Usually, in survival models with cure rate is assumed an scheme based on competitive risks to the concurrent causes, i.e., the failure time of the system is given by the minimum of the times related to those causes (first activation scheme). Recently, Cancho et al. (2013) proposed the so-called Destructive Negative Binomial cure rate model with different activation schemes (additionally to the presented scheme, it is used a last activation scheme and a random activation scheme based on the Uniform distribution). This model is a generalization of some cure models discussed in the literature. Among them, we highlight the model of Berkson and Gage (1952), the model of Chen et al. (1999), the model assuming the Negative Binomial distribution for the concurrent causes proposed in Rodrigues et al. (2008) and the Destructive weighted Poisson cure rate models proposed in Rodrigues et al. (2011).This project consists in extend the model of Cancho et al. (2013) in two different ways. The first part in the context that the observations are grouped in clusters. For example, in the medical studies it is usual patients to be treated in different clinics. Thus, we propose to include two random effects associated for each clinic: one to account for the influence of each clinic on the susceptible individuals and other to explain the influence of each clinic on the cure rate.In the second part, we propose a new alternative to the activation scheme proposed in thework of Cancho et al. (2013), assuming the Binomial distribution to the number ofconcurrent causes related to the failures for the individuals.
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