Abstract

In frailty models, the time-dependent correlation among observations is driven by the frailty distribution, which determines how this dependence evolves. This paper introduces a new approach where the frailty is modelled using a mixture of Birnbaum-Saunders (MBS) distributions. The parameterization of the mixture distribution directly defines the mixing weights, and the model's closed-form Laplace transform allows for the explicit calculation of Kendall's tau, a measure of dependence. We explore both parametric and semiparametric versions of this frailty model. Additionally, we present a hierarchical representation of the mixture, which simplifies the application of the expectation-maximization (EM) algorithm for parameter estimation. The effectiveness of the proposed model is demonstrated through Monte Carlo simulations and in an application to a cancer dataset. A comparative analysis with existing frailty models shows the strengths of our approach. The implementation of our methodology is available in the R package extrafrail. © 2025 Informa UK Limited, trading as Taylor & Francis Group.