Skip to main content
Download PDF

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

BMC Medical Research Methodology volume 23, Article number: 65 (2023) Cite this article

Abstract

Background

Overweight and obesity are severe public health problems worldwide. Obesity can lead to chronic diseases such as type 2 diabetes mellitus. Environmental factors may affect lifestyle aspects and are therefore expected to influence people’s weight status. To assess environmental risks, several methods have been tested using geographic information systems. Freely available data from online geocoding services such as OpenStreetMap (OSM) can be used to determine the spatial distribution of these obesogenic factors. The aim of our study was to develop and test a spatial obesity risk score (SORS) based on data from OSM and using kernel density estimation (KDE).

Methods

Obesity-related factors were downloaded from OSM for two municipalities in Bavaria, Germany. We visualized obesogenic and protective risk factors on maps and tested the spatial heterogeneity via Ripley’s K function. Subsequently, we developed the SORS based on positive and negative KDE surfaces. Risk score values were estimated at 50 random spatial data points. We examined the bandwidth, edge correction, weighting, interpolation method, and numbers of grid points. To account for uncertainty, a spatial bootstrap (1000 samples) was integrated, which was used to evaluate the parameter selection via the ANOVA F statistic.

Results

We found significantly clustered patterns of the obesogenic and protective environmental factors according to Ripley’s K function. Separate density maps enabled ex ante visualization of the positive and negative density layers. Furthermore, visual inspection of the final risk score values made it possible to identify overall high- and low-risk areas within our two study areas. Parameter choice for the bandwidth and the edge correction had the highest impact on the SORS results.

Discussion

The SORS made it possible to visualize risk patterns across our study areas. Our score and parameter testing approach has been proven to be geographically scalable and can be applied to other geographic areas and in other contexts. Parameter choice played a major role in the score results and therefore needs careful consideration in future applications.

Peer Review reports

Background

Overweight and obesity are severe problems worldwide, causing a number of diseases such as type 2 diabetes, and thus reducing expected life years and quality of life [1, 2]. In Germany, for example, the prevalence of being overweight or obese among adults was 54.0% according to the GEDA (GEDA, German Health Update) study from the Robert Koch Institute (a national public health institute in Germany) in 2014/2015, with men being affected more often than women [3]. Other personal aspects affecting obesity besides gender were low education and higher age according to Mader et al. [4]. In addition, several German cohort studies have shown that the average weight in middle-aged populations increased slightly during recent years [5].

Obesity has become a major public health concern, and recent studies describe regional heterogeneity [6, 7]. In obesity-related research, the term “obesogenic environment” describes environmental influences such as green space or fast food restaurants on the development of obesity [8, 9], which has been investigated intensively in the past [10]. Several approaches have been developed in order to analyze the effect of the environment on the risk of obesity. Examples include obesogeneity assessment via questionnaires [11] and via data visualization tools for obesity policy [12].

Some geographic modeling approaches were used to characterize the accumulation of environmental factors. Common techniques include kernel density estimation (KDE), a density method that allows for the estimation of a continuous risk surface [13, 14], as well as hot spot mapping [15] and further geographic information system (GIS) methods [16]. These methods can be used to develop obesity risk scores [17].

Online geocoding services offer low-cost geographic data for researchers that can be downloaded and used for spatial statistical analyses. Their validity has been investigated in the past with reasonable results regarding completeness of environmental factors and positional accuracy of their coordinates [18, 19]. Therefore, they offer a rich database on which geographic tools can be built. However, geocoding services such as Google Maps offer data only in a limited way. In contrast, geodata from OpenStreetMap (OSM) contain geographic information provided by volunteers and thus are less restricted [20]. In a recent study, we performed an extensive literature search to identify obesity-related environmental factors [18]. Furthermore, we operationalized and downloaded corresponding points of interest (POIs).

