Change-point detection in Weibull-accelerated failure time models via narrowest significance pursuit

Survival data are often subject to abrupt structural changes due to unforeseen natural or anthropogenic events, which may significantly alter the hazard function and introduce shifts in model parameters. Traditional survival models typically assume time-invariant hazard structures and are therefore inadequate in capturing such distributional shifts. To address this limitation, we adapt the Narrowest Significance Pursuit (NSP) methodology proposed by Fryzlewicz (2024) for change-point detection within the framework of accelerated failure time (AFT) models. The NSP algorithm employs a multiscale sup-norm loss to fit Weibull AFT models across varying subintervals, recursively identifying the narrowest intervals where linearity is statistically violated at a user-specified global significance level. Change-points are detected as abrupt changes in the underlying parameters of the survival model, and the method does not require prior specification of the number or location of these points. We conduct an extensive simulation study to evaluate the performance of the proposed approach under various change-point scenarios, censoring levels, and compare it with the existing methods in the literature. Additionally, a real-world dataset is analyzed to demonstrate the practical applicability of the method. The empirical results highlight the accuracy and robustness of NSP in detecting structural changes in survival distributions, making it a valuable tool for analyzing heterogeneous survival data in dynamic risk environments.