New Methodologies for Cure Fraction Modeling with Frailty and Defective Distributions

• Grant number: 24/23079-6
• Support Opportunities: Regular Research Grants
• Start date: May 01, 2025
• End date: April 30, 2027
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Applied Probability and Statistics
• Principal Investigator: Vera Lucia Damasceno Tomazella
• Grantee: Vera Lucia Damasceno Tomazella
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

One of the challenges in survival analysis is modeling heterogeneous populations, which can be addressed by including frailty terms to capture unobserved variability between individuals or groups. The cure model in survival analysis is used to describe situations where part of the population never experiences the event of interest, such as failures or deaths, due to a "cure" process. This model is particularly relevant in contexts like medicine, where treatments can lead to the "cure" of patients, meaning indefinite survival without the occurrence of the event, as in the case of cancer patients cured after treatment. Models with discrete frailty and defective distributions are useful for dealing with the cure fraction, where part of the population never experiences the event of interest, such as patients cured after treatment. Furthermore, the joint modeling of longitudinal data and survival analysis allows for understanding how variables that evolve over time influence the risk of events. However, the development of this project presents significant challenges, such as formulating statistical models that balance flexibility and parsimony, developing efficient inferential methods, and implementing robust computational approaches to handle complex and high-dimensional problems. On the other hand, the advantages of advancing this research include the creation of innovative methodologies that expand the understanding of complex phenomena and provide practical tools for decision-making in various fields. This project, composed of three sub-projects, aims to overcome these challenges by formulating advanced models, developing frequentist and Bayesian estimation methodologies, and generalizing existing approaches to provide more robust and applicable solutions. Additionally, a set of computational packages will be developed to allow the practical implementation of the proposed methodologies. Thus, the project will contribute both to the advancement of statistical theory and to practical applications in real-world contexts. (AU)