Parametric and semi-parametric cure rate models with spatial frailties for interval-censored data
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In this thesis, we extend some flexible cure rate models, such as the geometric, negative binomial and power series cure rate models, to allow for spatial correlations by including spatial frailties for the interval censored data setting. Parametric and semi-parametric cure rate models with independent and dependent spatial frailties are proposed and compared. The proposed models encompass several well-known cure rate models as its particular cases. Since these cure rate models are obtained by considering that the occurrence of an event of interest is caused by the presence of any non-observed risks, we also study the complementary cure model, which arises when the cure rate models are obtained by assuming the occurrence of an event of interest is caused when all of non-observed risks are activated. A new measure of model selection, based on the notion of predictive loss paradigm, for the interval-censoring data is also proposed. The MCMC method is used in a Bayesian inference approach and some Bayesian model selection criteria are used for model comparison. Moreover, we conduct an influence diagnostics to detect possible influential or extreme observations that can cause distortions on the results of analysis. Finally, the proposed models are applied to analyze a real dataset from a stop smoking study.