A new destructive Poisson odd generalized half-normal cure rate model
In this paper, we propose a new flexible cure rate survival model by assuming the initial number of competing causes of the event of interest follows a Poisson distribution and the time to event has the odd log-logistic generalized half-normal (OLLGHN) (Cordeiro et al., 2015) distribution. This new survival model describes a realistic interpretation for the biological mechanism of the occurrence of the event of interest in studies related to carcinogenesis (initiation of a tumor, promotion and progression of the tumor to a detectable cancer) in presence of the competing latent causes. This mechanism includes a process of destruction of tumor cells after an initial treatment or the capacity of an individual exposed to irradiation to repair initiated cells that result in cancer being induced. We estimate the model parameters using maximum likelihood. We derive the appropriate matrices for assessing local in influence diagnostics on the parameter estimates under different perturbation schemes. In addition, we define the martingale and modified deviance residuals to detect outliers and evaluate the model assumptions. Also, we demonstrate that the extended cure rate regression model can be very useful in the analysis of real survival data and provide more realistic fits than other survival regression models with cure rate commonly used in the literature. The potentiality of the new cure rate survival model is illustrated by means of a real data set.
