Generalized time-dependent logistic model with fragility

• Grant number: 09/06443-6
• Support type: Scholarships in Brazil - Master
• Effective date (Start): March 01, 2010
• Effective date (End): February 28, 2011
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Applied Probability and Statistics
• Principal researcher: Vera Lucia Damasceno Tomazella
• Grantee: Eder Angelo Milani
• Home Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

Several authors have preferred modeling survival data in the presence of covariates by the risk function, which is related to its interpretation. It describes how the instantaneous probability of failure is changing with time. In this context, one of the most used models is the Cox model (Cox, 1972) where the basic assumption for its use is that the failure rates are proportional. However, experience shows that there are data that can not be accommodated by the Cox model. This fact has been crucial in the development of various types of risk non-proportional. Among them we mention the accelerated failure model (Prentice, 1978). The hybrid risk model (Etezadi-Amoli and Ciampi, 1987) and generalized hybrid risk models (Louzada-Neto, 1999). In this context, MacKenzie (1996) proposed a new parametric family of continuous survival distribution for the analysis of non-proportional hazards data. The model is based on a generalization of the familiar logistic function to time-dependent form and is and is motivated in part, by considering the effect of time on your setting, and partly the need to consider parametric structure. In this project we want to consider an extension of the generalized time-dependent logistic model (GTDL) using the model of fragility as an alternative to model data that has no structure of proportional hazards. The frailty model (Vaupel et, al. 1979 Tomazella, 2003; Tomazella et al. 2004) is characterized by the use of a random effect, ie a random variable not observable, which represents the information that can not or do not were observed, as environmental and genetic factors, or information that, for some reason, were not considered in planning. The frailty is introduced in modeling of risk function in order to control non-observed heterogeneity of the units of study, including the dependence of the units that share the same risk factors.