A useful variance decomposition for destructive Waring regression cure model with an application to HIV data

Motivated by the works of Irwin and Rodríguez-Avi et al., a destructive Waring regression cure model is developed here. This model enables the patients to be protagonists for the treatment and also facilitates an understanding of the nature of overdispersion of competing risk factors to prevent higher risk of the event of interest. The cure rate and the destructive mechanism (immune system) are personalized and the overdispersion of risk factors is explained through the decomposition of variance components: randomness, external frailty (unknown covariates) and internal frailty (destructive mechanism). A simulation study demonstrates the effectiveness of the proposed model and associated inferential method. Finally, an illustrative example shows that the internal frailty is an important factor in recurrent sinus disease among HIV-positive patients.