Survival model induced by discrete frailty for modeling of lifetime data with long-term survivors and change-point

Frailty models are used for modeling heterogeneity in the data analysis of lifetimes. Analysis that ignore frailty when it is present leads to incorrect inferences. In survival analysis, the distribution of frailty is generally assumed to be continuous and, in some cases, it may be appropriate to consider a discrete frailty distribution. Survival models induced by frailty with a continuous distribution are not appropriate for situations in which survival data contain experimental units where the event of interest has not happened even after a long period of observation (survival data with cure fraction), that is, situations with units having zero frailty. In this paper, we propose a new survival model induced by discrete frailty for modeling survival data in the presence of a proportion of long-term survivors and a single change point. We use the maximum likelihood method to estimate the model parameters and evaluate their performance by a Monte Carlo simulation study. The proposed approach is illustrated by analyzing a kidney infection recurrence data set.