A New Mixed Gamma-Exponential Frailty Model under Heterogeneity Problem with Validation Testing for Emergency Care Data

Frailty models play a crucial role in survival analysis as they account for unobserved differences among individuals, which may arise from various factors like genetics, environment, or lifestyle. These models help in identifying such factors and assessing their influence on survival outcomes. In this research, we introduce a new frailty model called the Mixed Gamma-Exponential (MxGEF) model for survival analysis. To evaluate its appropriateness, we apply the Rao-Robson-Nikulin (RR-Ni) and and the Bagdonaviμcius and Nikulin (B-Ni) goodness-of-fit tests, analyzing the distribution’s characteristics and comparing its effectiveness against commonly used distributions in frailty modeling. Through simulation studies and real-world data applications, including a dataset collected from an emergency hospital in Algeria, we demonstrate how the MxGEF model effectively captures heterogeneity and improves model fitting. Our findings suggest that the MxGEF model is a promising alternative to existing frailty models, potentially enhancing the accuracy of survival analyses across various fields, including emergency care. Additionally, we explore the applicability of the MxGEF model in insurance through simulations and real data analysis, showcasing its versatility and potential impact in this domain.