Adjusting for sampling variability in sparse data: geostatistical approaches to disease mapping

Disease maps of crude rates from routinely collected health data indexed at a small geographical resolution pose specific statistical problems due to the sparse nature of the data. Spatial smoothers allow areas to borrow strength from neighboring regions to produce a more stable estimate of the areal value. Geostatistical smoothers are able to quantify the uncertainty in smoothed rate estimates without a high computational burden. In this paper, we introduce a uniform model extension of Bayesian Maximum Entropy (UMBME) and compare its performance to that of Poisson kriging in measures of smoothing strength and estimation accuracy as applied to simulated data and the real data example of HIV infection in North Carolina. The aim is to produce more reliable maps of disease rates in small areas to improve identification of spatial trends at the local level.

In all data environments, Poisson kriging exhibited greater smoothing strength than UMBME. With the simulated data where the true latent rate of infection was known, Poisson kriging resulted in greater estimation accuracy with data that displayed low spatial autocorrelation, while UMBME provided more accurate estimators with data that displayed higher spatial autocorrelation. With the HIV data, UMBME performed slightly better than Poisson kriging in cross-validatory predictive checks, with both models performing better than the observed data model with no smoothing.

Smoothing methods have different advantages depending upon both internal model assumptions that affect smoothing strength and external data environments, such as spatial correlation of the observed data. Further model comparisons in different data environments are required to provide public health practitioners with guidelines needed in choosing the most appropriate smoothing method for their particular health dataset.