  In the fight against hard-to-treat diseases such as cancer, it is often
difficult to discover new treatments that benefit all subjects. For regulatory
agency approval, it is more practical to identify subgroups of subjects for
whom the treatment has an enhanced effect. Regression trees are natural for
this task because they partition the data space. We briefly review existing
regression tree algorithms. Then we introduce three new ones that are
practically free of selection bias and are applicable to two or more
treatments, censored response variables, and missing values in the predictor
variables. The algorithms extend the GUIDE approach by using three key ideas:
(i) treatment as a linear predictor, (ii) chi-squared tests to detect residual
patterns and lack of fit, and (iii) proportional hazards modeling via Poisson
regression. Importance scores with thresholds for identifying influential
variables are obtained as by-products. A bootstrap technique is used to
construct confidence intervals for the treatment effects in each node. Real and
simulated data are used to compare the methods.
