Evolutionary induced survival trees for medical prognosis assessment

Survival analysis focuses on predicting the time of a specific event, known as failure. In the analysis of survival data, it is crucial to fully leverage censored observations for which we do not have precise event time information. Decision trees are among the most frequently applied machine learning techniques for survival analysis, but to adequately address this issue, it is necessary to transform them into survival trees. This involves equipping the leaves with, for instance, local Kaplan-Meier estimators. Until now, survival trees have predominantly been generated using a greedy approach through classical top-down induction that uses local optimization. Recently, one of the most promising directions in decision tree approach is global learning. The paper proposes an evolutionary algorithm for survival tree induction, which concurrently searches for the tree structure, univariate tests in internal nodes, and Kaplan-Meier estimators in leaves. The fitness function is based on an integrated Brier score, and by introducing a penalty term related to the tree size, it becomes possible to control the interpretability of the obtained predictor. The work investigated, among other aspects, the impact of censoring, and the results obtained from both synthetic and real-life medical datasets are encouraging. The comparison of the predictive ability of the proposed method with already-known univariate survival trees shows statistically significant differences.