This article is about the effects of adjusting observed rates to account for the impact that small-sample noise might have on estimated risk and its related spatial patterns. Spatial artifacts are defined as those cases where a spurious spatial pattern is identified even when the inferences are based on the correct model.

The authors use county level data (277 counties) for home radon levels in the mid-Atlantic region of the U.S. They examine the artifacts created assuming that the hierarchical normal model was the true model, using a within and between county standard deviations of 1.0 and 0.7. In addition, a Poisson/log normal model is estimated for ten-year kidney/uter cancer rates in counties in the U.S. From these data, the authors define a true distribution of cancer rates by assuming that underlying risk follows a Gamma distribution. Then the observed rate is drawn from a Poisson distribution for each county.

This article suggests that many of the spatial patterns seen in Bayes-smoothed cancer rates are artifacts. This article shows that the artifacts seen in the maps of posterior risk depend on the sample sizes of each county and the distribution of the county rates. Maps based on observed rates are shown to overemphasize counties with small population as maps based on posterior estimates are observed to highlight counties with larger populations.

The authors suggest a method for avoiding mapping artifacts by creating multiple imputed maps from the posterior distribution. A multiple imputation would generate several maps of the posterior risk, with each map corresponding to a different draw of the vector of county underlying rate parameters.

Three additional models are considered: One accounting for uncertainty in the hyperparameters of the distribution of the observed rates; a second one that adds regression predictors, and finally spatial modeling. The authors recognize that the advantages of multiple imputations are limited to exploratory analysis and modeling checking but no real solution is given for generating maps for presenting research results.

Last updated March 9, 2006