Regression Trees for Censored Survival Data With Applications to Subgroup Identification

Abstract

Regression Trees for Censored Survival Data With Applications to Subgroup Identification Wei-Yin Loh1 1Department of Statistics, University of Wisconsin at Madison, USA ?:? Previous regression tree algorithms for censored response data are?typically based on the CART (Breaiman et al. 1984) approach, which?searches for splits that maximally reduce some node impurity function.?Because the approach induces a selection bias toward variables that afford?more splits, the algorithms are similarly biased. Besides, the approach is?computationally costly, since the best split must be found for every?variable. As a result, the algorithms are limited in practice to piecewise?constant (in log hazard) models. An alternative algorithm based on the GUIDE (Loh 2002, 2009) approach is?proposed for fitting piecewise multiple-linear proportional hazards?models. ?It relies on an old trick that uses Poisson regression to fit?proportional hazards models. By utilizing a treatment variable as a linear?predictor, the method can also be used to identify subgroups of the data?that exhibit differential treatment effects. ?An importance ordering of?the variables is obtained as a by-product. Evaluations based on real and?simulated data show that the new methods are highly competitive compared?to other tree methods and to random survival forest, in their accuracy in?identifying the important variables and in computational speed. ?