The aim of our study extends this approach by developing and testing the spatial obesity risk score (SORS) based on data from OSM. The SORS calculates the obesity risk for each geographic point in a given region based on the local density of positive and/or negative obesity-related environmental factors. In our study, we developed a methodological framework for risk score estimation using KDE and tested the influence of five KDE parameters on the SORS values: (1) bandwidth, (2) edge correction via the size of the download area, (3) number of grid points, (4) risk interpolation method, and (5) weighting scheme of the environmental factors.

Methods

Overview of the study approach

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.

Fig. 1
figure 1

Modelling process for obesity risk score estimation. ANOVA = analysis of variances, KDE = kernel density estimation

Full size image

Area selection and data download

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.

Data processing

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.

Table 1 Schematic example of six processed POIs
Full size table

Spatial inhomogeneity and ex ante KDE visualization

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.

Risk score estimation

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.

Deterministic analysis

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.

Table 2 Overview on the sensitivity parameters
Full size table

Bandwidth selection

The bandwidth is an important parameter in KDE that determines the degree of smoothing. An increased bandwidth results in a higher smoothing level. For the base case, the oversmoothing bandwidth proposed by Terrell et al. [38] was chosen, which can be described as the maximum smoothing degree that can be suitably applied to a given data set. Within the deterministic scenarios, alternative higher and lower values in steps of 1/3 of the base case bandwidth were tested. We used a pooled bandwidth as described by Davies and colleagues [39].

Size of the download area (edge correction)

Restricting the observational window for KDE to the area boundaries would lead to an underestimation of the true densities at the borders. These effects are especially high if the observation window has a complex structure. To correct for edge effects, we defined a rectangular observation window around the area borders, which simultaneously served as the POI download area and as the KDE area. As a first step, a window was determined from the maximum latitude, maximum longitude, minimum latitude, and minimum longitude of the city boundaries. This minimum bounding rectangle around the study area will be called the “exact box”. For the base case, each side length of the rectangle was increased by 40%, and the resulting rectangle was held in a concentric orientation to the smaller rectangle from the step before. The whole observation window was used for the creation of the risk surface. However, risk score values were only evaluated at locations that lay within the boundaries of the respective study area. To determine the effects of the window size, we gradually increased the download area in steps of 40% of the exact box.

Number of grid points

A further central parameter of KDE is the number of grid points. These points were distributed equally on the estimation rectangle. Therefore, KDEs were generated for grid points lying both inside and outside the study area, and both types of grid points were used to estimate the risk score inside the borders of the study areas. A higher number of grid points means that the amount of interpolation is reduced, as more spatial points exist at which an exact estimation is known. To preserve the location of and distance between the inner grid points within the edge correction scenarios, we increased the number of grid points in 40% steps according to the increase in the side length of the download area. Setting the number of grid points to 25 × 25 for the exact box, this led to a base case grid of 35 × 35. For each of the following 40% steps of edge correction, again 10 additional grid points were added to each grid point dimension. Within the remaining grid point sensitivity analyses, increased numbers of 70 × 70 and 105 × 105 grid points were tested.

Interpolation method

The automatic interpolation function “interp.surface” of the R package “fields” [40] was applied within the base case. As an alternative interpolation approach, we used inverse distance weighting using the four grid points surrounding a targeted evaluation point. Furthermore, extraction of the score value of the grid point with the minimum distance to the targeted evaluation point was implemented as the third interpolation method [41]. As a fourth scenario, we chose ordinary Kriging which has proven its reliability for interpolating surfaces [42].

Weighting scheme of the environmental factors

Several approaches exist for the design of proper weighting schemes. One approach, for example, would be to weight factors according to the strength of evidence for a positive or negative correlation. Regarding our analysis, we chose an equal weighting scheme as a base case scenario. To test an alternative weighting scenario, we followed the approach of Jones-Smith et al. [34]. These authors gave a higher weighting to factors that generally reach more people because of their longer opening hours or size. For the deterministic sensitivity analysis, we therefore tested a double weighting of supermarkets and gyms.

