Inference for a Shared Random-Scale Frailty Birnbaum–Saunders Model Under Progressive Type-II Censoring

This paper introduces a shared gamma frailty Birnbaum–Saunders model for clustered lifetime data under progressive Type-II censoring. The frailty term acts on the scale parameter and accounts for unobserved variation among clusters. Likelihood-based and Bayesian formulations are developed, and posterior estimation and prediction are carried out using a Metropolis-within-Gibbs algorithm. A simulation study considers different shape parameters, frailty levels, numbers of clusters, and censoring schemes. The proposed method estimates the shape parameter accurately and gives generally satisfactory results for the frailty variance. Increasing the number of clusters improves estimation, and the frailty model gives lower prediction errors in almost all valid comparisons with the ordinary BS model. A real-data application to kidney catheter infection times illustrates the shared-frailty component of the proposed model.