In environmental epidemiology, long lists of relative risk estimates from exposed populations are compared to a reference to scrutinize the dataset for extremes. Here, inference on disease profiles for given areas, or for fixed disease population signatures, are of interest and summaries can be obtained averaging over areas or diseases. We have developed a multivariate hierarchical Bayesian approach to estimate posterior rank distributions and we show how to produce league tables of ranks with credibility intervals useful to address the above mentioned inferential problems. Applying the procedure to a real dataset from the report "Environment and Health in Sardinia (Italy)" we selected 18 areas characterized by high environmental pressure for industrial, mining or military activities investigated for 29 causes of deaths among male residents. Ranking diseases highlighted the increased burdens of neoplastic (cancerous), and non-neoplastic respiratory diseases in the heavily polluted area of Portoscuso. The averaged ranks by disease over areas showed lung cancer among the three highest positions.