title: Relaxed Poisson cure rate models.
abstract: The purpose of this article is to make the standard promotion cure rate model (Yakovlev and Tsodikov, ) more flexible by assuming that the number of lesions or altered cells after a treatment follows a fractional Poisson distribution (Laskin, ). It is proved that the well-known Mittag-Leffler relaxation function (Berberan-Santos, ) is a simple way to obtain a new cure rate model that is a compromise between the promotion and geometric cure rate models allowing for superdispersion. So, the relaxed cure rate model developed here can be considered as a natural and less restrictive extension of the popular Poisson cure rate model at the cost of an additional parameter, but a competitor to negative-binomial cure rate models (Rodrigues et al., ). Some mathematical properties of a proper relaxed Poisson density are explored. A simulation study and an illustration of the proposed cure rate model from the Bayesian point of view are finally presented.
authors.affiliation: Department of Applied Mathematics and Statistics, Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, São Carlos-SP, Brazil.
authors.forename: Josemar
authors.initials: J
authors.lastname: Rodrigues
authors.affiliation: Department of Statistics, Universidade Federal de Pernambuco, Recife-PE, Brazil.
authors.forename: Gauss M
authors.initials: GM
authors.lastname: Cordeiro
authors.affiliation: Department of Applied Mathematics and Statistics, Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, São Carlos-SP, Brazil.
authors.forename: Vicente G
authors.initials: VG
authors.lastname: Cancho
authors.affiliation: Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada.
authors.forename: N
authors.initials: N
authors.lastname: Balakrishnan
mesh_terms: D001499:Bayes Theorem; D006801:Humans; D016013:Likelihood Functions; D015233:Models, Statistical; D009369:Neoplasms / Q000628:therapy*; D016012:Poisson Distribution; D012008:Recurrence; D016896:Treatment Outcome
keywords: Bayesian inference; Fractional Poisson distribution; Geometric cure rate model; Mittag-Leffler relaxation function; Poisson cure rate model; Relaxed Poisson cure rate model