Investigate Factors Affecting Corneal Graft Rejection in Keratoconus Using Bayesian Analysis of Bivariate Weibull Hazard Function Based on Clayton Copula

Keratoconus is a bilateral corneal disease, which one way to cure it is to transplant. The transplantation may be rejected by recipient's immune system, which leads to failure of the graft. This study aimed to analysis the factors affecting bilateral corneal graft rejection based on copula function. A sample of bilateral graft rejection times was assessed. Since correlation exists between the times of corneal graft rejection, Clayton Archimedean copula was used. The parameters estimation was performed using Bayesian analysis based on Markov Chain Monte Carlo methods by WinBUGS. For modeling hazard function, Weibull hazard model was used. Corneal vascularization in the first graft and corneal freshness in the second graft had a significant impact on graft rejection time. The age at transplantation had also a significant partial effect on both the first and the second rejection. The correlation parameter of Clayton copula was estimated as 0.98, so Kendall,s tau correlation coefficients between the first and the second corneal graft rejection time obtained as 0.3. Results indicate a correlation between the first and the second transplant rejection time. Aging increases partially the graft rejection risk. Maintenance of corneal in solution and also presence of corneal vascularization increase the risk of corneal graft rejection.