Resampling approach to account for uncertainty in the distribution of the POIs

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.

Evaluation of the risk score estimates

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.

Fig. 2
figure 2

Algorithm describing the combination of deterministic and probabilistic analysis, BS = bootstrap sample, EC = edge correction

Full size image

Software

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].

Results

Spatial inhomogeneity and visual inspection of the study area

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.

Fig. 3
figure 3

Spatial inhomogeneity measured via Ripley’s K function for Augsburg (top) and Meitingen (bottom), r = interpoint distance, K(r) = Ripley’s K function, iso = isotropic edge correction, pois = Poisson point process

Full size image

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.

Fig. 4
figure 4

Contour lines of obesogenic and protective kernel densities in Augsburg (left) and Meitingen (right). Values of KDE are constant on a contour line with increasing values toward the respective KDE center

Full size image

Randomly drawn sample points

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.

Fig. 5
figure 5

Final set of randomly chosen spatial data points for Augsburg (left, N = 50) and Meitingen (right, N = 50)

Full size image

Effect of parameter variation within KDE estimation process

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.

Table 3 ANOVA F statistics for Augsburg and Meitingen
Full size table

Obesity risk score map

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.

Fig. 6
figure 6

Risk score maps for Augsburg (left) and Meitingen (right) showing the base case with the following parameters: bandwidth: method of Terrell [38]; edge correction: area side length: 1.4 * side length of the exact box; number of grid points: 35 × 35; weighting scheme of the environmental factors: equal weighting with unity, interpolation here via the “image.plot” function

Full size image
Fig. 7
figure 7

Risk Score map based on incremental intensities derived from inhomogeneous cluster point processes

Full size image

Discussion

We developed the SORS based on KDE using freely available data from online geocoding services. We tested several parameters which could potentially influence the final score values. Our tests showed that the SORS depended on the choice of bandwidth and the amount of edge correction applied to the KDE; the latter, however, for only one of the two study areas. In contrast, the interpolation method, the numbers of grid points, and an alternative weighting scenario had a small influence on the results.

The SORS was calculated by taking the difference of the positive and the negative kernel density surface. We followed a similar approach to that in the work of Jones-Smith et al. [34]. They estimated correlations of their score with obesity. In contrast, the aim of our study was to investigate the effect of parameter variation on the robustness of our score. Furthermore, we covered an extensive list of obesogenic and protective environmental factors that expanded the approach of a food score to a more comprehensive measure, also including the physical activity environment. Some alternative approaches using KDE were based on the division of the kernel density surfaces [54]. A major drawback of these quotients is the issue with division by zero leading to values approaching infinity and thus leading to instability. Our approach to the SORS avoids this and also the need for some adjustments correcting for the instability.

Previous studies used various approaches to estimate risk scores based on kernel techniques, both in obesity-related research areas and elsewhere. Fitzpatrick and colleagues [55], for example, developed the keeping score based on KDE to characterize crime patterns, which has often been used by the police. Crime heat maps can be generated with this technique. This approach is based on the locations of past events instead of geolocated environmental factors, and the authors assumed that the pattern of these historic events would be maintained in the future.

Some studies created kernel density surfaces based on POIs and extracted density estimations from these surfaces in order to investigate the association with weight status. Rundle et al. (2009) analyzed the effects of environmental factors on body mass index (BMI). Results of KDE analysis concerning healthy and unhealthy food outlets were used to classify the neighborhood environment of each individual within the study based on a quintile approach [56]. Furthermore, walkability, land use mix, and population density were considered. These variables could not be implemented in our study based on the chosen POI approach with OSM data.

The five chosen SORS parameters, bandwidth, edge correction, grid points, interpolation, and weights, have also been investigated in the literature. Laraia et al. (2017) used a business software and ArcGIS to geocode the information from the study data [57]. As in our analysis, several bandwidths were tested within their KDE approach, which was found to be a sensitive model parameter. Similarly, we also found a fundamental influence of bandwidth on the results.

