All analyses of spatially aggregated data are vulnerable to the modifiable areal unit problem (MAUP), which describes the sensitivity of analytical results to the arbitrary choice of spatial aggregation unit at which data are measured. The MAUP is a serious problem endemic to analyses of spatially aggregated data in all scientific disciplines. However, the impact of the MAUP is rarely considered, perhaps partly because it is still widely considered to be unsolvable. It was originally understood that a solution to the MAUP should constitute a comprehensive statistical framework describing the regularities in estimates of association observed at different combinations of spatial scale and zonation. Additionally, it has been debated how such a solution should incorporate the geographical characteristics of areal units (e.g. shape, size, and configuration), and in particular whether this can be achieved in a purely mathematical framework (i.e. independent of areal units). We argue that the consideration of areal units must form part of a solution to the MAUP, since the MAUP only manifests in their presence. Thus, we present a theoretical and statistical framework that incorporates the characteristics of areal units by combining estimates obtained from different scales and zonations. We show that associations estimated at scales larger than a minimal geographical unit of analysis are systematically biased from a true minimal-level effect, with different zonations generating uniquely biased estimates. Therefore, it is fundamentally erroneous to infer conclusions based on data that are spatially aggregated beyond the minimal level. Instead, researchers should measure and display information, estimate effects, and infer conclusions at the smallest possible meaningful geographical scale. The framework we develop facilitates this. The proposed framework represents a new minimum standard in the estimation of associations using spatially aggregated data, and a reference point against which previous findings and misconceptions related to the MAUP can be understood.

Background: In disease mapping, fine-resolution spatial health data are routinely aggregated for various reasons, for example to protect privacy. Usually, such aggregation occurs only once, resulting in ‘single-aggregation disease maps’ whose representation of the underlying data depends on the chosen set of aggregation units. This dependence is described by the modifiable areal unit problem (MAUP). Despite an extensive literature, in practice, the MAUP is rarely acknowledged, including in disease mapping. Further, despite single-aggregation disease maps being widely relied upon to guide distribution of healthcare resources, potential inefficiencies arising due to the impact of the MAUP on such maps have not previously been investigated. Results: We introduce the overlay aggregation method (OAM) for disease mapping. This method avoids dependence on any single set of aggregate-level mapping units through incorporating information from many different sets. We characterise OAM as a novel smoothing technique and show how its use results in potentially dramatic improvements in resource allocation efficiency over single-aggregation maps. We demonstrate these findings in a simulation context and through applying OAM to a real-world dataset: ischaemic stroke hospital admissions in Perth, Western Australia, in 2016. Conclusions: The ongoing, widespread lack of acknowledgement of the MAUP in disease mapping suggests that unawareness of its impact is extensive or that impact is underestimated. Routine implementation of OAM can help avoid resource allocation inefficiencies associated with this phenomenon. Our findings have immediate worldwide implications wherever single-aggregation disease maps are used to guide health policy planning and service delivery.

Drought is thought to impact upon the mental health of agricultural communities, but studies of this relationship have reported inconsistent results. A source of inconsistency could be the aggregation of data by a single spatiotemporal unit of analysis, which induces the modifiable areal and temporal unit problems. To investigate this, mental health-related emergency department (MHED) presentations among residents of the Wheat Belt region of Western Australia, between 2002 and 2017, were examined. Average daily rainfall was used as a measure of drought. Associations between MHED presentations and rainfall were estimated based on various spatial aggregations of underlying data, at multiple temporal windows. Wide variation amongst results was observed. Despite this, two key features were found: Associations between MHED presentations and rainfall were generally positive when rainfall was measured in summer months (rate ratios up to 1.05 per 0.5 mm of daily rainfall) and generally negative when rainfall was measured in winter months (rate ratios as low as 0.96 per 0.5 mm of daily rainfall). These results demonstrate that the association between drought and mental health is quantifiable; however, the effect size is small and varies depending on the spatial and temporal arrangement of the underlying data. To improve understanding of this association, more studies should be undertaken with longer time spans and examining specific mental health outcomes, using a wide variety of spatiotemporal units.