A general hazard model for lifetime data in the presence of cure rate

Abstract

Historically, the cure rate model has been used for modeling time-to-event data within which a significant proportion of patients are assumed to be cured of illnesses, including breast cancer, non-Hodgkin lymphoma, leukemia, prostate cancer, melanoma, and head and neck cancer. Perhaps the most popular type of cure rate model is the mixture model introduced by Berkson and Gage [1]. In this model, it is assumed that a certain proportion of the patients are cured, in the sense that they do not present the event of interest during a long period of time and can found to be immune to the cause of failure under study. In this paper, we propose a general hazard model which accommodates comprehensive families of cure rate models as particular cases, including the model proposed by Berkson and Gage. The maximum-likelihood-estimation procedure is discussed. A simulation study analyzes the coverage probabilities of the asymptotic confidence intervals for the parameters. A real data set on children exposed to HIV by vertical transmission illustrates the methodology.

Keywords:

• hazard modeling
• cure rate modeling
• HIV children
• vertical transmission

Acknowledgements

The authors sincerely thank the anonymous referees for their insight and very useful comments and suggestions which led to many improvements in the paper, and Adriana Nunes Fernandes da Silva and Afonso Dinis Costa Passos for the HIV data set. The research was partially supported by the Brazilian Organization CNPq and FAEPA.