The unknown or unobservable risk factors in the survival analysis cause heterogeneity between individuals. Frailty models are used to account for unobserved individual risks disease and death. To analyze bivariate data on related times, shared frailty were suggested. most common model is a which act multiplicatively hazard function. In this paper, we introduce inverse Gaussian with reversed rat...

Frailty models are often used in survival analysis to model multivariate time-to-event data. In infectious disease epidemiology, frailty models have been proposed to model heterogeneity in the acquisition of infection and to accommodate association in the occurrence of multiple types of infection. Although traditional frailty models rely on the assumption of lifelong immunity after recovery, re...

The dependence between individuals in a group is modeled by the group specific quantity, which can be interpreted as an unobserved covariates or “frailties” common to the individuals in the group and assumed to follow some distribution. We consider the shared frailty model in the frame work of parametric Cox proportional hazard model. The Cox regression model with the shared frailty factor allo...

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 corre...

In the analysis of survival data with parametric models, it is well known that the Weibull model is not suitable for modeling survival data where the hazard rate is non-monotonic. For such cases, where hazard rates are bathtub-shaped or unimodal (or hump-shaped), log-logistic, lognormal, Birnbaun-Saunders, and inverse Gaussian models are used for the computational simplicity and popularity amon...

Copulas and frailty models are important tools to model bivariate survival data. Equivalence between Archimedean copula models and shared frailty models, e.g., between the Clayton-Oakes copula model and the shared gamma frailty model, has often been claimed in the literature. In this note we show that, in both models, there is indeed the well known equivalence between the copula functions; the ...