Bayesian semi-parametric ZIP models with space-time interactions: an application to cancer registry data.

We analyse lymphoid leukemia incidence data collected between 1988 and 2002 from the cancer registry of Haut-Rhin, a region in north-east France. For each patient, sex, area of residence, date of birth and date of diagnosis are available. Incidence summaries in the registry are grouped by 3-year periods. A disproportionately large frequency of zeros in the data leads to a lack of fit for Poisson models of relative risk. The aim of our analysis was to model the spatio-temporal variations of the disease taking into account some non-standard requirements, such as count data with many zeros and space-time interactions. For this purpose, we consider a flexible zero-inflated Poisson model for semi-parametric regression which incorporates space-time interactions (modelled by means of varying coefficient model) using an extension of the methodology proposed in Fahrmeir & Osuna (2006, Structured additive regression for overdispersed and zero-inflated count data. Stoc. Models Bus. Ind., 22, 351-369). Inference is carried out from a Bayesian perspective using Markov chain Monte Carlo methods by means of the BayesX software. Our analysis of the geographical distribution of the disease and its evolution in time may be considered as a starting point for further studies.