Compound negative binomial shared frailty model with random probability of susceptibility

Abstract

The shared frailty models are now popular for modelling heterogeneity in survival analysis. It assumes that the same frailty is shared by all individual members within the families. Also, it is believed that all the individuals in the population are susceptible to the event of interest and will eventually experience the event. This may not always be the situation in reality. There may be a certain fraction of the population which is non-susceptible for an event and hence may not experience the event under study. Non-susceptibility is modelled by frailty models with compound frailty distribution. Further, susceptibility may be different for different families. This can be attained by randomizing the parameter of frailty distribution. This paper incorporates both the things, non-susceptibility and different susceptibility for different families by considering compound negative binomial distribution with random probability of susceptibility as frailty distribution. The inferential problem is solved in a Bayesian framework using Markov Chain Monte Carlo methods. The proposed model is then applied to a real-life data set.

Keywords:

• Bayesian estimation
• beta distribution
• compound negative binomial distribution
• shared frailty
• generalized exponential distribution
• MCMC algorithm

Acknowledgments

The author is thankful to the Editor and the Referees for their comments and suggestions for improvements.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Author hasn't received any grant for research.