How does Poisson kriging compare to the popular BYM model for mapping disease risks?

Background: Geostatistical techniques are now available to account for spatially varying population sizes and spatial patterns in the mapping of disease rates. At first glance, Poisson kriging represents an attractive alternative to increasingly popular Bayesian spatial models in that: 1) it is easier to implement and less CPU intensive, and 2) it accounts for the size and shape of geographical units, avoiding the limitations of conditional auto-regressive (CAR) models commonly used in Bayesian algorithms while allowing for the creation of isopleth risk maps. Both approaches, however, have never been compared in simulation studies, and there is a need to better understand their merits in terms of accuracy and precision of disease risk estimates. Results: Besag, York and Mollie's (BYM) model and Poisson kriging (point and area-to-area implementations) were applied to age- adjusted lung and cervix cancer mortality rates recorded for white females in two contrasted county geographies: 1) state of Indiana that consists of 92 counties of fairly similar size and shape, and 2) four states in the Western US (Arizona, California, Nevada and Utah) forming a set of 118 counties that are vastly different geographical units. The spatial support (i.e. point versus area) has a much smaller impact on the results than the statistical methodology (i.e. geostatistical versus Bayesian models). Differences between methods are particularly pronounced in the Western US dataset: BYM model yields smoother risk surface and prediction variance that changes mainly as a function of the predicted risk, while the Poisson kriging variance increases in large sparsely populated counties. Simulation studies showed that the geostatistical approach yields smaller prediction errors, more precise and accurate probability intervals, and allows a better discrimination between counties with high and low mortality risks. The benefit of area-to-area Poisson kriging increases as the county geography becomes more heterogeneous and when data beyond the adjacent counties are used in the estimation. The trade-off cost for the easier implementation of point Poisson kriging is slightly larger kriging variances, which reduces the precision of the model of uncertainty. Conclusion: Bayesian spatial models are increasingly used by public health officials to map mortality risk from observed rates, a preliminary step towards the identification of areas of excess. More attention should however be paid to the spatial and distributional assumptions underlying the popular BYM model. Poisson kriging offers more flexibility in modeling the spatial structure of the risk and generates less smoothing, reducing the likelihood of missing areas of high risk.