Survival Analysis with Time-varying Relative Risks: A Tree-Based Approach

Abstract

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

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