This article discusses and extends statistical models to jointly analyse the spatial variation of rates of several diseases with common risk factors. We start with a review of methods for separate analyses of diseases, then move to ecological regression approaches, where the rates from one of the diseases enter as surrogate covariates for exposure. Finally, we propose a general framework for jointly modelling the variation of two or more diseases, some of which share latent spatial fields, but with possibly different risk gradients. In our application, we consider mortality data on oral, oesophagus, larynx and lung cancers for males in Germany, which all share smoking as a common risk factor. Furthermore, the first three cancers are also known to be related to excessive alcohol consumption. An empirical comparison of the different models based on a formal model criterion as well as on the posterior precision of the relative risk estimates strongly suggests that the joint modelling approach is a useful and valuable extension over individual analyses.
SUMMARYUsing data from a cohort study conducted by the Veterinary Laboratories Agency (VLA), evidence of spatial clustering at distances up to 30 km was found for S. Agama and S. Dublin (P values of 0 . 001) and borderline evidence was found for spatial clustering of S. Typhimurium (P=0 . 077). The evolution of infection status of study farms over time was modelled using a Markov Chain model with transition probabilities describing changes in status at each of four visits, allowing for the effect of sampling visit. The degree of geographical clustering of infection, having allowed for temporal effects, was assessed by comparing the residual deviance from a model including a measure of recent neighbourhood infection levels with one excluding this variable. The number of cases arising within a defined distance and time period of an index case was higher than expected. This provides evidence for spatial and spatio-temporal clustering, which suggests either a contagious process (e.g. through direct or indirect farm-to-farm transmission) or geographically localized environmental and/or farm factors which increase the risk of infection. The results emphasize the different epidemiology of the three Salmonella serovars investigated.
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