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Disease mapping studies have been widely performed at univariate level, that is considering only one disease in the estimated models. Nonetheless, simultaneous modelling of different diseases can be a valuable tool both from the epidemiological and from the statistical point of view. In this paper we propose a model for multivariate disease mapping that generalizes the univariate conditional auto-regressive distribution. The proposed model is proven to be an effective alternative to existing multivariate models, mainly because it overcome some restrictive hypotheses underlying models previously proposed in this context. Model performances are checked via a simulation study and via application to a case study.

Lactobacillus helveticus is a homofermentative thermophilic lactic acid bacterium used extensively for manufacturing Swiss type and aged Italian cheese. In this study, the phenotypic and genotypic diversity of strains isolated from different natural dairy starter cultures used for Grana Padano, Parmigiano Reggiano, and Provolone cheeses was investigated by a classification tree technique. A data set was used that consists of 119 L. helveticus strains, each of which was studied for its physiological characters, as well as surface protein profiles and hybridization with a species-specific DNA probe. The methodology employed in this work allowed the strains to be grouped into terminal nodes without difficult and subjective interpretation. In particular, good discrimination was obtained between L. helveticus strains isolated, respectively, from Grana Padano and from Provolone natural whey starter cultures. The method used in this work allowed identification of the main characteristics that permit discrimination of biotypes. In order to understand what kind of genes could code for phenotypes of technological relevance, evidence that specific DNA sequences are present only in particular biotypes may be of great interest.

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