Processing and analysis are undertaken using the following software: ArcGIS Pro 3.1 for the dasymetric mapping, building feature calculation and resampling of grids; QGIS 3.22, including ORS plugin for the catchment zone/isochrone calculation for physician locations; Python 3.9, including the packages numpy, xgboost, sklearn, pandas, geopandas and pyogrio for the AI-based population estimation, E2SFCA analysis and difference + grid calculation; RStudio (version 2023.09.0+463) for distribution analysis by regional type.

The data on primary care physicians includes not only their spatial locations, but also the total amount of working time or “Full-time equivalent” (FTE) provided. One full-time equivalent equals one person working for 40 hours a week. The main method used for calculating the access is the Enhanced Two-Step Floating Catchment Area (E2SFCA) method (Luo/Qi 2009). It is commonly used in medical geography (Jörg/Lenz/Wetz et al. 2019: 17) and generally well-suited for mapping access to services of general interest (Seisenberger/Pajares/Hecht et al. 2023: 130). A schematic workflow of the entire process is shown in Figure 3. Due to technical reasons, all of the following processing steps are implemented individually on the level of the 16 federal states of Germany. To ensure that cross-border relationships between states are included in the analysis, each state including physician locations and population is buffered by 50 km just for the calculation and the results are clipped to the actual extent of the state afterwards.

Figure 3 Schematic workflow for physician access calculation

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In the next step, four general graduations/catchment zones of access are defined, which are later needed for the calculation of distance decay: 5, 10, 15 and 20 minutes, with car travel being the mode of transport (see Figure 4). The maximum value of 20 minutes is defined following the limits indicated by the Landesentwicklungsprogramm Bayern (LEP) (Bayerische Staatsregierung 2023: 39) and the Federal Office for Building and Regional Planning (BBSR 2023: 6). This step considers that people farther away from any given facility have less accessibility to services than those located closer.

Figure 4 Example of an individual physician location and corresponding isochrones/catchments within the city of Munich

Source: openrouteservice.org by HeiGIT (isochrones); OpenStreetMap Contributors (road data).

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The four catchment zones are represented by isochrones generated using the OpenRouteService (ORS) (HeiGIT 2023). This service calculates network-based driving times based on the OpenStreetMap (OSM) road network (see Table 1) for different modes of transport. For our analysis, we use the “Isochrones from point”-functionality provided by the ORS-Tools plugin for QGIS. The profile for the mode of transport is set to car travel, with the range set to time dimensions of 5, 10, 15 and 20 minutes. The same network is used for calculations for 2022 and 2011, since there is no suitable network snapshot available for 2011.

Data preparation for the actual access mapping begins with summarizing the full-time equivalents of primary care physicians at any given location. Dissolving these points prevents the double processing of locations. For every obtained primary care physician location, the population within each of the four catchment zones is weighted and summarized. The weights are derived by fitting the subzones into a Gaussian distance-weighting function following Jörg/Lenz/Wetz et al. (2019: 29), resulting in 0.93 for 5 minutes, 0.57 for 10 minutes, 0.21 for 15 minutes and 0.05 for 20 minutes. By dividing the full-time equivalents at each physician location by the weighted population, the supply-demand ratio in FTE/person is calculated. Thereby, it is important to note that the calculated amount is a theoretical maximum, since competition between individual physicians is not considered.

Then, for each population location (e.g. individual buildings), the supply/demand ratios of all accessible physicians from this location are weighted depending on the catchment zone and then summarized again, using the same zones and weights as before. The result is the weighted supply/demand index (WSDI), i.e. the sum of all accessible weighted FTEs/person for each population location. The value is then converted to available working minutes per physician in one year by multiplying the WSDI by 105,600 (since 1 FTE = 40 h/week x 44 weeks x 60 min = 105,600 working minutes per year). We name this value Minutes and it should be understood as the theoretical maximum amount of time any person can spend at primary care physicians in a year (within a maximum travel distance of 20 minutes by car). The higher the value, the better the access to service provision. We apply this additional step because the Minutes value is a more understandable unit for the reader than the underlying basic WSDI, which only contains very small values.

Then, the Minutes of each individual population location (e.g. buildings) are summarized into a grid with 100 m resolution by calculating the mean for all buildings within a cell. The cell in which a building is located is determined by its address point location. This step is necessary because the buildings of 2011 do not exactly match the buildings of 2022 (due to construction or demolition of buildings). The entire process is applied identically for the years 2011 and 2022, respectively. Finally, the dynamic in service provision is derived by comparing both grids cell-by-cell. The resulting grid with the Minutes, population and FTE values is also made available for download (Reiter/Jehling/Hecht 2024).

