Estimation of a Change Point in the Cox Hazard Model

Abstract

Survival analysis is a set of statistical methods or tools for analyzing time-to-event data. Survival analysis is a very active field of inquiry that has applications in numerous areas of study, including engineering, physical, biological, and social sciences. The hazard function represents the rate of failure at a specific time t, considering the individual has survived up to that point. The Cox proportional hazards model is widely employed in survival analysis to explore the relationship between covariates and the hazard rate. Covariates can influence the hazard function, causing it to vary, which may lead to the occurrence of a change point. This study centers around the estimation of change point in the Cox proportional hazard model, involving an examination of three distinct hazard models. We utilize maximum likelihood method to estimate change points within these proposed hazard models. Through a thorough Monte Carlo simulation study, we assess the consistency and performance of our methods as sample size and censorship percentages vary. The chronic granulotamous disease (CGD) dataset is used as a practical application and results showed that the proposed models are effective in estimating the change point.