A Bayesian Poisson mixed modelling approach to survival model with compound Poisson distributed frailty

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University of New Brunswick
In survival studies, a subgroup of subjects may have zero susceptibility to the event of interest. For example, some people may be immune to a certain disease. These kind of data occur widely in medicine, social science and environment studies. The frailties therefore consist of a mix of zero and positive values. This poses some challenges in data analysis as there is no standard distribution for the frailties. Our work is motivated by Ma et al. (2003 & 2009). They have presented a multilevel frailties Poisson model for the survival data. In this thesis, we propose a Bayesian mixed model for survival data with zero-inflated frailties. With our approach, the zero and positive frailties are modeled using a compound Poisson distribution in an integral manner. We use the Markov chain Monte Carlo algorithm (MCMC) and the Bayesian approach to estimate the regression parameters and the frailties. Two data sets, jail time data and third birth data, are used to illustrate our proposed method.