Authors: David D. Hanagal; Alok D. Dabade
Addresses: Department of Statistics, University of Pune, Pune-411007, India ' Department of Statistics, University of Pune, Pune-411007, India
Abstract: Shared frailty models are often used to model heterogeneity in the survival analysis. The most common shared frailty model is a model in which hazard function is a product of random factor (frailty) and the baseline hazard function which is common to all individuals. There are certain assumptions about the baseline distribution and the distribution of frailty. Mostly assumption of the gamma distribution is considered for frailty distribution. To compare the results with the gamma frailty model, we introduce three shared frailty models with the Weibull as baseline distribution. The other three shared frailty models are the inverse Gaussian shared frailty model, the compound Poisson shared frailty model and the compound negative binomial shared frailty model. We fit these models to a real life bivariate survival dataset of McGilchrist and Aisbett (1991) related to kidney infection data using the Markov chain Monte Carlo (MCMC) technique. Model comparison is made using the Bayesian model selection criteria and the inverse Gaussian frailty model model is suggested for this data.
Keywords: Bayesian model comparison; compound negative binomial distribution; compound Poisson distribution; gamma distribution; inverse Gaussian distribution; likelihood ratio test; Markov chain Monte Carlo; MCMC; predictive density; shared frailty models; Weibull distribution; kidney infection data; survival analysis.
International Journal of Mathematical Modelling and Numerical Optimisation, 2014 Vol.5 No.4, pp.342 - 373
Received: 28 Feb 2014
Accepted: 08 Jun 2014
Published online: 23 Oct 2014 *