Joint models for longitudinal and survival data considering cure fraction via defective distributions with frailty

• Grant number: 24/07832-6
• Support Opportunities: Scholarships in Brazil - Doctorate (Direct)
• Start date: February 01, 2025
• End date: July 31, 2027
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Applied Probability and Statistics
• Principal Investigator: Vera Lucia Damasceno Tomazella
• Grantee: Dionisio Alves da Silva Neto
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Associated research grant: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry, AP.CEPID

Abstract

The models of cure fraction in survival data studies have become an important research field within the area, attracting researchers' attention. Cure fraction models through defective distributions have the advantage of modeling the proportion of cured individuals without adding extra parameters to a model, contrary to what happens in the main models in the literature. In the literature, only two distributions with this characteristic were found: the Gompertz and the Inverse Gaussian. These distributions are extended using the Marshall-Olkin and Kumaraswamy families, creating four new defective distributions with greater flexibility. In recent years, there has been a growing interest in considering longitudinal biomarkers as additional information to understand the behavior of time to an event. This type of modeling is known as joint models for longitudinal and survival data, where a longitudinal model shares information with a survival model through latent components (e.g., random effects). It is also possible to consider a linear submodel of mixed effects for the longitudinal outcome and a submodel of proportional frailty for cause-specific survival data of competing risks, linked together by some latent random effects. The proposal of this direct doctoral project is to consider, in the joint modeling, the extension of cure fraction models via defective distributions with a frailty term. For the estimation process, both classical and Bayesian approaches will be used.