For optimized analysis and visualization on different spatial levels and to emphasize the scalability of the approach, the data is additionally aggregated to raster levels of 1 km and 10 km resolution. The basic raster with 100 m resolution is suited for local analysis, for example on the level of an individual city, while 1 km is more appropriate for regional analysis (a federal state) and 10 km is intended for nationwide application. To this end, the values of the 100 m cells are summarized. For population, full-time equivalent and their absolute differences, the sum of all 100 m cells within a 1/10 km cell is calculated, for the respective relative values the mean is used when summarizing.

To analyse the results produced by this method, we differentiate between different regional types. For this purpose, we use the subset Combined Regional Statistical Spatial Type taken from the Regional Statistical Spatial Typology for Mobility and Transport Research (RegioStaR7; Bundesministerium für Digitales und Verkehr 2021). The key importance of this typology lies in the definition of urban (metropolis, regiopolis and large city, medium-sized city/urban area, small-town area/village area) and rural regions (central city, medium city/urban area, small-town area/village area).

We then set the change in access against the change in population to identify dynamics in access. Figure 8 shows these key results. This approach allows problematic regions with opposite trends in both dimensions to be separated from regions with more similar developments.

Figure 8 Change in population combined with relative change in access

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Based on these findings, we define several types of regions. The first type (“surplus in population”) includes regions with supply issues, where a loss of access results from strong population growth (Figure 8, brown colour). The second type (“surplus in access”) consists of regions with demand issues, where access is rising due to population shrinkage (Figure 8, light blue colour). The third type describes regions with a positive trend in both dimensions (Figure 8, dark blue colour), whereas the fourth type includes regions with a negative trend in both dimensions (Figure 8, light yellow colour).

In the southern states of Germany, we mainly see the first and third types, in the eastern states there is a mix of all types. Within the Münster/Paderborn region, the first type dominates strongly. The cites of Berlin, Hamburg and Munich, where there is the strongest influx of population, are of the first type.

When looking at the results for the change in access set against the change in full-time equivalents, we can see a more heterogeneous pattern than before (Figure 9). The results of this mostly support the aforementioned typology of regions. We can see that in parts of the Münster/Paderborn region as well as in Saxony, the reduction in access is worsened by a decline in full-time equivalents (Figure 9, light yellow colours).

Figure 9 Change in full-time equivalents combined with relative change in access

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To support the map-based visual analysis, we also categorize the changes in access according to the chosen regional type RegioStaR7, as explained in Section 2.4 (see Figure 10). Each cell of the 100 m raster was mapped to this typology. We can see that in all regional types, average access is declining. Rural regions observe the strongest decline, followed by metro- and regiopolis regions. In large and central cities, the trend is closer to 0 than in other regional types.

Figure 10 Distribution of cell-level differences across urban and rural region types following the RegioStaR7 nomenclature. Displayed are differences in relative access (top), absolute population (middle) and absolute full-time equivalents (bottom). Note: for both population and full-time equivalents only non-zero cells are analysed

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For the population, it can be said that within both the urban and rural groups, the bigger the town/city, the higher the population growth on average and the smaller the share of municipalities with shrinking populations (see Figure 10). It is interesting to note that medium-sized cities are growing more strongly than central and large cities.

There is no clear trend visible for full-time equivalents, positive and negative changes mostly even themselves out (see Figure 10).

Between the individual federal states, some differences are noticeable. Density plots for relative difference in access (calculated on the 100 m raster level) show that in the majority of states, urban regions tend to have slightly higher gains in access (see Figure 11). Noteworthy exceptions are Saxony, Saxony-Anhalt and North Rhine-Westphalia, where even in urban regions access is deteriorating. Very interestingly, on this small scale we can clearly see that access in most of the eastern and central states of Germany (Brandenburg, Mecklenburg-Vorpommern, Saxony-Anhalt and Thuringia) is evolving more positively than in the southern parts of the country.

Figure 11 Distribution of relative change in access per rural and urban regions by federal state. Dotted lines show the national mean for rural and urban areas

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Our analytical results show that, in general, access to primary care physicians in Germany slightly increased over the investigated period of 11 years. This increase is not evenly distributed across the spatial dimension, though. This is in line with Weingarten and Steinführer (2020: 654), who point out that in rural regions of Germany, the public discourse often revolves around the supposed “deprivation” of these regions, especially in terms of infrastructural facilities including medical services. It is therefore necessary to further analyse this problem. Our study aims to provide an understanding of the underlying dynamics, which are not entirely driven by supply issues. Küpper and Peters’ (2019: 111) analysis of other indicators also supports the thesis of rural regions not being as badly placed as often claimed in the popular media discourse.

