Bayesian analysis of an inverse Gaussian correlated frailty model

Many analyses in the epidemiological and the prognostic studies and in the studies of event history data require methods that allow for unobserved covariates or "frailties". We consider the shared frailty model in the framework of parametric proportional hazard model. There are certain assumptions about the distribution of frailty and baseline distribution. The exponential distribution is the commonly used distribution for analyzing lifetime data. In this paper, we consider shared gamma frailty model with bivariate exponential of Marshall and Olkin (1967) distribution as baseline hazard for bivariate survival times. We solve the inferential problem in a Bayesian framework with the help of a comprehensive simulation study and real data example. We fit the model to the real-life bivariate survival data set of diabetic retinopathy data. We introduce Bayesian estimation procedure using Markov Chain Monte Carlo (MCMC) technique to estimate the parameters involved in the proposed model and then compare the true values of the parameters with the estimated values for different sample sizes.

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“…They also considered positive stable frailty models. Kheiri et al (2007) considered inverse Gaussian correlated frailty model .…”

Section: Marshall-olkin's Bvegf Regression Modelmentioning

confidence: 99%

Bayesian Inference in Marshall–Olkin Bivariate Exponential Shared Gamma Frailty Regression Model under Random Censoring

Hanagal

Sharma

2014

Communications in Statistics - Theory and Methods

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“…The traditional maximum likelihood approach to estimation is commonly used in survival analysis, but it can encounter difficulties with frailty models. Moreover, standard maximum likelihood based inference methods may not be suitable for small sample sizes or situations in which there is heavy censoring (see Kheiri et al (2007)). Thus, in our problem a Bayesian approach, which does not suffer from these difficulties, is a natural one, even though it is relatively computationally intensive.…”

Section: Likelihood Specification and Bayesian Estimation Of Parametersmentioning

confidence: 99%

The Transmuted Generalized Gamma Distribution: Properties and Application

Lucena¹,

Silva²,

Cordeiro³

2021

Journal of Data Science

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The unknown or unobservable risk factors in the survival analysis cause heterogeneity between individuals. Frailty models are used in the survival analysis to account for the unobserved heterogeneity in individual risks to disease and death. To analyze the bivariate data on related survival times, the shared frailty models were suggested. The most common shared frailty model is a model in which frailty act multiplicatively on the hazard function. In this paper, we introduce the shared inverse Gaussian frailty model with the reversed hazard rate and the generalized inverted exponential distribution and the generalized exponential distribution as baseline distributions. We introduce the Bayesian estimation procedure using Markov Chain Monte Carlo(MCMC) technique to estimate the parameters involved in the models. We present a simulation study to compare the true values of the parameters with the estimated values. Also we apply the proposed models to the Australian twin data set and a better model is suggested.

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“…The gamma distribution is most commonly used frailty distribution because of its mathematical convenience. However, it has drawbacks (see Kheiri et al, 2007) for example it may weaken the effect of covariates. Alternative to the gamma distribution Hougaard (1984) introduced inverse Gaussian as a frailty distribution.…”

Section: Inverse Gaussian Frailty Modelmentioning

confidence: 99%

A Comparative Study of Shared Frailty Models for Kidney Infection Data with Generalized Exponential Baseline Distribution

Hanagal¹,

Dabade²

2021

Journal of Data Science

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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 assumptions 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.

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Bayesian analysis of an inverse Gaussian correlated frailty model

Cited by 50 publications

References 17 publications

Bayesian Inference in Marshall–Olkin Bivariate Exponential Shared Gamma Frailty Regression Model under Random Censoring

Bayesian Inference in Marshall–Olkin Bivariate Exponential Shared Gamma Frailty Regression Model under Random Censoring

The Transmuted Generalized Gamma Distribution: Properties and Application

A Comparative Study of Shared Frailty Models for Kidney Infection Data with Generalized Exponential Baseline Distribution

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