Title
Multivariate Survival Trees
Speaker
Xiao-Gang Su, Department of Statistics, University of California, Davis
Abstract
Extension of tree based methods are made, in two different ways, to classify correlated failure times. Both approaches inherit most of the optimal properties of CART procedure (Breiman et al. 1984). In the first approach, the splitting criterion is built on the basis of maximizing between-node difference in survival, where the difference is measured by a robust logrank statistic coming from the marginal approach to multivariate survival data by Wei, Lin and Wessfeld (1989). The split-complexity pruning algorithm proposed by LeBlanc and Crowley (1993) is adapted for direct use. In the second approach, the tree is grown by minimizing within-node error. To do so, a simple model with a Gamma-distributed frailty term is used as the basic model for correlated survival data. The log likelihood score is adopted as an error term into the standard CART algorithm of Breiman et al. (1984). To reduce computational burden, the likelihood score computed after the first iteration in a EM algorithm is used. Further simplification could be achieved by assuming a constant baseline hazard, which actually facilitates a multivariate generalization of exponential trees proposed by Davis and Anderson (1991).
Large sample consistency associated with multivariate survival trees is discussed. Simulations and data analysis are made to investigate the capability of two splitting statistics in choosing right cutpoints and the efficiency of proposed methods in detecting data structure.
