Testing for unusual aggregation of health risk in semiparametric models

We present a method for surface estimation over some area of interest using spatial multilevel semiparametric models, in which the spatial correlation is modeled through splines with random coefficients associated with a set of knots. Multiple sets of random effects are associated with partitions of the entire area of interest that allow flexibility for testing unusual rates within sub-regions of larger areas. To test departures from the null value of no unusual rates, we derive a score-based test statistic, partially by using some of the results available for singular information problems. The test is robust in that it does not require specifying the joint distribution of the random effect. In an extensive simulation study this overall general test shows correct levels, and it is highly sensitive to clustering across all the scenarios considered. Once a departure is detected, a second, finer grid of knots can be superimposed on the existing grid, and the proposed procedure can be applied to test the homogeneity within two or more sub-areas. The proposed model is applied to lung cancer deaths in South Carolina in the year 2000 and to data on airborne mercury in vegetation around a solid waste incinerator in Oxford, New Jersey.