Parametric frailty models using two-parameter xgamma distribution with an application of survival analysis

Abstract

When the actual observation measurement is expensive and difficult, an effective approach for estimating the population parameters is applied, such as ranked set sampling. In a survival or time-to-event analysis, a frailty model is a random effects model where the random effect (the frailty) has a multiplicative effect on the hazard. One of the traditional distributions, the Xgamma distribution, is frequently utilized in reliability and regular survival models (frailty-free), but not in frailty models. Due to its inherent flexibility, the Xgamma distribution and its generalizations have become significantly important in survival analysis in recent years. In this study, we attempt to fit two-parameter X-gamma baseline distribution (TPXGD) with parametric frailty models and apply them to the two real-life data sets. The study results revealed that TPXGD with Gamma frailty model is good choice for Kidney infection data and recurrent asthma attack in children. To make studies of time-to-event data with covariates easier, we propose the Two-parameter Xgamma baseline distribution (TPXGD) with frailty models as suitable alternate models.