Oblique Survival Trees in Discrete Event Time Analysis

One of the main objectives of survival analysis is to predict the failure time that is usually considered as a continuous variable. In longitudinal studies, the data are often collected at every certain period of time, for example, monthly, quarterly, or yearly. Such data require appropriate techniques to handle the discrete time values that often have incomplete information about the failure occurrence-so-called "censored cases." Tree-based models are common, assumption-free methods of survival prediction. In this paper, the author proposes three recursive partitioning techniques able to cope with discrete-time censored survival data, which, in contrast to already-existing models limited to univariate trees, allow splits to have a form of any hyperplane. The performance of proposed methods, expressed as a mean absolute error, was examined on the basis of both synthetic and real data sets available in the literature and compared with existing tree-based models. To demonstrate the applicability of the methods in identifying subgroups of patients with a similar survival experience and to assess the influence of covariates on the risk of failure, a Veteran's Administration lung cancer data set was used. The results confirm proposed models to be good prediction tools for discrete-time survival data.