تحليل بيزي مدل شكنندگي همبسته وايبول بااستفاده از روش هاي مونت كارلوي زنجير ماركوفي و كاربرد آن در شناسايي عوامل موثر بر دفع پيوند قرنيه دو طرفه

In survival analysis, one way to explaining all unknown risk factors is using frailty model. One extended frailty models are known as correlated frailty model. In this model, the frailty for each individual is sum of two independent components, which are known as shared and individual frailties. The shared component describes shared unknown risk factors and individual frailty component describes individual unknown risk factors. In this paper, Bayesian analysis of the weibull based correlated frailty model has been worked. Analytical solution of the problem is not possible due to complexity of the model and hence a Markov chain Monte Carlo approach applied using Gibbs sampling, Metropolis algorithm, rejection sampling and free adoptive rejection sampling algorithms. The Bayesian analysis of the weibull correlated frailty model has been applied for analyzing the risk factors in a sample of bilateral corneal graft rejections in Keratoconus. The results showed that the extent of corneal vascularisation is an important risk factor and the age of recipient and sever ocular allergy are, however, slightly significant. The sex of reception and fresh or preserve in cornea solution of donor cornea are not important in graft rejection. Also, in a similar way, the Bayesian analysis of weibull model and weibull shared frailty model have been done on this data set and the estimated parameters of risk factors have been investigated for the three models. The models were compared via posterior log likelihood. The results showed that the correlated frailty model, by explaining effects of unknown genetic and environmental risk factors in the bilateral corneal graft rejections, has better model fitting than two other models.