- Unrealistic geographical assumptions: The mapping either assumes that the subjects are evenly distributed across the areal unit or all are concentrated on one point, e.g., the centroid of the polygon ; and
- Unidentifiable spatial uncertainty: While it is a known fact that data aggregation causes spatial uncertainty due to location imprecision (use a polygon to represent a point) and inaccuracy (use the polygon centroid to represent all locations in the polygon), with a conventional polygon map, there is no effective way to estimate, represent, and present this uncertainty [18,19].
- In the previous studies, this method was employed to deal with the situation that the location data is a mixture of point-level and polygon-level data (typically P.O. Box numbers), in which the primary function of RCMC is to disaggregate the polygon-level portion to make them compatible with the point-level data, so that the following disease mapping process (e.g., kernel density estimation or KDE) can be applied. In this study, we further pushed this method to the situation that the data are entirely aggregate in the first place, which is more common in disease mapping practice. By doing this, conceptually we took this method as a general approach to incorporating auxiliary information (e.g., detailed background population data) for the purpose of improving and evaluating spatial certainty of the data used for disease mapping, as well as mitigating the problems associated with mapping based on irregularly defined large areal units.
- In previous studies, the RCMC method was applied to a disease (lung cancer) that has a broad cohort (i.e., not limited to a specific category in population), and therefore the background data (expected count) were able to be directly derived from the data of general population and represented as raster. Technically, in those studies the RCMC for disease cases and the following KDE were directly run over the raster backgrounds. Differently, the diseases we addressed in this study, birth defects, have a very specific cohort (infants) rather than general population. The location data of cohort are also aggregate and need to be disaggregated through RCMC. The disaggregation of disease cases and the following KDE need to be based on the disaggregated cohort locations, instead of directly on the general population (or its derivatives). In other words, instead of the case-background two-level structure in the previous studies, in this study we were dealing with a case-cohort-population three-level hierarchy. The extra layer of cohort brings about a great complexity to the implementation of the RCMC method.
2.1. Birth Defect Data and All-Birth Data
|Age||BD Infants||All Births||Ratio|
2.2. Spatially Detailed Population Data
3.2. Intensity Estimation
3.3. Statistical Significance and Spatial Uncertainty
5. Discussion and Conclusions
- The disaggregation allows analytical processes designed for individual data to be applied, which avoids or mitigates the problems associated with aggregate data.
- The resulting raster maps have resolutions at the pixel level (100 m in this study), which presents more detailed spatial distribution of disease, compared with the conventional polygon map. Those details give the raster maps advantage in detecting spatial associations between birth defects and certain environmental factors.
- The RCMC process maximizes the use of available spatial information. First of all, restricting the randomization with the smallest aggregate units maximizes the use of the spatial information represented by the polygon. Furthermore, controlling the randomization with the background data layer provides an open mechanism ready to take into account any available information that can help reduce spatial uncertainty and improve analysis quality. In this study, the background data layer of females in a certain age category eventually incorporates rich information from different sources, including the total number of people from the LandScan data and age and sex information from the Census data. The LandScan data are a product of a sophisticated model that incorporates information about population, land use, terrain, night lights, traffic, and others [39,40]. Other information, if available, can find its way into the background layer used by RCMC. For example, if a socioeconomic factor is known to be a confounding factor of a disease, and detailed information about its spatial distribution is available, it can be incorporated into the background layer.
- The RCMC process explicitly quantifies the spatial uncertainty caused by data aggregation. Little, if any, information about the spatial uncertainty in a polygon map can be conveyed to the user of the map. RCMC resolves this problem by running the randomization iteration many times. The variance in the results from these iterations represents the uncertainty caused by aggregation, which can be explicitly and easily quantified. Essentially, this is an approach based on the idea of sensitivity analysis that empirically models variance through intensive computation.
Conflicts of Interest
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