The Poisson-exponential regression model under different latent activation schemes

Abstract

Abstract. In this paper, a new family of survival distributions is presented. It is derived by considering that the latent number of failure causes follows a Poisson distribution and the time for these causes to be activated follows an exponential distribution. Three different activation schemes are also considered. Moreover, we propose the inclusion of covariates in the model formulation in order to study their effect on the expected value of the number of causes and on the failure rate function. Inferential procedure based on the maximum likelihood method is discussed and evaluated via simulation. The developed methodology is illustrated on a real data set on ovarian cancer.Mathematical subject classification: 62N01, 62N99.

Statistical modeling of V th distribution in ovonic threshold switches based on physical switching models

“…In addition, at each relaxation time, the number of quenched defects N T followed a Poisson distribution with mean 〈N T 〉. If both of these are true, the total relative V th shift follows a Poisson-exponential (PE) distribution, [40][41][42][43] as expressed in Eq. ( 16):…”

On truncated Poisson exponential proportional hazard model

“…, T r ). The probability density function of Y 0 as well as survival function, hazard function and p th quantile times under TPE distribution are (Kuş 2007;Louzada et al , 2012).…”

“…Bereta et al (2011) introduced Poisson-Weibull three parameters lifetime distribution in the presence of more than one causes responsible for the occurrence of event. To examine how a set of covariates influence the survival time Louzada et al (2012) suggested Poisson-exponential survival regression model. As the interpretation of regression parameters of this model is not straight forward, in this paper, a Truncated Poisson Exponential (TPE) proportional hazard model has been proposed so that one can interpret the regression parameter easily.…”

“…Kuş (2007) proposed a two-parameter distribution known as exponential-Poisson distribution, which has decreasing failure rate. Louzada et al (2012) proposed a class of hierarchical models with latent competing risks and different activation schemes, where the lifetime associated with a particular cause is not observable, rather only the minimum, maximum or a randomly lifetime value among all cause is observed, with the lifetimes following an exponential distribution. To examine the influence of covariates on the survival time, Louzada et al (2012) incorporated covariates into the Poisson-Exponential distribution by replacing hazard parameter of exponential distribution and parameter of zero-truncated Poisson distribution with linear predictor using log link function.…”

“…The main limitation of this suggested model is that interpretation of regression coefficients is not tractable. Regression coefficients only provide the pattern of change in survival quantities, but using the model suggested by Louzada et al (2012) it is not possible to determine to what extent survival survival quantities change with the change in the value of covariates. As a remedy of this difficulty, following proportional hazard (PH) model (Cox, 1972), a parametric survival regression model has been proposed based on a Truncated Poisson Exponential (TPE) distribution.…”