A comparison of estimated proportional hazards models and regression trees

We present examples of the usage of regression trees for censored response via two real world datasets, one a rheumatoid arthritis survival study and the other a hip replacement study, and draw comparisons with the results of Cox proportional hazards modelling. The two methods pursue different goals. Motivation of the tree techniques is the desire to extract meaningful prognostic groups while the proportional hazards model enables assessment of the impact of risk factors. The methods are thus complementary. For the arthritis study the two techniques corroborate one another, although the flavour of the conclusions derived differ. For the hip replacement study, however, the regression tree approach reveals structure that would not emerge from a routine proportional hazards analysis. We also discuss the treatment of data analytic issues such as the handling of missing values and influence in the presence of non-uniform censoring.