A bayesian analysis of multivariate survival data from multi-stage cluster sampling

Large scale sample surveys often collect survival times that are clustered at a number of hierarchical levels. Only the case where three levels are nested is considered here: that is, individual response times (level- i) are grouped into larger units (level-2) which in turn are grouped into much larger units (level-3). It is assumed that individuals in a unit share a common, unobservable and specific random frailty which induces an association between survival times in the unit. A Bayesian hierarchical analysis of the data is examined by modelling the survival time (level-1) using a semipanmietric Cox proportional hazards and specific level-2 and level-3 random frailty effects are assumed independent and modelled as gamma distributions. The complete posterior distribution of all the model parameters is estimated using the Gibbs sampler, a Monte Carlo method.