# The negative binomial beta prime regression model with cure rate

## TL;DR

This paper proposes a new cure rate survival model using a beta prime distribution for event times and a negative binomial distribution for causes, offering greater flexibility in skewness, kurtosis, and hazard shapes.

## Contribution

It introduces a novel cure rate model combining beta prime and negative binomial distributions, with new estimation and influence analysis methods.

## Key findings

- Model exhibits flexible hazard shapes including upside-down bathtub.
- Numerical simulations validate estimation procedures.
- Application to real data demonstrates practical utility.

## Abstract

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.