Survival analysis with time-varying relative risks: A tree-based approach

A tree-based method for estimating time-varying effects of baseline patient characteristics on survival is introduced. A Cox-type model for censored s urvival 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 fa st algorithm using maximized score statistics is utilized to determine the optimal change points; 2. A pruning algorithm is applied to obtain more par simonious models; 3. Selection of a final tree, which may be either via boo tstrap resampling or based on a measure of explained variation. The piecewise constant model is more suitable for clinical interpretation o f the regression parameters than the more continuously time-varying models (spline, loess, etc.) that have been proposed previously.