Effective analysis of spatially and temporally structured health outcome data requires stabilization of estimated disease rates or relative risks in small areas while retaining sufficient geographic resolution for conducting health assessments, informing health policy and drawing informative maps. These goals require an appropriate sampling model, an accounting for covariate effects and an accounting for spatio-temporal correlation. Hierarchical Bayesian models have proven very effective in accomplishing these goals. Stabilization results from Bayesian "borrowing information'' from other regions, usually with relatively higher weight given to nearby regions via a prior distribution that includes spatial correlation.

Generally, the posterior mean is used to estimate region-specific values and these are used as input to a variety of assessments. However, the histogram or empirical distribution function (EDF) of the posterior means is underdispersed and never valid. Therefore, to compare distributions (among states or over time) or to estimate the number of values above a threshold, an alternative to the posterior mean is needed. Furthermore, the ranks of region-specific values prioritize environmental assessments and ranking posterior means can be inappropriate. Hierarchical Bayesian models structure addressing the three goals and produce summaries which properly account for all uncertainties.

Though no set of values can be optimal for estimating individual values, the histogram and ranks; communication and credibility will be enhanced by reporting a single set of estimates with good performance for all three. This presentation uses a case study of county-specific lip cancer relative risk in Scotland to motivate the three goals, show how Bayesian modeling structures an assessment and propose a "triple goal" approach. We estimate covariate regression slopes, county-specific relative risks, their EDF and ranks and discuss the influence of the prior distribution