title: New defective models based on the Kumaraswamy family of distributions with application to cancer data sets.
abstract: An alternative to the standard mixture model is proposed for modeling data containing cured elements or a cure fraction. This approach is based on the use of defective distributions to estimate the cure fraction as a function of the estimated parameters. In the literature there are just two of these distributions: the Gompertz and the inverse Gaussian. Here, we propose two new defective distributions: the Kumaraswamy Gompertz and Kumaraswamy inverse Gaussian distributions, extensions of the Gompertz and inverse Gaussian distributions under the Kumaraswamy family of distributions. We show in fact that if a distribution is defective, then its extension under the Kumaraswamy family is defective too. We consider maximum likelihood estimation of the extensions and check its finite sample performance. We use three real cancer data sets to show that the new defective distributions offer better fits than baseline distributions.
authors.affiliation: 1 Universidade Federal de São Carlos, Departamento de Estatística, São Carlos, SP, Brasil.
authors.forename: Ricardo
authors.initials: R
authors.lastname: Rocha
authors.affiliation: 2 University of Manchester, School of Mathematics, Manchester, UK.
authors.forename: Saralees
authors.initials: S
authors.lastname: Nadarajah
authors.affiliation: 1 Universidade Federal de São Carlos, Departamento de Estatística, São Carlos, SP, Brasil.
authors.forename: Vera
authors.initials: V
authors.lastname: Tomazella
authors.affiliation: 3 Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, São Carlos, SP, Brasil.
authors.forename: Francisco
authors.initials: F
authors.lastname: Louzada
authors.affiliation: 1 Universidade Federal de São Carlos, Departamento de Estatística, São Carlos, SP, Brasil.
authors.forename: Amanda
authors.initials: A
authors.lastname: Eudes
mesh_terms: D003110:Colonic Neoplasms / Q000401:mortality; D066264:Datasets as Topic; D006801:Humans; D053208:Kaplan-Meier Estimate; D007938:Leukemia / Q000401:mortality; D016013:Likelihood Functions; D008545:Melanoma / Q000401:mortality; D009369:Neoplasms; D016011:Normal Distribution
keywords: Cure fraction; Gompertz distribution; Kumaraswamy family; defective distributions; inverse Gaussian distribution; survival analysis