Kumaraswamy-G family to analyze data from long-term survival

• Grant number: 13/04437-4
• Support type: Scholarships in Brazil - Master
• Effective date (Start): October 01, 2013
• Effective date (End): February 28, 2015
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics
• Principal Investigator: Vera Lucia Damasceno Tomazella
• Grantee: Amanda Morales Eudes
• Home Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

In studies involving the time until the occurrence of some event of interest (failure) there is a possibility that not always all study subjects experiment the event of interest even if these individuals is observed a very long time. These individuals are said to be cured or immune to the event of interest and, consequently, its population has a proportion of cure. Generally the time until the occurrence of some event of interest has a probability distribution. Kumaraswamy (1980) proposed a new probability distribution and more recently based on this distribution, Lamb and Castro (2011) describe a new family of generalized distributions Kumaraswamy-G. This distribution is flexible and contains other distributions as special cases. In this study, we investigate the application of G-Kumaraswamy distribution to a standard mixture model proposed by Berkson and Gage (1952) to find the estimated cure rate. The mixture model Kumaraswamy-G offers great flexibility to model the distribution of survival time of patients not cured, and effects of covariates on the rate of cure. This model can potentially discover survival data structure that would otherwise be missed using other parametric mixture models in the literature.