  This paper introduces a cure rate survival model by assuming that the time to
the event of interest follows a beta prime distribution and that the number of
competing causes of the event of interest follows a negative binomial
distribution. This model provides a novel alternative to the existing cure rate
regression models due to its flexibility, as the beta prime model can exhibit
greater levels of skewness and kurtosis than those of the gamma and inverse
Gaussian distributions. Moreover, the hazard rate 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 a real data
set.
