A Bayesian approach for multi-stage models with linear time-dependent hazard rate

Abstract

Abstract Multi-stage models have been used to describe progression of individuals which develop through a sequence of discrete stages. We focus on the multi-stage model in which the number of individuals in each stage is assessed through destructive samples for a sequence of sampling time. Moreover, the stage duration distributions of the model are effected by a time-dependent hazard rate. The multi-stage models become complex with a stage having time-dependent hazard rate. The main aim of this paper is to derive analytically the approximation of the likelihood of the model. We apply the approximation to the Metropolis–Hastings (MH) algorithm to estimate parameters for the model. The method is demonstrated by applying to simulated data which combine non-hazard rate, stage-wise constant hazard rate and time-dependent hazard rates in stage duration distributions.