A Stabilized Kriging Method for Mapping Disease Rates

Mapping disease rates is an important aspect of epidemiological research because it helps inform public health policy. Disease maps are often drawn according to local administrative areas (LAAs), such as counties, cities, or towns. In LAAs with small populations, disease rates are unstable and are prone to appear extremely high or low. The empirical Bayes methods consider variance differences among different LAAs, thereby stabilizing the disease rates. The methods of kriging break the constraints of geopolitical boundaries and produce a smooth curved surface in the form of contour lines, but the methods lack the stabilizing effect of the empirical Bayes methods.

An easy-to-implement stabilized kriging method is proposed to map disease rates, which allows different errors in different LAAs.

Monte Carlo simulations revealed that the stabilized kriging method had smaller symmetric mean absolute percentage error than three other types of methods (the original LAA-based method, empirical Bayes methods, and traditional kriging methods) in nearly all scenarios considered. Real-world data analysis of oral cancer incidence rates in men from Taiwan demonstrated that the age-standardized rates in the central mountainous sparsely-populated region of Taiwan were stabilized using our proposed method, with no more large differences in numerical values, whereas the rates in other populous regions were not over-smoothed. Additionally, the stabilized kriging map had improved resolution and helped locate several hot and cold spots in the incidence rates of oral cancer.

We recommend the use of the stabilized kriging method for mapping disease rates.