A Mixture Model for Survival Data with Both Latent and Non-Latent Cure Fractions

One of the most popular cure rate models in the literature is the Berkson and Gage mixture model. A characteristic of this model is that it considers the cure to be a latent event. However, there are situations in which the cure is well known, and this information must be considered in the analysis. In this context, this paper proposes a mixture model that accommodates both latent and non-latent cure fractions. More specifically, the proposal is to extend the Berkson and Gage mixture model to include the knowledge of the cure. A simulation study was conducted to investigate the asymptotic properties of maximum likelihood estimators. Finally, the proposed model is illustrated through an application to credit risk modeling.