Effects at the edge of the study area were estimated in a simulation study concerning cluster models for food outlets [58]. Estimations at the boundaries were biased, and the authors came to the conclusion that edge effects should be corrected in studies considering measures of availability and accessibility. This underlined the importance of edge correction, which was also a major topic in our study. In addition, extending the study area has been proven to be a valuable edge correction method.

Finding the optimal number of grid points was also discussed in the literature. Some authors suggested that a choice between 100 and 500 grid points gives reasonable results [59]. In our analysis, we chose 25 × 25 points for the minimum bounding rectangle, i.e., 625 grid points, and chose some additional amount of edge correction for the base case. In addition, we performed some adjustments to preserve the distance between the grid points for the edge correction scenarios. In this case, the number of grid points was extended proportionally to the amount of edge correction applied, i.e., to the amount of study area extension. This made it possible to analyze grid point and edge effects separately. The choice of grid points in our base case and sensitivity analysis was chosen in accordance with default grid sizes implemented in KDE packages.

An inverse distance weighting method was applied in the past in KDE estimation regarding homicide locations as a parameter of area safety [60]. This method could be used to estimate effects at specific locations. We used such an inverse distance method in our model as an alternative to the automatic interpolation function of the base case. As a further common method, linear interpolation has been applied within the literature [61]. The “interp.surface” function applied to our SORS model was based on bilinear weights.

It was challenging to find a suitable weighting scheme applicable within our analysis. For the base case, we assumed that each factor has the same positive or negative weight, although this might look different in reality. Additionally, we tested an example from the literature [34]. We found that double weighting of supermarkets and physical activity facilities had little effect on the results. Owing to several possible weighting methods for spatial POIs, it is necessary to test further alternatives within future studies.

Finally, the SORS was graphically compared to a risk score that was derived from incremental intensities of inhomogeneous spatial point processes. Although the methodology applied here changed from KDE-based to intensity-based estimations, similar visual patterns could be derived from the two score approaches for protective patterns, which further underlines the robustness of our chosen algorithm.

Implications of the SORS on obesity-related research and policy

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.

Strengths and limitations

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.

Conclusion

KDE has been proven to be a useful methodology in the development of an obesity risk score, predominantly on account of the nature of the continuous estimation approach enabling efficient generation of risk score maps. However, some parameters of KDE have a large effect on score results. Parameter optimization should therefore play a major role during score model development.

Availability of data and materials

The data generated for this study were downloaded from OSM using the tool Overpass turbo [https://overpass-turbo.eu/. Accessed 11 Aug 2022], and the exemplary code is included in this published article.

Abbreviations

ANOVA:

Analysis of variances

API:

Application Programming Interface

BC:

Base case

BS:

Bootstrap sample

BW:

Bandwidth

EC:

Edge correction

EP:

Evaluation point

GEDA:

(GEDA, German Health Update)

GIS:

Geographic information systems

GP:

Grid points

INT:

Interpolation

JSON:

JavaScript Object Notation

KDE:

Kernel density estimation

OSM:

OpenStreetMap

POI:

Point of interest

SORS:

Spatial obesity risk score

WT:

Weighting

References

  1. Bluher M. Obesity: global epidemiology and pathogenesis. Nat Rev Endocrinol. 2019;15:288–98.

    Article  PubMed  Google Scholar 

  2. Elbe AM, Elsborg P, Dandanell S, Helge JW. Correlates and predictors of obesity-specific quality of life of former participants of a residential intensive lifestyle intervention. Obes Sci Pract. 2018;4:188–93.

    Article  PubMed  Google Scholar 

  3. Schienkiewitz A, Mensink G, Kuhnert R, Lange C. Overweight and obesity among adults in Germany; 2017.

    Google Scholar 

  4. Mader S, Rubach M, Schaecke W, Röger C, Feldhoffer I, Thalmeier E-M. Healthy nutrition in Germany: a survey analysis of social causes, obesity and socioeconomic status. Public Health Nutr. 2020;23:2109–23.

