Developing Multivariate Survival Trees with a Proportional Hazards Structure

by Feng Gao, Amita K. Manatunga, Shande Chen

Journal of Data Science, v.4, no.3, 343-356

Abstract

In this paper, a tree-structured method is proposed to extend Classification and Regression Trees (CART) algorithm to multivariate survival data, assuming a proportional hazard structure in the whole tree. The method works on the marginal survivor distributions and uses a sandwich estimator of variance to account for the association between survival times. The Wald-test statistics is defined as the splitting rule and the survival trees are developed by maximizing between-node separation. The proposed method intends to classify patients into subgroups with distinctively different prognosis. However, unlike the conventional tree-growing algorithms which work on a subset of data at every partition, the proposed method deals with the whole data set and searches the global optimal split at each partition. The method is applied to a prostate cancer data and its performance is also evaluated by several simulation studies.

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