Prediction trees with soft nodes for binary outcomes.

Consider the problem of predicting the occurrence of an event, the onset of diabetes mellitus, say, from a vector of continuous and discrete predictors. We propose a new algorithm for the construction of a tree-structured predictor for the event of interest, which uses a new approach for dealing with continuous predictors. The novelty is that the tree uses splits for continuous variables. This means that at each node an individual goes to the right branch with a certain probability, function of a predictor. The predictor as well as the particular shape of the function is chosen from the data by the proposed algorithm. We evaluate its performance on several real data sets, in particular comparing it with a standard tree-growing algorithm. We also present an analysis of a well-known data set, the Pima Indian diabetes data set, to illustrate the application of the method in biostatistics.