The Negative Binomial Beta Prime Regression Model with Cure Rate: Application with a Melanoma Dataset

This paper introduces a cure rate survival model by assuming that the time to the event of interest follows a beta prime (BP) distribution and that the number of competing causes of the event of interest follows a negative binomial distribution. The proposed model provides a novel alternative to the existing cure rate regression models due to its flexibility, as the BP model can exhibit greater levels of skewness and kurtosis than these of the gamma and inverse Gaussian distributions. Moreover, the hazard rate function of this model can have an upside-down bathtub or an increasing shape. We approach both parameter estimation and local influence based on likelihood methods. In special, three perturbation schemes are considered for local influence. Numerical evaluation of the proposed model is performed by Monte Carlo simulations. In order to illustrate the potential for practice of our model, we apply it to the real medical dataset from a population-based study of incident cases of melanoma diagnosed in the state of São Paulo, Brazil.