A model with long-term survivors: negative binomial Birnbaum-Saunders

Abstract

We propose a cure rate survival model by assuming that the number of competing causes of the event of interest follows the negative binomial distribution and the time to the event of interest has the Birnbaum-Saunders distribution. Further, the new model includes as special cases some well-known cure rate models published recently. We consider a frequentist analysis for parameter estimation of the negative binomial Birnbaum-Saunders model with cure rate. Then, we derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes. We illustrate the usefulness of the proposed model in the analysis of a real data set from the medical area.

Keywords:

• Birnbaum-Saunders distribution
• Cure fraction model
• Lifetime data
• Negative binomial distribution
• Sensitivity analysis.

Mathematics Subject Classifications:

• 62N01, 62N02, 62N03

Acknowledgments

We thank the Associate Editor and the reviewer for constructive comments.

Funding

The financial support from FAPESP and CNPq is gratefully acknowledged.