Recovering individual-level spatial inference from aggregated binary data
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Binary regression models are commonly used in disciplines such as epidemiology and ecology to determine how spatial covariates influence individuals. In many studies, binary data are shared in a spatially aggregated form to protect privacy. For example, rather than reporting the location and result for each individual that was tested for a disease, researchers may report that geopolitical units were either free or not free from the disease. Often, the spatial aggregation process obscures the values of response variables, spatial covariates, and locations of each individual, which makes recovering individual-level inference diffcult. We show that applying a series of transformations, including a change of support, to a bivariate point process model allows researchers to recover individual-level inference for spatial covariates from spatially aggregated binary data. The series of transformations preserves the convenient interpretation of desired binary regression models that are commonly applied to individual-level data. Using a simulation experiment, we compare the performance of our proposed method applied under varying types of spatial aggregation against the performance of standard approaches using the original individual-level data. We illustrate our method by modeling individual-level disease risk in a population using a data set that has been aggregated for privacy protection. Our simulation experiment and data illustration demonstrate the utility of the proposed method when access to original unprotected data is impractical or prohibited.
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