Bayesian long-term survival model including a frailty term: Application to melanoma data

In this paper, we propose a flexible cure rate model including a frailty term, which was obtained by incorporating a random effect in the risk function of latent competing causes. The number of competing causes of the event of interest follows a negative binomial distribution, and the frailty variable follows a power variance function distribution, 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 data, which are suitable for populations with a long-term survivors. Besides, it allows quantification of the degree of unobserved heterogeneity induced by unobservable risk factors, which is important to explain the lifetime. Once the posterior density function is not expressed in the closed form, Markov chain Monte Carlo algorithms are performed for the estimation procedure. Simulation studies were considered in order to evaluate the proposed model performance, and its practical relevance was illustrated in a real medical dataset from a population-based study of incident cases of melanoma diagnosed in the state of Sao Paulo, Brazil.