Abstract
Shared frailty models are often used to model heterogeneity in survival analysis. The most common shared frailty model is a model in which hazard function is a product of random factor (frailty) and baseline hazard function which is common to all individuals. There are certain as sumptions about the baseline distribution and distribution of frailty. Mostly assumption of gamma distribution is considered for frailty distribution. To compare the results with gamma frailty model, we introduce three shared frailty models with generalized exponential as baseline distribution. The other three shared frailty models are inverse Gaussian shared frailty model, compound Poisson shared frailty model and compound negative binomial shared frailty model. We fit these models to a real life bivariate survival data set of McGilchrist and Aisbett (1991) related to kidney infection using Markov Chain Monte Carlo (MCMC) technique. Model comparison is made using Bayesian model selection criteria and a better model is suggested for the data.
Highlights
Survival models have been extensively used in medical research during last several years
Hazard rate increases from zero to a finite constant, when shape parameter α increases and hazard rate decreases from infinity to a finite number when α is less than one
A nearly constant rate after a certain time period implies that the occurrence of failure is purely random and is independent of past life; this is a property of the failure rate of an exponential distribution which has been extensively used in reliability studies
Summary
Survival models have been extensively used in medical research during last several years. In Cox proportional hazards model, we include explanatory variables or covariates to study the effect of covariates on distribution of survival times. A genetic factor as we do not know all possible genes having influence on survival This unknown or unobservable risk factor of the hazard function is often termed as the heterogeneity or frailty. We consider shared frailty model with baseline as generalized exponential distribution and four frailty distributions, gamma, inverse Gaussian, compound Poisson and compound negative binomial distribution. In the same Section we propose the four frailty models, gamma, inverse Gaussian, compound Poisson and compound negative binomial shared frailty models with generalized exponential baseline distribution respectively.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
