A New Long-Term Survival Model with Interval-Censored Data

Abstract

We propose a flexible cure rate survival model by assuming that the number of competing causes of the event of interest has a negative binomial distribution and the time to event has a Weibull distribution for interval-censored data. An advantage is that this model includes as special cases some well-known cure rate models discussed in the literature. We also propose the negative binomial Weibull distribution, which is a quite flexible model to analyze positive data. We provide explicit expressions for the moments and generating function. We consider a frequentist analysis and nonparametric bootstrap for parameter estimation of the negative binomial Weibull regression model for interval-censored data with cure rate. Further, 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. We analyze two real data sets from the medical area to prove the flexibility of the proposed models.