Detecting Clinical Risk Shift Through log–logistic Hazard Change-Point Model

The change–point problem is about identifying when a pattern or trend shifts in time–ordered data. In survival analysis, change–point detection focuses on identifying alterations in the distribution of time–to–event data, which may be subject to censoring or truncation. In this paper, we introduce a change–point in the hazard rate of the log–logistic distribution. The log–logistic distribution is a flexible probability distribution used in survival analysis, reliability engineering, and economics. It is particularly useful for modeling time–to–event data exhibiting decreasing hazard rates. We estimate the parameters of the proposed change–point model using profile maximum likelihood estimation. We also carry out a simulation study and Bayesian analysis using the Metropolis–Hastings algorithm to study the properties of the proposed estimators. The proposed log–logistic change–point model is applied to survival data from kidney catheter patients and acute myeloid leukemia (AML) cases. A late change–point with a decreasing scale parameter in the catheter data reflects an abrupt increase in risk due to delayed complications, whereas an early change–point with an increasing scale parameter in AML indicates high early mortality followed by slower hazard progression in survivors. We find that the log–logistic change–point model performs better in comparison to the existing change–point models.