    Article  PubMed  Google Scholar 

  5. Haftenberger M, Mensink GB, Herzog B, Kluttig A, Greiser KH, Merz B, et al. Changes in body weight and obesity status in German adults: results of seven population-based prospective studies. Eur J Clin Nutr. 2016;70:300–5.

    Article  CAS  PubMed  Google Scholar 

  6. Merlo J, Wagner P, Leckie G. A simple multilevel approach for analysing geographical inequalities in public health reports: the case of municipality differences in obesity. Health Place. 2019;58:102145.

    Article  PubMed  Google Scholar 

  7. Zhou Y, Wu K, Shen H, Zhang J, Deng H-W, Zhao L-J. Geographical differences in osteoporosis, obesity, and sarcopenia related traits in white American cohorts. Sci Rep. 2019;9:12311.

    Article  PubMed  PubMed Central  Google Scholar 

  8. Elinder LS, Jansson M. Obesogenic environments--aspects on measurement and indicators. Public Health Nutr. 2009;12:307–15.

    PubMed  Google Scholar 

  9. Hobbs M, Griffiths C, Green MA, Jordan H, Saunders J, McKenna J. Associations between the combined physical activity environment, socioeconomic status, and obesity: a cross-sectional study. Perspect Public Health. 2018;138:169–72.

    Article  CAS  PubMed  Google Scholar 

  10. Mackenbach JD, Rutter H, Compernolle S, Glonti K, Oppert JM, Charreire H, et al. Obesogenic environments: a systematic review of the association between the physical environment and adult weight status, the SPOTLIGHT project. BMC Public Health. 2014;14:233.

    Article  PubMed  PubMed Central  Google Scholar 

  11. Rendina D, Campanozzi A, De Filippo G. Methodological approach to the assessment of the obesogenic environment in children and adolescents: a review of the literature. Nutr Metab Cardiovasc Dis. 2019;29:561–71.

    Article  CAS  PubMed  Google Scholar 

  12. Monsivais P, Francis O, Lovelace R, Chang M, Strachan E, Burgoine T. Data visualisation to support obesity policy: case studies of data tools for planning and transport policy in the UK. Int J Obes. 2018;42:1977–86.

    Article  Google Scholar 

  13. Daley D, Bachmann M, Bachmann BA, Pedigo C, Bui MT, Coffman J. Risk terrain modeling predicts child maltreatment. Child Abuse Negl. 2016;62:29–38.

    Article  PubMed  Google Scholar 

  14. Caplan JM, Kennedy LW, Barnum JD, Piza EL. Risk terrain modeling for spatial risk assessment. Cityscape. 2015;17:7–16.

    Google Scholar 

  15. Ripoche M, Lindsay LR, Ludwig A, Ogden NH, Thivierge K, Leighton PA. Multi-scale clustering of Lyme disease risk at the expanding leading edge of the range of Ixodes scapularis in Canada. Int J Environ Res Public Health. 2018;15:603.

    Article  PubMed  PubMed Central  Google Scholar 

  16. Lafontaine SJV, Sawada M, Kristjansson E. A direct observation method for auditing large urban centers using stratified sampling, mobile GIS technology and virtual environments. Int J Health Geogr. 2017;16:6.

    Article  PubMed  PubMed Central  Google Scholar 

  17. Cebrecos A, Diez J, Gullon P, Bilal U, Franco M, Escobar F. Characterizing physical activity and food urban environments: a GIS-based multicomponent proposal. Int J Health Geogr. 2016;15:35.

    Article  PubMed  PubMed Central  Google Scholar 

  18. Präger M, Kurz C, Bohm J, Laxy M, Maier W. Using data from online geocoding services for the assessment of environmental obesogenic factors: a feasibility study. Int J Health Geogr. 2019;18:13.

