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In this work we propose a new long-term survival model called Lindley-Weibull with a cure rate (LWcr). We consider that the event of interest can be caused by M different latent risk factors. We assume that M follows a discrete Lindley distribution and the activation time of j-th factor follows a Weibull distribution. For the estimation of the parameters of interest we developed a Bayesian approach with non-informative prior distributions. To obtain the parameter estimates based on their posterior distributions, we used Monte Carlo Markov Chain (MCMC) methods. In order to detect influential observations, it was used the Bayesian method of influence analysis of case deletion based on ψ-divergence. We apply the proposed model to simulated and an actual dataset as an illustration.
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