A correlated frailty model for analysing risk factors in bilateral corneal graft rejection for Keratoconus: a Bayesian approach

Abstract

There are many unknown causes that increase the rate of corneal graft rejection. In bilateral cases, some of these unknown causes are common, and some are individual factors. In this paper, we use a correlated frailty model to analyse risk factors for bilateral corneal graft in Keratoconus. Applying the piecewise constant baseline hazard model, we have performed a Bayesian analysis of the correlated frailty model using the Markov chain Monte Carlo method. The correlated frailty model and the shared frailty model are compared by deviance information criterion. The results show more accurate and better fit for the correlated frailty model.

Non-mixture cure correlated frailty models in Bayesian approach

“…Kheiri et al [11] used piecewise exponential distribution as risk function and additive gamma distribution for correlated frailty variable to analyze these data in the Cox frailty model (without cure rate). The model parameters were estimated by the Bayesian approach and show more accurate and better fit for the correlated frailty models in comparison with the shared frailty model.…”

“…Additive models are used for those distributions that their Laplace transform can be written in closed form, such as gamma, inverse Gaussian, positive stable function and power variance function [11,12,17,32]. However, using additive models has two disadvantages.…”

“…The available information includes: the time of the first graft rejection or the last visit, gender, age at the time of surgery having severed ocular allergy corneal vascularization and factor related to the donor such as freshness or keep in corneal solution [11].…”

Bayesian statistics in medicine: a 25 year review

“…Modelling risks of a second complication following a first complication of diabetes used conditional modelling and survival models [521]. Recurrent events such as infections in patients with an inherited immune disease were modelled using time-dependent frailties [522] Correlated frailty models were used to analyse risk factors in bilateral corneal graft rejection [523] Proportional hazards models with time-varying regression coefficients were illustrated in a study of ovarian cancer patients [524]. Dental restorations involving clustered grouped survival data were modelled using multilevel Cox regression [525] A patternmixture model was used for repeated measures quality of life with right-censored survival times in a trial of congestive heart failure [526].…”

A frailty modeling approach for parental effects in animal breeding

“…[18,19,21,22,38]). In the correlated frailty model, unobserved risk factors are not assumed to be the same in each group and frailty is allowed to be individual-specific exactly as in the univariate framework.…”