A spatial obesity risk score for describing the obesogenic environment using kernel density estimation: development and parameter variation

We describe the general strategy of obesity risk score estimation, which consists of several steps, by applying it to two regions in Bavaria, Germany. First, we chose our study area and downloaded POIs related to obesogenic environmental factors (cf. [18]). Second, the data were processed to adjust for some imprecisions and minimize redundancy, e.g., we adapted the coordinate units to represent the same length. Third, we analyzed the spatial heterogeneity of the study area and inspected the study area visually to get first insights regarding the distribution of POIs. Fourth, we presented the basic risk score estimation approach, as well as a deterministic sensitivity analysis, in which a spatial POI resampling approach was integrated. This approach made it finally possible in a last step to evaluate the deterministic parameter selection via the ANOVA F statistic. An overview of the risk score estimation process is shown in Fig. 1. Further details regarding each step are given below.

We based our analysis on the overall obesogenic and protective environmental factors identified in our previous study [18]. The list of chosen variables for the score was derived via an extensive literature review, i.e., previous work by Mackenbach et al. [10], Jia et al. [21], and enriched with our own further searches.

We chose two areas in the south of Bavaria, Germany, to illustrate our approach and develop the SORS. Our aim was to base the geographical analysis on different levels of urbanity. The first area was the city of Augsburg with about 300,000 inhabitants covering an area of 147 km². A more rural region, the town of Meitingen with 11,000 inhabitants and a size of 30 km² lying 20 km north of Augsburg, was chosen as the second area. Information on these regions was available from the German Federal Statistical Office [22]. We selected the region around the city of Augsburg, as it is well known within obesity- and diabetes-related research [23].

Spatial POIs related to the selected variables, such as fast food restaurants and parks (compare Additional file 1), were downloaded from OSM using the online data filtering tool Overpass turbo [24]. Data regarding the area borders of Augsburg and Meitingen were downloaded in shape file format from a geographic online portal provided by the Bavarian government [25]. We directly downloaded maps intended for graphical visualization of results from the OSM web page [26]. Additional file 2 contains further information regarding data download.

The downloaded GeoJSON files contained information on each POI regarding name, type of obesity-related environmental factor, spatial coordinates in latitude and longitude format, and other characteristics such as opening hours and street addresses. The relevant information, i.e., name, coordinates, and type of environmental factor, was extracted for each spatial POI and processed into lists and data frames. Table A1 of Additional file 1 gives an overview of the downloaded and processed variables from OSM.

As a further pre-processing step, we introduced a synthetic origin to the south-west of both study areas and adapted the length of a longitudinal coordinate unit to the length of a latitudinal coordinate unit. The schematic structure after the introduction of the origin and the coordinate adaptation is shown in Table 1. The single bus stops were reduced from POIs to centroids of dense regions of bus stops. Further details regarding these additional pre-processing steps can be found within Additional file 2.

Ripley’s K function was calculated for the unweighted obesogenic and protective POIs separately to describe the spatial inhomogeneity of the two study areas. The K function is a second-order moment function that is based on the variance of the radial interpoint distance r around each POI [28]. It compares the cumulative number of actual POIs with the number of expected POIs under random distribution assumption [29]. This random comparison process is realized via the Poisson process, which has a K value of r²π [30]. K functions lying above the K values of a random process therefore represent clustered patterns, whereas smaller values indicate regular processes [31]. We examined the spatial inhomogeneity to investigate ex ante whether clusters are expected to occur in our subsequent POI analysis. The isotropic edge correction, which is a method based on weighting of the POIs according to the probability of their next neighbors being within the study area, was applied to the K function [32]. In order to test whether the K functions of the POIs were significantly different from the K function of a random point pattern, we estimated bootstrap confidence bands around the K functions of the POIs based on the method of Loh with 1000 simulations [33].

In order to visualize the spatial distribution of the POIs, we created KDEs separately for positive and negative spatial data points [34]. These density layers were superimposed and shown together on a single map. Within this process, we defined certain parameter choices as the base case, which were then changed as part of the sensitivity analysis in a later step.

We estimated the SORS based on the integration of obesogenic and protective kernel densities into a combined score. The aim of KDE is to provide a smooth and continuous estimation of the accumulation of spatial data points based on a sliding window technique. The geographic plane is represented by two dimensions and the estimated densities account for a third dimension, which thus leads to a three-dimensional mountainous structure, a so-called “risk surface”. To visualize this structure on a map, the level of the density coordinate can be plotted by contour lines or via coloring [35]. An overview of this method is provided by Hastie et al., for example, as well as by King et al. [36, 37].

