an:06573943
Zbl 1381.62281
Rodrigues, Josemar; Cordeiro, Gauss M.; Cancho, Vicente G.; Balakrishnan, N.
Relaxed Poisson cure rate models
EN
Biom. J. 58, No. 2, 397-415 (2016).
00353978
2016
j
62P10 62F15
Bayesian inference; fractional Poisson distribution; geometric cure rate model; Mittag-Leffler relaxation function; Poisson cure rate model; relaxed Poisson cure rate model
Summary: The purpose of this article is to make the standard promotion cure rate model [\textit{A. Yu. Yakovlev} and \textit{A. D. Tsodikov}, Stochastic models of tumor latency and their biostatistical applications. Singapore: World Scientific Publishing (1996; Zbl 0919.92024)] more flexible by assuming that the number of lesions or altered cells after a treatment follows a fractional Poisson distribution [\textit{N. Laskin}, Commun. Nonlinear Sci. Numer. Simul. 8, No. 3--4, 201--213 (2003; Zbl 1025.35029)]. It is proved that the well-known Mittag-Leffler relaxation function [\textit{M. N. Berberan-Santos}, J. Math. Chem. 38, No. 4, 629--635 (2005; Zbl 1101.33015)] 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 [the first author et al., J. Stat. Plann. Inference 139, No. 10, 3605--3611 (2009; Zbl 1173.62074)]. 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.
Zbl 0919.92024; Zbl 1025.35029; Zbl 1101.33015; Zbl 1173.62074