Machine learning for survival analysis: a case study on recurrence of prostate cancer

Abstract

Machine learning techniques have recently received considerable attention, especially when used for the construction of prediction models from data. Despite their potential advantages over standard statistical methods, like their ability to model non-linear relationships and construct symbolic and interpretable models, their applications to survival analysis are at best rare, primarily because of the difficulty to appropriately handle censored data. In this paper we propose a schema that enables the use of classification methods — including machine learning classifiers — for survival analysis. To appropriately consider the follow-up time and censoring, we propose a technique that, for the patients for which the event did not occur and have short follow-up times, estimates their probability of event and assigns them a distribution of outcome accordingly. Since most machine learning techniques do not deal with outcome distributions, the schema is implemented using weighted examples. To show the utility of the proposed technique, we investigate a particular problem of building prognostic models for prostate cancer recurrence, where the sole prediction of the probability of event (and not its probability dependency on time) is of interest. A case study on preoperative and postoperative prostate cancer recurrence prediction shows that by incorpo- rating this weighting technique the machine learning tools stand beside modern statistical methods and may, by inducing symbolic recurrence models, provide further insight to relationships within the modeled data