Optimal Cox Survival Trees

Abstract

Survival analysis is a branch of statistics concerned with studying and estimating the expected time duration until some event, such as biological death, occurs. Survival distributions are fitted based on historical data, where some instances are censored, meaning that the actual time of the event is not known precisely. Survival trees extend on the classical statistical methods developed and can capture complex non-linear relations between the variables by recursively splitting the instances by generated rules and fitting a different survival distribution in each leaf. Moreover, decision trees are desirable models due to their interpretable nature. We extend existing optimal survival tree methods by considering Cox Proportional Hazard models in each leaf node, which allows us to find more complex yet interpretable relationships than existing methods. The experiments show that our model outperforms state-of-the-art methods for creating survival trees, SurTree, OST, and CTree, especially in determining the relative risks between out-of-sample observations while generating significantly smaller trees.