    Article  PubMed  PubMed Central  Google Scholar 

  19. Lemke D, Mattauch V, Heidinger O, Hense HW. Who Hits the Mark? A Comparative Study of the Free Geocoding Services of Google and OpenStreetMap. Gesundheitswesen (Bundesverband der Arzte des Offentlichen Gesundheitsdienstes (Germany)). 2015;77:e160–5.

    CAS  Google Scholar 

  20. Mocnik F-B, Mobasheri A, Zipf A. Open source data mining infrastructure for exploring and analysing OpenStreetMap. Open Geospatial Data, Software and Standards. 2018;3:7.

    Article  Google Scholar 

  21. Jia P, Cheng X, Xue H, Wang Y. Applications of geographic information systems (GIS) data and methods in obesity-related research. Obes Rev. 2017;18:400–11.

    Article  CAS  PubMed  Google Scholar 

  22. Statistische Ämter des Bundes und der Länder. Gemeinsames Statistikportal. Gemeindeverzeichnis-Online. https://www.statistikportal.de/de/produkte/gemeindeverzeichnis. Accessed 10 Jun 2020.

  23. Meisinger C, Döring A, Thorand B, Heier M, Löwel H. Body fat distribution and risk of type 2 diabetes in the general population: are there differences between men and women? The MONICA/KORA Augsburg cohort study. Am J Clin Nutr. 2006;84:483–9.

    Article  CAS  PubMed  Google Scholar 

  24. Overpass turbo. https://overpass-turbo.eu/. Accessed 11 Aug 2021.

  25. Bayerische Vermessungsverwaltung. OpenData. https://www.ldbv.bayern.de/produkte/weitere/opendata.html. Accessed 11 Aug 2021.

  26. Export | OpenStreetMap. https://www.openstreetmap.org/export. Accessed 11 Aug 2021.

  27. Map features. https://wiki.openstreetmap.org/wiki/Map_features. Accessed 20 Jul 2021.

  28. Ripley BD. Modelling spatial patterns. J R Stat Soc Series B Stat Methodol. 1977;39:172–92.

    Google Scholar 

  29. Dai D, Taquechel E, Steward J, Strasser S. The impact of built environment on pedestrian crashes and the identification of crash clusters on an urban university campus. West J Emerg Med. 2010;11:294–301.

    PubMed  PubMed Central  Google Scholar 

  30. Haase P. Spatial pattern analysis in ecology based on Ripley’s K-function: introduction and methods of edge correction. J Veg Sci. 1995;6:575–82.

    Article  Google Scholar 

  31. ExplainKplot. http://spatstat.org/explainKplot.html. Accessed 11 Aug 2021.

  32. Gabriel E. Estimating second-order characteristics of inhomogeneous Spatio-temporal point processes. Methodol Comput Appl Probab. 2014;16:411–31.

    Article  Google Scholar 

  33. Loh JM. A valid and fast spatial bootstrap for correlation functions. Astrophys J. 2008;681:726.

    Article  Google Scholar 

  34. Jones-Smith JC, Karter AJ, Warton EM, Kelly M, Kersten E, Moffet HH, et al. Obesity and the food environment: income and ethnicity differences among people with diabetes: the diabetes study of northern California (DISTANCE). Diabetes Care. 2013;36:2697–705.

    Article  PubMed  PubMed Central  Google Scholar 

  35. Klemelä JS. Smoothing of multivariate data: density estimation and visualization: John Wiley & Sons; 2009.

    Book  Google Scholar 

  36. Hastie T, Tibshirani R, Friedman JH. The elements of statistical learning: data mining, inference, and prediction: Springer; 2009.

    Book  Google Scholar 

  37. King TL, Bentley RJ, Thornton LE, Kavanagh AM. Using kernel density estimation to understand the influence of neighbourhood destinations on BMI. BMJ Open. 2016;6:e008878.

