Page 169 - Contributed Paper Session (CPS) - Volume 7

CPS2055 Asanao S. et al.

Construction of a survival tree based on
concordance probability
Asanao Shimokawa, Etsuo Miyaoka
Tokyo University of Science, Tokyo, Japan

Abstract
Survival tree is one of the popular analysis method for time-to-event data in
the field of medical research. It is well known that setting of the splitting
criterion to construct the tree model is especially important in the analysis.
Various authors have proposed several criterions. For example, Log-rank test
statistics, exponential log-likelihood loss, and residual-based methods are
used. In this study, we consider the concordance probability-based splitting
criterions for constructing a survival tree. Concordance probability is one of
the measure for prediction accuracy of the survival model. We propose the
new method to construct the tree model that maximizes prediction accuracy
based on the classification and regression tree algorithm. We study the
performance of the splitting ability of the criterion based on concordance
probabilities, and compare the survival trees constructed by proposed method
and conventional methods through simulations.

Keywords
CART; C-index; Prediction accuracy; Tree structure

1. Introduction
In the medical research, analysis of time-to-event data is an important
subject. In order to handle a regression problem that includes censored data
based on covariates, the Cox proportional hazard model Cox (1972) has been
most widely used. In addition to the simpleness of inference, this semi-
parametric model has an advantage in that it can easily describe the covariate
effects. However, this model requires proportional hazard assumptions, and
certain assumptions about the relationship between covariates and response
variables. Moreover, when this model includes many covariates, interpretation
is difficult. In this study, we deal with survival trees, which involve constructing
a tree structure model based on covariates. Because the proposed method
uses a hierarchical structure, the relationship between covariates and hazards
can be determined easily. Moreover, it is easy to incorporate a new patient
into the model.
One of the most widely used method for constructing a survival tree is the
classification and regression tree (CART) algorithm, proposed by Breiman et
al. (1984), that is composed of three steps: splitting, pruning, and selection.
Samples are recursively dichotomized in the splitting step, and a maximum

156 | I S I W S C 2 0 1 9