Often in practice the data on the mortality of a living unit correlation is due to the location of the observations in the study. One of the most important issues in the analysis of survival data with spatial dependence, is estimation of the parameters and prediction of the unknown values in known sites based on observations vector. In this paper to analyze this type of survival, Cox regression model with piecewise exponential function used as a hazard and spatial dependence as a Gaussian random field and as a latent variable is added to the model. Because there is no closed form for posterior distribution and full conditional distributions, also long computing for Markov chain Monte Carlo algorithms, to analyze the model are used the approximate Bayesian methods.
A practical example of how to implement an approximate Bayesian approach is presented.