About frailty models
No Thumbnail Available
Date
2026
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Université Badji Mokhtar Annaba
Abstract
Survival analysis often assumes that individuals within a population are homogeneous with regard to their susceptibility to an event, such as death or failure. However, real world data typically exhibit unobserved heterogeneity, where individuals are affected by latent factors such as genetic, environmental, or social influences. If this variability is ignored, it can lead to biased estimates of survival rates and hazard functions. To address this issue, we propose a novel frailty model that incorporates unobserved heterogeneity through a frailty variable following the Two-Parameter Lindley (TPL) distribution. The model is estimated using maximum likelihood estimation, and we examine its perfor-mance with several common baseline hazard functions, including Weibull, Exponential,Gompertz, and Pareto distributions. Through extensive simulation studies, we assess the model’s ability to capture heterogeneity and compare it with other widely used frailty models. We also employ Nikulin-Rao-Robson and Bagdonavicius-Nikulin goodness of fit tests to validate the model’s accuracy. To demonstrate its practical applicability, we analyze a real medical dataset from an emergency hospital in Algeria, along with heart attack data, where the proposed frailty model outperforms traditional models in capturing unobserved heterogeneity and providing more reliable survival predictions.
Description
Keywords
Frailty models; Goodness-of-fit testing; Hazard function; Laplace transform