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http://dx.doi.org/10.29220/CSAM.2018.25.5.471

A Bayesian cure rate model with dispersion induced by discrete frailty  

Cancho, Vicente G. (Department of Applied Mathematics and Statistics, University of Sao Paulo)
Zavaleta, Katherine E.C. (Department of Statistics, Federal University of Sao Carlos)
Macera, Marcia A.C. (Department of Applied Mathematics and Statistics, University of Sao Paulo)
Suzuki, Adriano K. (Department of Applied Mathematics and Statistics, University of Sao Paulo)
Louzada, Francisco (Department of Applied Mathematics and Statistics, University of Sao Paulo)
Publication Information
Communications for Statistical Applications and Methods / v.25, no.5, 2018 , pp. 471-488 More about this Journal
Abstract
In this paper, we propose extending proportional hazards frailty models to allow a discrete distribution for the frailty variable. Having zero frailty can be interpreted as being immune or cured. Thus, we develop a new survival model induced by discrete frailty with zero-inflated power series distribution, which can account for overdispersion. This proposal also allows for a realistic description of non-risk individuals, since individuals cured due to intrinsic factors (immunes) are modeled by a deterministic fraction of zero-risk while those cured due to an intervention are modeled by a random fraction. We put the proposed model in a Bayesian framework and use a Markov chain Monte Carlo algorithm for the computation of posterior distribution. A simulation study is conducted to assess the proposed model and the computation algorithm. We also discuss model selection based on pseudo-Bayes factors as well as developing case influence diagnostics for the joint posterior distribution through ${\psi}-divergence$ measures. The motivating cutaneous melanoma data is analyzed for illustration purposes.
Keywords
Bayes factor; Bayesian inference; cure rate models; frailty models; Kullback-Leibler; zero-inflated power series distribution;
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