Accelerated lifetime modelling with frailty in a non-homogeneous Poisson Process for analysis of recurrent events data

Abstract

In survival analysis, the hazard function for each individual may be influenced by risk variables, but commonly we have some variables that cannot be observed nor measured. Besides, when lifetime data present more than one observed event for each individual, frailty is a common factor among such recurrence times. In this paper, we present a natural extension of the conventional accelerated failure time (AFT) model for recurrent events with frailty, in order to take into account possible correlations and heterogeneity between event times. We include the effects of covariates on the intensity function of the non-homogeneous Poisson process for recurrent events. The proposed model retains the direct physical interpretation of the original AFT model in that the role of the covariates is to accelerate or decelerate the time to each recurrence. These include parametric approaches to model fitting, we consider to estimate the vector of regression parameters under this model and the parameter in the baseline hazard functions. This methodology is illustrated with a simulation study and also with a known real dataset.