Survival Analysis with Time-varying Relative Risks: A Tree-Based Approach - Xu, R.; Adak, S. (Methods of Information in Medicine, 2001)
A tree-based method for estimating time-varying effects of baseline patient characteristics on survival is introduced. A Cox-type model for censored survival data is used in which the time-varying relative risks are modelled as piecewise constants.The tree method consists of three steps: 1. Growing the tree, in which a fast algorithm using maximized score statistics is utilized to determine the optimal change points; 2. A pruning algorithm is applied to obtain more parsimonious models; 3. Selection of a final tree, which may be either via bootstrap resampling or based on a measure of explained variation.The piecewise constant model is more suitable for clinical interpretation of the regression parameters than the more continuously time-varying models (spline, loess, etc.) that have been proposed previously.
Keywords: Change Point; Classification and Regression Tree; Maximized Score Test; Non-proportional Hazards; Time-varying Regression Effect