Flexible Hazard Modeling with Segmented Distributions

This paper introduces a flexible family of segmented proportional hazard distributions designed to model abrupt changes in hazard rates, which are often observed in medical and engineering applications. The proposed framework generalizes the proportional hazard transformation to segmented distributions, including new forms of the Rayleigh, log-logistic, Lindley, and Laplace PH models. We develop a maximum likelihood estimation procedure incorporating right censoring, a key feature of real-world survival data. The segmented hazard models effectively capture structural breaks in the hazard function, providing a robust alternative to traditional survival models that assume constant hazard dynamics. A case study based on IQ score data illustrates the improved flexibility and interpretability of the segmented Laplace PH model in detecting latent change points. The proposed models enhance the capacity to model complex survival patterns with abrupt changes in risk, contributing to a deeper understanding of dynamic hazard processes.