Keywords: Bayesian hierarchical models, shrinkage estimation, subgroup analysis
Sample estimates of treatment effects across regions tend to have too much variation relative to the true underlying treatment effects, hampering interpretation. Bayesian hierarchical modeling addresses this unwanted variation. When considered exchangeable in a one-way hierarchical structure, the estimated treatment effects across regions have posterior means that shrink the sample estimates toward the overall estimate. The amount of shrinkage increases as the variation between relative to within the regions decreases. Because the shrinkage estimates borrow strength from the overall estimate, Bayesian subgroup analysis is more precise than separate analyses of the sample treatment effects. An example will be provided using shrinkage estimation over regions.