Estimating cancer incidence using a Bayesian back-calculation approach.

We propose a Bayesian hierarchical model for the calculation of incidence counts from mortality data by a convolution equation that expresses mortality through its relationship with incidence and the survival probability density. The basic idea is to use mortality data together with an estimate of the survival distribution from cancer incidence to cancer mortality to reconstruct the numbers of individuals who constitute previously incident cases that give rise to the observed pattern of cancer mortality. This model is novel because it takes into account the uncertainty from the survival distribution; thus, a Bayesian-mixture cure model for survival is introduced. Furthermore, projections are obtained starting from a Bayesian age-period-cohort model. The main advantage of the proposed approach is its consideration of the three components of the model: the convolution equation, the survival mixture cure model and the age-period-cohort projection within a directed acyclic graph model. Furthermore, the estimation are obtained through the Gibbs sampler. We applied the model to cases of women with stomach cancer using six age classes [15-45], [45-55], [55-65], [65-75], [75-85] and [85-95] and validated it by using data from the Tuscany Cancer Registry. The model proposed and the program implemented are convenient because they allow different cancer disease to be analysed because the survival time is modelled by flexible distributions that are able to describe different trends.