Additive Positive Stable Frailty Models

In this article, we describe an additive stable frailty model for multivariate times to events data using a flexible baseline hazard, and assuming that the frailty component for each individual is described by additive functions of independent positive stable random variables with possibly different stability indices. Dependence properties of this frailty model are investigated. To carry out inference, the likelihood function is derived by replacing high-dimensional integration by Monte Carlo simulation. Markov chain Monte Carlo algorithms enable estimation and model checking in the Bayesian framework.