In this thesis, we consider a competing cause scenario that incorporates a dependence structure. The correlated dependence generalized power series (CDGPS) cure rate model, used by Borges et al. (2012), is employed which captures the real life mechanisms that exist for dependent competing causes. Our approach assumes that the number of initial competing causes follows the generalized power series with a destructive process following an administered treatment. This destructive process allows us to capture the undamaged portion of the initial competing causes in a competitive scenario. The objective is to use the estimation-maximization (EM) algorithm on special cases of the CDGPS model to test its effectiveness at estimating model parameters, through a simulation study carried out under various parameter settings. Finally, the EM algorithm and the models are applied to two real melanoma data sets, where model discrimination is conducted through information-based methods.