The ROC region of a regression tree

Multiple alternative diagnostic tests for one disease are commonly available to clinicians. It is important to use all the good diagnostic predictors simultaneously to establish a new predictor with higher diagnostic accuracy. The linear combinations of multiple predictors are often of particular interest to clinicians. In this paper, we focused on tree-based nonlinear combinations of multiple predictors. A receiver operating characteristic region and its area under the upper boundary were used to evaluate diagnostic utilities for these algorithms. Some mathematical properties were discussed and non-parametric estimation methods were presented.