Bayesian superposition of pure-birth destructive cure processes for tumor latency

In this paper, a new Bayesian stochastic cure rate model, based on the individual frailty as the total number of descendent cells of each damaged cell (known as the volume of the tumor) up to specific time and the repair mechanism (known as the destructive mechanism), is formulated as a superposition of pure-birth stochastic processes (Yule processes). The proposed model deals with combined modeling of long-term effects (cure rate) and short-term effects (tumor growth) which can be regarded as a Bayesian alternative to the Cox regression and promotion cure rate models when the proportional hazards assumption is violated, such as in the case of crossing survival functions. A simulation study and an application to a melanoma data, using the Bayesian RStan package, are provided to illustrate the usefulness of the proposed model and also to evaluate the impact of cancer treatment over the long-term effect and the progression stage of the tumor (tumor growth). Besides this interesting new biological interpretation of the tumor growth, the model can be viewed as an extended Bayesian version of the destructive cure rate model of Rodrigues et al. and an alternative to the two-sample semiparametric model of Yang and Prentice.