Investigating modelling approaches to deal with small numbers and missing values in disease mapping

In this thesis we have presented results from a simulated data set based on the 1997 Belgian Health Interview Survey. The aim was to describe the distribution of the disease with respect to the place of occurrence. Several methods in the Bayesian framework have been considered. We have shown in these results that basing our conclusion on the SMRs alone to describe the disease risk may prove inadequate.

Bayesian smoothing methods bring a good flavour into our results. While the Poisson- Gamma and Poisson-Lognormal models seem to do quite well in removing the data random variability due to small counts, their results are not as appealing as when we incorporate the spatial correlation in the BMY and CAR models. Based on these latter models (BMY and CAR), we can single out Nijvem, Charleroi, Brussels, Marche-en-Femenne and Brugge as areas with high risk, while Diksmuide and Maaseik as low risk areas.

Through a sensitivity analysis on the missing expected counts, the results show that the Poisson-Gamma and the Poisson-Lognormal give poor predictions of the imputed disease risks. On the other hand, the imputed disease risks based on the Conditional Autoregressive model seem to be pretty good. This is attributed to fact that in the Poisson-Gamma and Poisson-Lognormal models we do not take spatial correlation into account, as is the case with CAR model. This is quite an important finding since the imputation seems not to depend only on the mean structure, but also on the correlation structure.

We can conclude from all these findings that Bayesian smoothing and the incorporation of spatial correlation in modeling the geographical distribution of the disease risk are very important aspects.