  In medical studies, it is common the presence of a fraction of patients who
do not experience the event of interest. These patients are people who are not
at risk of the event or are patients who were cured during the research. The
proportion of immune or cured patients is known in the literature as cure rate.
In general, the traditional existing lifetime statistical models are not
appropriate to model data sets with cure rate, including bivariate lifetimes.
In this paper, it is proposed a bivariate model based on a defective Gompertz
distribution and also using a Clayton copula function to capture the possible
dependence structure between the lifetimes. An extensive simulation study was
carried out in order to evaluate the biases and the mean squared errors for the
maximum likelihood estimators of the parameters associated to the proposed
distribution. Some applications using medical data are presented to show the
usefulness of the proposed model.