    Article  PubMed  PubMed Central  Google Scholar 

  38. Terrell GR. The maximal smoothing principle in density estimation. J Am Stat Assoc. 1990;85:470–7.

    Article  Google Scholar 

  39. Davies TM, Marshall JC, Hazelton ML. Tutorial on kernel estimation of continuous spatial and spatiotemporal relative risk. Stat Med. 2018;37:1191–221.

    Article  PubMed  Google Scholar 

  40. Nychka D, Furrer R, Paige J, Sain S. fields: Tools for spatial data; 2017. https://doi.org/10.5065/D6W957CT. (URL: http://doi.org/10.5065/D6W957CT), R package version 9.6, <URL: www.image.ucar.edu/~nychka/Fields>

    Google Scholar 

  41. Wong DW, Yuan L, Perlin SA. Comparison of spatial interpolation methods for the estimation of air quality data. J Expo Anal Environ Epidemiol. 2004;14:404–15.

    Article  CAS  PubMed  Google Scholar 

  42. Kethireddy SR, Tchounwou PB, Ahmad HA, Yerramilli A, Young JH. Geospatial interpolation and mapping of tropospheric ozone pollution using geostatistics. Int J Environ Res Public Health. 2014;11:983–1000.

    Article  PubMed  PubMed Central  Google Scholar 

  43. Wang X, Wiegand T, Wolf A, Howe R, Davies SJ, Hao Z. Spatial patterns of tree species richness in two temperate forests. J Ecol. 2011;99:1382–93.

    Article  Google Scholar 

  44. R Core Team. R: a language and environment for statistical computing. Vienna: Austria; 2016.

    Google Scholar 

  45. Wickham H. ggplot2: elegant graphics for data analysis. New York: Springer-Verlag; 2009.

    Book  Google Scholar 

  46. Baddeley A, Rubak E, Turner R. Spatial point patterns: methodology and applications with R. London: Chapman and hall/CRC press; 2015. URL http://www.crcpress.com/Spatial-Point-Patterns-Methodology-and-Applications-with-R/Baddeley-Rubak-Turner/9781482210200/

    Book  Google Scholar 

  47. Venables WN, Ripley BD. Modern Applied Statistics with S. Fourth Edition. New York: Springer; 2002. ISBN 0-387-95457-0.

  48. Bivand R, Keitt T, Rowlingson B. Rgdal: bindings for the geospatial data abstraction library. R package version 1; 2016. p. 2–4.

    Google Scholar 

  49. Mouselimis L. geojsonR: a GeoJson processing toolkit. R package version 1.0.0; 2017.

    Google Scholar 

  50. G. Jay Kerns (2018). Prob: elementary probability on finite sample spaces. R package version 1.0–1. https://CRAN.R-project.org/package=prob.

    Google Scholar 

  51. Pebesma EJ. Multivariable geostatistics in S: the gstat package. Comput Geosci. 2004;30:683–91.

    Article  Google Scholar 

  52. Simon Urbanek (2013). Png: read and write PNG images. R package version 0.1–7. https://CRAN.R-project.org/package=png.

    Google Scholar 

  53. Michael Hahsler and Matthew Piekenbrock (2017). Dbscan: density based clustering of applications with noise (DBSCAN) and related algorithms. R package version 1.1–1. https://CRAN.R-project.org/package=dbscan.

    Google Scholar 

  54. Loo BP, Yao S, Wu J. Spatial point analysis of road crashes in Shanghai: a GIS-based network kernel density method. In: 2011 19th international conference on geoinformatics IEEE. 2011. p. 1–6.

  55. Fitzpatrick DJ, Gorr WL, Neill DB. Keeping score: predictive analytics in policing. Annu Rev Criminol. 2019;2:473–91.

    Article  Google Scholar 

  56. Rundle A, Neckerman KM, Freeman L, Lovasi GS, Purciel M, Quinn J, et al. Neighborhood food environment and walkability predict obesity in new York City. Environ Health Perspect. 2009;117:442–7.

