  In this paper, we propose a flexible cure rate model with frailty term in
latent risk, which is obtained by incorporating a frailty term in risk function
of latent competing causes. The number of competing causes of the event of
interest follows negative binomial distribution and the frailty variable
follows power variance function distribution, in which includes other frailty
models such as gamma, positive stable and inverse Gaussian frailty models as
special cases. The proposed model takes into account the presence of covariates
and right-censored survival data suitable for populations with a cure rate.
Besides, it allows quantifying the degree of unobserved heterogeneity induced
by unobservable risk factors, in which is important to explain the survival
time. Once the posterior distribution has not close form, Markov chain Monte
Carlo simulations are considered for estimation procedure. We performed several
simulation studies and the practical relevance of the proposed model is
demonstrated in a real data set.
