Survival analysis with semi-supervised predictive clustering trees

Many clinical studies follow patients over time and record the time until the occurrence of an event of interest (e.g., recovery, death, …). When patients drop out of the study or when their event did not happen before the study ended, the collected dataset is said to contain censored observations. Given the rise of personalized medicine, clinicians are often interested in accurate risk prediction models that predict, for unseen patients, a survival profile, including the expected time until the event. Survival analysis methods are used to detect associations or compare subpopulations of patients in this context. In this article, we propose to cast the time-to-event prediction task as a multi-target regression task, with censored observations modeled as partially labeled examples. We then apply semi-supervised learning to the resulting data representation. More specifically, we use semi-supervised predictive clustering trees and ensembles thereof. Empirical results over eleven real-life datasets demonstrate superior or equivalent predictive performance of the proposed approach as compared to three competitor methods. Moreover, smaller models are obtained compared to random survival forests, another tree ensemble method. Finally, we illustrate the informative feature selection mechanism of our method, by interpreting the splits induced by a single tree model when predicting survival for amyotrophic lateral sclerosis patients.