PubMed2004
The simplest way to study the spatial pattern of a disease is the geographical representation of its cases (or some indicators of them) over a map. Maps based on raw data are generally "wrong" since they do not take into consideration for sampling errors. Indeed, the observed differences between areas (or points in the map) are not directly interpretable, as they derive from the composition of true, structural differences and of the noise deriving from the sampling process. This problem is well known in human epidemiology, and several solutions have been proposed to filter the signal from the noise. These statistical methods are usually referred to as Disease Mapping. In geographical analysis a first goal is to evaluate the statistical significance of the heterogeneity between areas (or points). If the test indicates rejection of the hypothesis of homogeneity the following task is to study the spatial pattern of the disease. The spatial variability of risk is usually decomposed into two terms: a spatially structured (clustering) and a non spatially structured (heterogeneity) one. The heterogeneity term reflects spatial variability due to intrinsic characteristics of the sampling units (e.g. igienic conditions of farms), while the clustering term models the association due to proximity between sampling units, that usually depends on ecological conditions that vary over the study area and that affect in similar way breedings that are close to each other. Hierarchical bayesian models are the main tool to make inference over the clustering and heterogeneity components. The results are based on the marginal posterior distributions of the parameters of the model, that are approximated by Monte Carlo Markov Chain methods. Different models can be defined depending on the terms that are considered, namely a model with only the clustering term, a model with only the heterogeneity term and a model where both are included. Model selection criteria based on a compromise between degree of complexity and goodness of fit are then needed to discriminate among them, because each specification has a different biological meaning. Our aim is to demonstrate that these techniques can be used to study the geographical distribution of a parasite infection. Our analyses are based on data collected in 142 farms of the province of Latina. In each breeding a fixed number of sheeps has been sampled (20) and checked for the presence of C. daubneyi. We have specified a Binomial model for the proportion of infected animals in each breeding. The heterogeneity component is modelled in a standard way, while we have used different prior specifications for the clustering term to show how they affect the results. When we use the usual specification also for clustering, the two models show a completely different spatial pattern of infection, probably because the intrinsic spatial structure of the clustering term tend to bias our inferences. The selection criterion indicates in this case the heterogeneity model as the "best" one. However, if we modify the prior so that a lower degree of spatial interaction is assumed, the clustering model is less complex and its goodness of fit better and it should be preferred.