Optimal Survival Trees With the Iterative Breslow Estimator and the Integrated Brier Score Objective

Abstract

Survival analysis predicts survival functions that give the probability of survival until a given time. Many applications of survival analysis involve health care, which requires interpretability of the models used to predict the survival function. Provably optimal decision trees have shown to be an interpretable alternative to so-called black box models. However, these algorithms often choose estimators that are fast, yet not necessarily most accurate. Moreover, the objective functions of optimal decision tree algorithms tend to make (possibly incorrect) assumptions about the survival function. In this paper, we tackle both problems. We implement the iterative Breslow estimator in an already existing optimal survival tree algorithm in order to iteratively improve the Nelson-Aalen estimator. This approach has great potential, as we show by using it on artificial datasets, but we do not see an improvement in accuracy on real world data. To eliminate the assumptions made by the objective function, we implement the Integrated Brier Score objective, which causes a significant improvement on training accuracy. However, we see no improvement on out-of-sample accuracy