Comparison of Splitting Methods on Survival Tree

Shimokawa Asanao (), Kawasaki Yohei () and Miyaoka Etsuo ()
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Shimokawa Asanao: Department of Mathematical information Science, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan
Kawasaki Yohei: Department of Mathematics, Tokyo University of Science, Tokyo, Japan
Miyaoka Etsuo: Department of Mathematics, Tokyo University of Science, Tokyo, Japan

The International Journal of Biostatistics, 2015, vol. 11, issue 1, 175-188

Abstract: We compare splitting methods for constructing survival trees that are used as a model of survival time based on covariates. A number of splitting criteria on the classification and regression tree (CART) have been proposed by various authors, and we compare nine criteria through simulations. Comparative studies have been restricted to criteria that suppose the survival model for each terminal node in the final tree as a non-parametric model. As the main results, the criteria using the exponential log-likelihood loss, log-rank test statistics, the deviance residual under the proportional hazard model, or square error of martingale residual are recommended when it appears that the data have constant hazard with the passage of time. On the other hand, when the data are thought to have decreasing hazard with passage of time, the criterion using the two-sample test statistic, or square error of deviance residual would be optimal. Moreover, when the data are thought to have increasing hazard with the passage of time, the criterion using the exponential log-likelihood loss, or impurity that combines observed times and the proportion of censored observations would be the best. We also present the results of an actual medical research to show the utility of survival trees.

Keywords: survival tree; CART; recursive partitioning (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1515/ijb-2014-0029

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