A New Class of Survival Regression Models with Cure Fraction

Abstract

In this paper, we propose a flexible 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 event follows a generalized gamma distribution. We define the negative binomial-generalized gamma distribution, which can be used to model survival data. The new model includes as special cases some of the well-known cure rate models discussed in the literature. We consider a frequentist analysis and nonparametric bootstrap for parameter estimation of a negative binomial-generalized gamma regression model with cure rate. Then, we derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes and present some ways to perform global influence analysis. Finally, we analyze a real data set from the medical area.