  In this article, we particularly address the problem of assessing the impact
of clinical stage and age on the specific survival times of men with breast
cancer when cure is a possibility, where there is also the interest of
explaining this impact on different quantiles of the survival times. To this
end, we developed a quantile regression model for survival data in the presence
of long-term survivors based on the generalized distribution of Gompertz in a
defective version, which is conveniently reparametrized in terms of the q-th
quantile and then linked to covariates via a logarithm link function. This
proposal allows us to obtain how each variable affects the survival times in
different quantiles. In addition, we are able to study the effects of
covariates on the cure rate as well. We consider Markov Chain Monte Carlo
(MCMC) methods to develop a Bayesian analysis in the proposed model and we
evaluate its performance through a Monte Carlo simulation study. Finally, we
illustrate the advantages of our model in a data set about male breast cancer
from Brazil.
