A Bayesian destructive generalized Waring regression cure model with a variance decomposition and application in colorectal cancer data

In this paper, we develop a Bayesian two-stage cure rate model whose biological destructive mechanism (immune system) of the competing risk factors of death is suitable for detecting the impact on the long-term survival function of three sources of variance well-known in accident theory: randomness, liability and proneness. From a survival analysis viewpoint, proneness means individual effect or destructive mechanism and liability corresponds to external effects or covariates. The flexibility of the generalized Waring frailty distribution in capturing these variance components separately enables one to understand the nature of overdispersion of the risk factors involved in studying risk of death after a long-term treatment of the patient. A new cure rate, involving covariate and destructive mechanism, is developed here under a competing cause scenario. A simulation study and an application to colorectal cancer data set are finally presented to demonstrate the usefulness of the proposed model and the inferential results developed here.