The defective generalized Gompertz distribution and its use in the analysis of lifetime data in presence of cure fraction, censored data and covariates

Survival analysis methods are widely used in studies where the variable of interest is related to the time until the occurrence of an event. The usual methods assume that all individuals under study are subject to this event, but there are practical situations where this assumption is unrealistic. In some cases it is possible that a percentage of individuals are immune to the event of interest or, especially in cancer clinical trials, they were cured from their disease after a given treatment. In the literature, this percentage is usually referred as "cure fraction". In the present paper, we have proposed a model based on a modification of the generalized Gompertz distribution introduced by El-Gohary et al. (2013) to account for the presence of a cure fraction. We also considered the presence of censored data and covariates. Maximum likelihood and Bayesian methods for estimation of the model parameters are presented. A simulation study is provided to evaluate the performance of the maximum likelihood method in estimating parameters. In the Bayesian analysis, posterior distributions of the parameters are estimated using the Markov chain Monte Carlo (MCMC) method. An example involving a real data set is presented