Survival analysis studies and predicts the time of death, or other singular unrepeated events, based on historical data, while the true time of death for some instances is unknown. Survival trees enable the discovery of complex nonlinear relations in a compact human comprehensible model, by recursively splitting the population and predicting a distinct survival distribution in each leaf node. We use dynamic programming to provide the first survival tree method with optimality guarantees, enabling the assessment of the optimality gap of heuristics. We improve the scalability of our method through a special algorithm for computing trees up to depth two. The experiments show that our method's run time even outperforms some heuristics for realistic cases while obtaining similar out-of-sample performance with the state-of-the-art.

翻译：生存分析基于历史数据研究并预测死亡时间或其他单一非重复事件的发生时间，其中部分实例的真实死亡时间未知。生存树通过递归划分人群并在每个叶节点预测不同的生存分布，能够在紧凑且人类可理解的模型中揭示复杂的非线性关系。我们采用动态规划方法，首次提出具有最优性保证的生存树方法，从而能够评估启发式方法的最优性差距。通过一种专门用于计算深度至多为二的树的算法，我们提升了该方法的可扩展性。实验表明，我们的方法在实际案例中的运行时间甚至优于某些启发式方法，同时在样本外性能上与现有最优方法相当。