To estimate risk score values, several steps have been performed. First, the positive spatial data points were included into a single positive spatial data layer. Analogously, the negative spatial data points were integrated into a data layer. Second, an observation window together with a grid of suitable size was set up and laid on the respective study area. For each of the following calculations, the same grid was used. Third, KDEs were performed to generate a risk surface based only on positive environmental factors and a second risk surface based only on negative environmental factors. Following this process, a density value based on positive factors and a value based on negative factors were generated at each grid point. Fourth, these positive and negative estimates were set against each other by taking the difference, which results in the final score values at the grid points [34]. Finally, to determine the risk value at the exact desired spatial location, interpolation methods were applied.

The procedure described above implies several parameter choices within its different steps. We tested alternative values for five of these parameters: bandwidth, edge correction, number of grid points, interpolation method, and an alternative weighting scheme (see overview in Table 2). For each given parameter variation, the remaining KDE parameters were set to their base case values (see also Table 2). Further explanations regarding the parameters are provided below.

Uncertainty concerning POIs was integrated into density score estimations via a spatial bootstrapping method. We generated 1000 bootstrap samples for the positive and 1000 bootstrap samples for the negative environmental POIs at random with replacement. For each of the samples, the parameter variation described above was executed. This made it possible to integrate probabilistic variation of POIs into SORS value estimation for each deterministic scenario. These uncertainty estimates were used for the calculation of the ANOVA F statistic, which we applied to compare the deterministic sensitivity scenarios for a given parameter. We describe further details regarding the sampling process in Additional file 2.

A random sample (N = 50) of spatial data points (evaluation points, EPs) was drawn from each of the two areas for which we calculated and compared risk score results across the scenarios defined above. Our aim was to develop a robust and stable score that accounts for uncertainty and exhibits discriminatory power. To describe how much the choice of parameter values influences the discrimination of data points with low and high risk, we performed analysis of variance (ANOVA) between all 50 EPs based on their bootstrap replications. Thus, for each EP, 1000 bootstrap replicates of the SORS constituted an ANOVA group of estimates for a given parameter scenario. We calculated the F statistic in order to determine the degree of separation between the 50 groups of estimates with higher F values indicating higher degrees of separation. Therefore, the highest value of the F statistic within a given parameter variation analysis in this sense indicates the best result. The relative influence of the parameters on model results is estimated based on a normalization of the F statistic values. The algorithm used to implement deterministic and probabilistic analysis is shown in Fig. 2. Finally, we created heat maps based on the risk score estimates of the base case. For this purpose, the KDE values were again transferred back to the original map dimensions that were used in the pre-visualization step. To compare this base case risk map to an alternative visualization using a common geographical methodology, we estimated an inhomogeneous cluster point process with polynomial trend of degree two for positive and negative POIs that is designed to provide similar cluster structures compared to our KDE approach. Subsequently, we derived intensities for risk score plotting in a comparable way as it was done for the kernel density approach, i.e., via setting off the surfaces. We tested several point process types, such as “Thomas” and MatClust”, and chose the model with the best fit based on the Akaike Information Criterion [43]. The code for data download, data processing, and analysis of the scenarios defined above can be found in the supplementary information.

The spatial POIs were processed and analyzed using R version 4.0.2 [44]. For graphical visualization, R packages “ggplot2” [45], “graphics” [44], and “fields” [40] were used. We applied the “spatstat” [46] package to estimate Ripley’s K function and the bootstrap confidence bands around it. For KDEs, the packages “MASS” [47] and “sparr” [39] were chosen. Spatial data objects were built and handled via the packages “rgdal” [48], “geojsonR” [49], “prob” [50], and “spatstat” [46]. For interpolation and for the generation of risk score maps, the packages “fields” [40] and “gstat” [51] were used. To plot spatial objects on maps, we used the package “png” [52]. Finally, the DBSCAN algorithm was applied using the package “dbscan” [53].

The upper part of Fig. 3 shows estimates of Ripley’s K function for Augsburg, separately for the obesogenic and the protective POIs. The point pattern for Augsburg was significantly clustered, as the lower confidence bands of the K functions lay above the random Poisson processes for each interpoint distance r, which means that the actual number of POIs within a distance r was greater than the number of expected POIs under random distribution assumptions [31]. This underlined the importance of subsequent KDE analysis, as the spatial pattern was suitable for clustering tasks. Estimates of the obesogenic and the protective K functions for Meitingen also revealed significantly clustered patterns, as the lower confidence bands lay above the random pattern for all or at least for several interpoint distances r, which is shown in the bottom part of Fig. 3.

The separate obesogenic and protective risk surfaces are shown in Fig. 4 for Augsburg and Meitingen. The obesogenic and protective kernel densities for Augsburg accumulated within a region lying to the northwest within the city boundaries, whereas the eastern and the southern areas showed no dense region. In contrast, kernel densities for Meitingen showed several dense regions outside the town borders.

The final set of randomly chosen EPs for the evaluation of the risk score for Augsburg (N = 50) and Meitingen (N = 50) is presented in Fig. 5. As seen within the graphics, the sample points generated via the random drawing process inside the study areas widely covered the respective regions under consideration.

