Bootstrapping a Change-Point Cox Model for Survival Data

TL;DR

This paper examines bootstrap methods for change-point detection in Cox survival models, identifying inconsistencies in standard approaches and proposing a new consistent model-based bootstrap method.

Contribution

It introduces a novel model-based bootstrap approach for change-point Cox models and proves its consistency, addressing limitations of traditional bootstrap methods.

Findings

Nonparametric bootstrap is inconsistent for change-point estimation.

The proposed model-based bootstrap is consistent.

Simulation studies demonstrate improved performance of the new method.

Abstract

This paper investigates the (in)-consistency of various bootstrap methods for making inference on a change-point in time in the Cox model with right censored survival data. A criterion is established for the consistency of any bootstrap method. It is shown that the usual nonparametric bootstrap is inconsistent for the maximum partial likelihood estimation of the change-point. A new model-based bootstrap approach is proposed and its consistency established. Simulation studies are carried out to assess the performance of various bootstrap schemes.