Dynamics in supply and demand show regional differences in rural and urban settings. We identify a lot of rural regions where access to physicians is slightly rising due to the fact that the population is declining faster than the number of physicians. This does not necessarily mean that service provision in general is sufficient in these regions, but that people can potentially receive more treatment time per year in terms of absolute values. In other regions, we observe the exact opposite effect: the population is outgrowing the number of physicians and therefore access is deteriorating and treatment time per year is dropping, even though there are more physicians present. This is not limited to big cities, especially in southern Germany. Here, challenges in access arise not through the distance to facilities (accessibility) but in their capacity (availability) on a local level (Khan/Bhardwaj 1994; Guagliardo 2004: 2; Neumeier/Osigus 2024). We also observe parallel trends in larger cities, where access and population changes are both positive. These conclusions show that the analysis and interpretation of general service provision in rural and urban areas should not be dealt with by using one-dimensional approaches, e.g. change in physician numbers alone.

Generally speaking, planning for service provision is considered an important task of government and administration at multiple levels (Mause 2018; Seisenberger/Reiter 2022: 218) and is regulated in the German Spatial Planning Law (Raumordnungsgesetz).¹ However, the implementation of such planning is not regulated. Medical service provision is also a special case in planning and needs to comply with additional regulations. Currently, it is defined that supply of primary care physicians is measured as a simple ratio of physicians divided by population within sharply defined planning regions (Gemeinsamer Bundesausschuss 2023). However, this falls short of real needs and possibilities in practice, as is widely confirmed by the literature (Ahlmeyer/Wittowsky 2018; Baier/Pieper/Schweikart et al. 2020; Bukow 2021).

Concerning possible solutions to these problems on the planning side, it is important to note that the planning of medical services in Germany is currently based on a demand-planning system (Bedarfsplanung) by law (§ 99 SGB V)² using sharply defined zones (Krügel/Mäs 2023). There have been various propositions for changing this approach (Sundmacher/Schang/Schüttig et al. 2018), but no changes have so far been implemented. With our study, we show that it is possible to calculate a more sophisticated basis for future planning processes with nationwide coverage, one that considers real world travel times, actual physician capacity and population distribution on a small scale. Our findings imply that these regulatory measures should be complemented by further multi-dimensional approaches to ensure that planning and, more fundamentally, policy making can anticipate the described regional and local trends. It is also important to highlight the possibility of transferring the proposed approach to other planning tasks which require the consideration of different scales across boundaries, as shown by Seisenberger, Pajares, Hecht et al. (2023).

In our study, the E2SFCA method proved a suitable method for measuring spatial access to medical facilities. However, the approach also has limitations, as competition on the supply side is not considered (Wan/Zou/Sternberg 2012; Lingwei Chen/Chen/Lan et al. 2023). Furthermore, the calculated Minutes represent rather a theoretical maximum value of physician time to which each individual person potentially has access. However, the results of the approach are easier to understand and communicate than those of a more sophisticated, technically superior method that may be too difficult to interpret and communicate for real-life planning purposes.

Due to technical limitations, it was not possible to calculate access for the entirety of Germany in a single run, as calculating everything at once exceeded the available system memory of 256 gigabytes. Therefore, we split the data into the 16 individual federal states of Germany. To ensure continuity at the state borders, we buffered each state by 50 km for the calculations. Values directly at the outer borders of Germany suffer from a cut-off-effect though, since normally there is a co-supplying relationship between neighbouring regions (Sundmacher/Schang/Schüttig et al. 2018), but we did not have access to data outside of Germany.

The overall quality of the population data predicted for 2022 is difficult to assess as no comprehensive reference data is available on a large scale. Judging from the analysis for the city of Munich presented in Section 2.2.2, we assume that the quality is good enough to use the data in this study. It seems that our model both over- and underestimates population in Munich, which leads to a smoothing out of errors on an overall scale. In a more rural setting where housing forms are not as variable, the model seems to perform very well, which suggests the overall quality is a bit higher than results from our testing might indicate. Limited access to reference data on micro-scale population thus hinders more extensive validation. Possible improvements could tackle the issue of classification errors when separating residential and non-residential buildings, which we believe is currently the biggest source of error in the model. There is also potential for improvement with the dasymetric mapping by adding additional data sources that might improve the mapping results and ultimately the model training data.

Regarding the approach of resampling the 100 m raster to coarser resolutions, it should be noted that this induces the modifiable areal unit problem (MAUP) (Openshaw 1983), which leads to slightly differing analysis results after aggregating smaller areal units into bigger ones. This also affects rasters (Lyn 2001: 43). Between the different spatial scales presented, the values of access slightly differ when comparing overlying cells on different scales. We argue that the benefits of resampling according to the optimal spatial scale of a specific problem outweighs this effect.

The developed approach has advantages over existing transportation planning tools (for example as shown in Krügel/Mäs 2023) in that it combines a population estimation approach with the E2SCA approach for analyses that can be applied at different spatial scales. This allows a very flexible application to other topics or in other areas.