    Article  PubMed  Google Scholar 

  57. Laraia BA, Downing JM, Zhang YT, Dow WH, Kelly M, Blanchard SD, et al. Food environment and weight change: does residential mobility matter?: the diabetes study of northern California (DISTANCE). Am J Epidemiol. 2017;185:743–50.

    Article  PubMed  PubMed Central  Google Scholar 

  58. Van Meter EM, Lawson AB, Colabianchi N, Nichols M, Hibbert J, Porter DE, et al. An evaluation of edge effects in nutritional accessibility and availability measures: a simulation study. Int J Health Geogr. 2010;9:40.

    Article  PubMed  PubMed Central  Google Scholar 

  59. Raykar VC, Duraiswami R, Zhao LH. Fast computation of kernel estimators. J Comput Graph Stat. 2010;19:205–20.

    Article  Google Scholar 

  60. Weiss CC, Purciel M, Bader M, Quinn JW, Lovasi G, Neckerman KM, et al. Reconsidering access: park facilities and neighborhood disamenities in new York City. J Urban Health. 2011;88:297–310.

    Article  PubMed  PubMed Central  Google Scholar 

  61. Van Kerm P. Adaptive kernel density estimation. Stata J. 2003;3:148–56.

    Article  Google Scholar 

  62. Geofabrik downloads. Germany. https://download.geofabrik.de/europe/germany.html. Accessed 10 May 2021.

  63. Planet.osm. https://wiki.openstreetmap.org/wiki/Planet.osm. Accessed 10 May 2021.

  64. Carr LJ, Dunsiger SI, Marcus BH. Walk score as a global estimate of neighborhood walkability. Am J Prev Med. 2010;39:460–3.

    Article  PubMed  PubMed Central  Google Scholar 

Download references

Acknowledgments

This study is partly based on a grant by the Federal Ministry of Health, Germany (FKZ: GE20160324) as part of the German Diabetes Surveillance Project conducted by the Robert Koch Institute, Berlin.

Funding

Open Access funding enabled and organized by Projekt DEAL.

Author information

Authors and Affiliations

  1. Department of Sport and Health Sciences, Technical University of Munich, Munich, Germany

    Maximilian Präger & Michael Laxy

  2. Institute for Medical Information Processing, Biometry, and Epidemiology (IBE), Ludwig-Maximilians-University Munich, Munich, Germany

    Maximilian Präger, Rolf Holle & Werner Maier

  3. Munich School of Management and Munich Center of Health Sciences, Ludwig-Maximilians-University Munich, Munich, Germany

    Christoph Kurz

  4. German Center for Diabetes Research, Neuherberg, Germany

    Michael Laxy

Authors
  1. Maximilian Präger
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Christoph Kurz
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Rolf Holle
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Werner Maier
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Michael Laxy
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

WM initiated the cooperation. RH and WM supervised the project. MP programmed the database queries, processed the data, and visualized the results on maps. RH and CK provided statistical input. All authors were involved in the development and evaluation concept of the SORS algorithm. MP programmed the SORS code. ML and WM provided health scientific input. MP wrote the manuscript. All authors read previous versions of the manuscript, commented on, and approved the final version of the manuscript for submission.

Corresponding author

Correspondence to Maximilian Präger.

Ethics declarations

Ethics approval and consent to participate

Not applicable.

Consent for publication

Not applicable.

Competing interests

The authors declare that they have no conflicts of interests.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary Information

Additional file 1.

Complete list of chosen variables.

Additional file 2.

Methodological details.

Additional file 3.

Rights and permissions

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated in a credit line to the data.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Präger, M., Kurz, C., Holle, R. et al. A spatial obesity risk score for describing the obesogenic environment using kernel density estimation: development and parameter variation. BMC Med Res Methodol 23, 65 (2023). https://doi.org/10.1186/s12874-023-01883-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1186/s12874-023-01883-y

Keywords

BMC Medical Research Methodology

ISSN: 1471-2288

Contact us