With rapid improvements in medical treatment and health care, many datasets dealing with time to relapse or death now reveal a substantial portion of patients who are cured (i.e., who never experience the event). Extended survival models called cure rate models account for the probability of a subject being cured and can be broadly classified into the classical mixture models of Berkson and Gage (BG type) or the stochastic tumor models pioneered by Yakovlev and extended to a hierarchical framework by Chen, Ibrahim, and Sinha (YCIS type). Recent developments in Bayesian hierarchical cure models have evoked significant interest regarding relationships and preferences between these two classes of models. Our present work proposes a unifying class of cure rate models that facilitates flexible hierarchical model-building while including both existing cure model classes as special cases. This unifying class enables robust modeling by accounting for uncertainty in underlying mechanisms leading to cure. Issues such as regressing on the cure fraction and propriety of the associated posterior distributions under different modeling assumptions are also discussed. Finally, we offer a simulation study and also illustrate with two datasets (on melanoma and breast cancer) that reveal our framework's ability to distinguish among underlying mechanisms that lead to relapse and cure.

The emergence of geographical information systems and related softwares nowadays enables medical databases to incorporate the geographical information on patients, allowing studies in spatial associations. Public health administrators and researchers are often interested in detecting variation in survival patterns by region or county in order to understand the possible factors that contribute towards such spatial discrepancies. These issues have led statisticians to develop survival models that account for spatial clustering and variation. Additionally, with rapid developments in medical and health sciences, researchers increasingly encounter data sets where a substantial portion of patients are cured. Models accounting for cure in the population assist in the prognosis of potentially terminal diseases. This article proposes a Bayesian modelling framework that models spatial associations for areally referenced survival data using a general class of cure models proposed by Cooner et al. The special models we outline are alternatives to the traditional proportional hazards models and can be fitted using standard Bayesian software such as WinBUGS.

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