Parametric and semi-parametric cure rate models with spatial frailties for interval-censored data
Abstract
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.