variables than RPART and random survival forest. The methods are demonstrated on two real data sets.