Frailty Models with Cure Fraction via Hazard Modeling Non Proportional to Analyze Data Long-Term Survival

• Grant number: 11/19502-0
• Support Opportunities: Scholarships abroad - Research
• Start date: February 06, 2012
• End date: August 05, 2012
• 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 Investigator: Saralees Nadarajah
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Institution abroad: University of Manchester, England

Abstract

Models based on hazard function have achieved great prominence in the survival analysis from the construction of the proportional hazards model of Cox (1972). One of the reasons this model has become so popular is its interpretative power and ease with which the technical difficulties arising from the censures were circumvented. Naturally, the construction of the model allows the covariates are related to the risk of failure, so that influence the level of risk for different subgroups. Yet experience shows that there are data that can not be accommodated by the model of Cox. His model advocates that the ratio of the failure rates of any two individuals are proportional. There are very strong assumptions that may not conform to various practical situations. This fact has been determinant in the developing of several types of non-proportional hazard models. Among them we mention the accelerated failure model (Prentice, 1978), the hybrid hazard model (Etezadi-Amoli and Ciampi, 1987) and the extended hybrid hazard models (Louzada-Neto, 1979 eLouzada-Neto, 1999) and generalized time-dependent logistic (GTDL) model Mackenzie (1996). This project aims to discuss the overall survival model with cure fraction considering the proportional hazards and non-proportional, while the unobserved heterogeneity among individuals risk is modeled by a random factor called term fragility. Let us consider the traditional model of Cox proportional hazards (Cox, 1972) and the model proposed by MacKenzie (1996) based on the generalization of the familiar logistic risk function considering a time dependent manner that allows an interpretation of fragility when you have a homogeneous population called "generalized logistic risk model time-dependent (GTDL)". The development of this research project will allow relevant scientific advances in the development of statistical modeling. These advances we can cite the development of a new methodology for analyzing data from long-term survival (non-proportional hazard model with cure fraction)