Parametric frailty models under two-parameter Lindley distribution with applications to time-to-event analysis

Abstract

A frailty model is a random effects model in survival or time-to-event analysis, where the random effect (the frailty) has a multiplicative effect on the hazard. Lindley distribution is one of the classical distributions, which is widely used in reliability and ordinary survival models (without frailty) but not in the frailty models. In recent years, Lindley distribution and its generalizations have played an important role in survival analysis due to its natural flexibility. In this study, we attempt to fit parametric frailty models with Two-parameter Lindley baseline distribution (TPLD) and apply them to the two real-life disease data sets of the (i) Recurrent asthma attacks in children’s (Asthma attacks) and (ii) Culling of dairy heifer cow’s (Culling) data. Comparison and assed the model's fitness were done using a minimum value of Akaike's Information Criteria (AIC) and Bayesian Information Criteria (BIC). The study results revealed that TPLD with the Lognormal frailty model is a good choice for Culling data and Lindley with Gamma frailty model is the best for Asthma data. So, we suggest that the Two-parameter Lindley baseline distribution (TPLD) with frailty models are potential alternative models and will facilitate analyses of time-to-event data with covariates.