Extending cure-fraction defective models for financial, industrial and medical data

• Grant number: 16/12796-2
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: September 01, 2016
• End date: August 31, 2017
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Statistics
• Principal Investigator: Francisco Louzada Neto
• Grantee: Ricardo Ferreira da Rocha
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry, AP.CEPID

Abstract

The modeling of a cured fraction in survival data studies has formed an important field in the area and has attracted the attention of researchers. The literature regarding to cure rate models is very large and have several different approaches on how estimate the quantities ofinterest. One way to model cure rates is to use defective distributions. These distributions have the advantage of estimate a cured proportion without adding any extra parameters in the model, as it happens in most literature cases, and it does not require any assumption of the existence of a cure rate before the modeling. A distribution is defective when the integral of its density function takes value in (0,1), when changed the original domain of its parameters. There are only few distributions with this characteristic in the literature. The purpose of this post-doctoral project is to extend the cure rate models via defective distributions and explore the computational issues regarding to the implementation in financial, industrial and medical data. This project is based on five subprojects: a Bayesian approach to defective cure fraction to model data in the presence of a cure rate, a defective cure rate models with frailty term, the development of a computational package in R for all the functions of interest related to the defective models and the proposal of the zero-inflated cure rate regression model based on a defective distribution. (AU)