Table 3 summarizes the values of the ANOVA F statistic for each scenario of base case and deterministic sensitivity analysis. The higher the F statistic for a given parameter variation, the higher the degree of separation between the sample point groups, and thus higher values were more preferable. Values of the F statistic for Augsburg and Meitingen increased with the amount of bandwidth for the first three scenarios. This trend continued for Meitingen with decreasing slope, whereas it showed a rather inverted u-shaped functional behavior for Augsburg. Regarding edge correction for Augsburg and Meitingen, increasing the study area to some degree led to the highest F statistic, but this effect was not permanently observed with increasing amounts of edge correction. For Augsburg, the second grid point scenario was preferred according to the ANOVA value, in contrast to Meitingen, for which the base case was preferred. Furthermore, the inverse distance weighting had the highest F value in Meitingen and Augsburg,. Finally, the second weighting scenario had a higher F value than the equal weighting scenario in Augsburg, whereas the opposite was seen for Meitingen. Overall, the bandwidth and the edge correction had the highest influence on the values of the F statistic.

Figure 6 depicts the risk score maps for Augsburg and Meitingen in which the five parameters bandwidth, edge correction, number of grid points, interpolation method and weighting, were set to their base case. The score values of the SORS are depicted as incremental densities resulting from subtracting the negative surface from the positive surface. The risk score map shows a composite picture of the separate estimates illustrated in Fig. 4. There was little heterogeneity in risk scores for the region of Augsburg except for a small area with higher obesogenic scores at the northwestern city boundary. The risk score map for Meitingen showed high risk scores for the northwestern part of the town as well as for the area north of the town borders. The risk score map based on point processes for comparison purposes is shown in Fig. 7. A region with a low obesity level is present in Figs. 6 and 7 for both study areas partly at similar places, however, obesity hotspots could only be derived from the SORS KDE plot in Fig. 6.

The SORS is a helpful tool to understand the spatial distribution of health-related harmful environmental factors in relation to health-promoting environmental factors. Risk score maps allow for an overall intuitive view on summarized structures, which can be a valuable help in obesity-related research and also within policy. Although the actual use of those structures might look different in reality, it nevertheless gives a composite simplifying measure of the environment and can be further extended to a more comprehensive tool accounting for several health dimensions affecting individuals simultaneously.

Several strengths exist regarding our study. The automated processing of data and the automated testing of several important KDE parameters makes it possible to repeat the application of risk score estimation for other areas efficiently, given that the spatial data points and the shape files of the city or town boundaries have been downloaded before. This enables the user to describe, compare, and monitor (if done repeatedly) risk scores as well as the influence of relevant risk score parameters within several areas of interest, within other regions worldwide, and also on a larger geographic scale. For example, the analysis could be performed for a whole country in order to identify national inequalities regarding environmental obesity risks or to guide and prioritize prevention efforts that concentrate on the food and the physical activity environment. To achieve this on a regional scale, the data download area simply has to be increased to cover a larger area for the subsequent data download from OSM. The data files would be of a manageable size, as only a small number of features are important for this kind of analysis. For Augsburg, i.e., for the larger of our two study areas, the data file size was 8 MB. For larger areas, e.g., for Germany, other portals such as Geofabrik should be used. In this case, no query process is needed, and the data files are directly ready for download. The data size for Germany, for example, would be 3.1 gigabytes in this case [62]. Furthermore, using so-called planet OSM files, data disk space of around one terabyte (compressed 89 GB) or less is required [63].

We integrated uncertainty into our analysis by performing a spatial bootstrap. Subsequently, we used the samples directly for the evaluation of our method. This allowed us to assess the stability of the score values against POI variations and helped us to compare deterministic parameter scenarios based on the ANOVA F statistic. On the one hand, the impact of each parameter on score results could be assessed. In addition, the values of the F statistic could be used to find optimal parameter combinations for the SORS.

We checked the robustness of the score and repeated our analysis several times for a given area. Results were qualitatively equivalent, i.e., for each given parameter variation, the repeated analysis could be used to rank the scenarios in the same order.

However, there are also some limitations regarding the study. First, some of the environmental factors discovered during the literature search could not be implemented based on spatial POIs, especially complex constructs such as land use mix or walkability.

Second, the categorization of positive and negative obesogenic factors was based on data from pre-existing literature, and it is not known whether POIs categorized as “positive” or “negative” are really positively or negatively associated with obesogenic health (behavior). Further studies could compare the SORS with external data sources, such as walk scores in a given region, in order to test these associations [64].

As the content of OSM is generated by users, it is necessary to assess the data quality within validation studies. Within our previous work, we calculated sensitivity, specificity, and positive predictive values for OSM and compared the results with the corresponding values for Google Maps [18]. It became evident that both geocoding services performed adequately. OSM had higher positive predictive value but, in contrast, lower sensitivities than Google Maps.