Ensemble survival trees for identifying subpopulations in personalized medicine

Recently, personalized medicine has received great attention to improve safety and effectiveness in drug development. Personalized medicine aims to provide medical treatment that is tailored to the patient's characteristics such as genomic biomarkers, disease history, etc., so that the benefit of treatment can be optimized. Subpopulations identification is to divide patients into several different subgroups where each subgroup corresponds to an optimal treatment. For two subgroups, traditionally the multivariate Cox proportional hazards model is fitted and used to calculate the risk score when outcome is survival time endpoint. Median is commonly chosen as the cutoff value to separate patients. However, using median as the cutoff value is quite subjective and sometimes may be inappropriate in situations where data are imbalanced. Here, we propose a novel tree-based method that adopts the algorithm of relative risk trees to identify subgroup patients. After growing a relative risk tree, we apply k-means clustering to group the terminal nodes based on the averaged covariates. We adopt an ensemble Bagging method to improve the performance of a single tree since it is well known that the performance of a single tree is quite unstable. A simulation study is conducted to compare the performance between our proposed method and the multivariate Cox model. The applications of our proposed method to two public cancer data sets are also conducted for illustration.