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

Eduardo Yoshio Nakano (), Frederico Machado Almeida and Marcílio Ramos Pereira Cardial
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Eduardo Yoshio Nakano: Department of Statistics, University of Brasilia, Campus Darcy Ribeiro, Asa Norte, Brasilia 70910-900, Brazil
Frederico Machado Almeida: Department of Statistics, University of Brasilia, Campus Darcy Ribeiro, Asa Norte, Brasilia 70910-900, Brazil
Marcílio Ramos Pereira Cardial: Institute of Mathematics and Statistics, Federal University of Goias, Goiania 74001-970, Brazil

Stats, 2025, vol. 8, issue 3, 1-15

Abstract: 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.

Keywords: cure rate models; long-term survival; survival analysis; mixture model; credit scoring (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2025
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