A hierarchical Bayesian approach to age-specific back-calculation of cancer incidence rates.

We propose a Bayesian hierarchical model to estimate age-specific cancer incidence per year from age-specific cancer mortality. The model is based upon the empirical Bayesian approach of Liao and Brookmeyer (1995) and extends that model by consideration of the dependence on age. The incident cases per year are considered as observations from a discrete-time stochastic process following an autoregressive structure within a Poisson regression model. The model assumes that the survival probability among those with cancer is known. We have investigated the sensitivity of the model to the choice of this distribution and have found that this is the most sensitive part of the model. By comparison the predictions of the model are relatively robust to changes in other key areas, such as the number of years an incident case contributes before death, assumptions about parameter equality for identification and the initial prior distributions. The proposed methodology has been investigated using lung cancer mortality data from Scotland. Parameter estimates were obtained through Markov chain Monte Carlo methods, implemented using BUGS.