Mapping Bicycle Crash Risk Patterns on the Local Scale - MDPI

safety Article

Mapping Bicycle Crash Risk Patterns on the Local Scale Martin Loidl *, Gudrun Wallentin, Robin Wendel and Bernhard Zagel Department of Geoinformatics—Z_GIS, University of Salzburg, 5020 Salzburg, Austria; [email protected] (G.W.); [email protected] (R.W.); [email protected] (B.Z.) * Correspondence: [email protected]; Tel.: +43-662-8044-7534 Academic Editor: Jake Olivier Received: 21 March 2016; Accepted: 22 August 2016; Published: 1 September 2016

Abstract: Currently, mainly aggregated statistics are used for bicycle crash risk calculations. Thus, the understanding of spatial patterns at local scale levels remains vague. Using an agent-based flow model and a bicycle crash database covering 10 continuous years of observation allows us to calculate and map the crash risk on various spatial scales for the city of Salzburg (Austria). In doing so, we directly account for the spatial heterogeneity of crash occurrences. Additionally, we provide a measure for the statistical robustness on the level of single reference units and consider modifiable areal unit problem (MAUP) effects in our analysis. This study is the first of its kind. The results facilitate a better understanding of spatial patterns of bicycle crash rates on the local scale. This is especially important for cities that strive to improve the safety situation for bicyclists in order to address prevailing safety concerns that keep people from using the bicycle as a utilitarian mode of (urban) transport. Keywords: bicycle; crash; risk; geographical information systems (GIS); spatial analysis; scale; modifiable areal unit problem (MAUP)

1. Introduction Road safety should be an integral part of any effort to promote the bicycle as a sustainable, healthy, and cost-efficient mode of transport. There is strong evidence from the literature that safety concerns are among the most relevant reasons that keep people from using the bicycle for utilitarian trips [1–5], although positive environmental [6,7] and health effects [8–12] are apparent. The need for evidence-based planning approaches that aim for the provision of safe infrastructure brings risk calculations for bicyclists into the focus. Risk (also referred to as incident- or crash-rate [13,14]) in the context of this study is defined by the ratio of incidents to the underlying population (exposure data) within the time of investigation (10 years). Risk calculations, based on geolocated crash records, allow for the identification of dangerous areas and help to allocate resources and interventions efficiently. Generally, it can be stated that the minimization of the risk of being involved in a bicycle crash is a pre-requirement for any comprehensive bicycle promotion strategy [2,15,16]; risk awareness is especially high amongst female bicyclists for children [17–20]. To date, risk calculations and derived maps are mainly based on aggregated statistics, with different levels of aggregation. On a national level (USA), Beck et al. [21] calculate a non-fatal injury rate of 1461 incidents per 100 million kilometers travelled. On the level of municipalities Vandenbulcke et al. [22] calculate an average casualty rate for Belgium of 7 per 10 million minutes cycled, with distinct regional, spatial patterns. The number of studies sharply decreases with the level of spatial aggregation. To our current knowledge Yiannakoulias et al. [23] is the only study that provides incident rates on the level of census districts. They calculated an average of 7.25–8.95 crashes per 100,000 km travelled, with a high spatial variability among census districts for the city of Hamilton (Canada). Safety 2016, 2, 17; doi:10.3390/safety2030017

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Although risk calculations based on spatially aggregated statistics are relevant for a number of purposes (e.g., comparing the safety performance of countries), they are of less value when it comes to concrete interventions within cities. Consequently, the need for methods that calculate and map bicycle crash risk patterns on the local scale is obvious. In doing so, implications, such as spatial heterogeneity and the modifiable areal unit problem (MAUP), must be addressed. With these aspects in mind, we developed a conceptual workflow for the identification of adequate spatial reference units (shape) and suitable levels of spatial aggregation (scale, size). This workflow is transferable, given that the necessary input data are available. Before we present a method for mapping bicycle risk patterns on the urban scale that is based on an extensive bicycle crash database and simulated bicycle flows as exposure data, we will set the stage for this research. We will first argue for why the investigation on the local scale level would contribute to a better understanding of bicycle safety within cities before we briefly discuss two essential implications of risk calculations on this scale level, namely the delineation of reference units and exposure data. 1.1. Spatial Heterogeneity Aggregated statistics do not allow for further differentiation within the respective reference units. Hence, these units are implicitly regarded as homogeneous. When it comes to spatial crash analysis, aggregation inevitably leads to generalization and information loss; variabilities on the local scale level are not captured. This could lead to severe impacts on models, analysis results and derived conclusions [24]. Several authors [25–28] propose methods for how to adequately account for spatial heterogeneity and autocorrelation in spatial risk models. Neglecting these fundamental spatial characteristics can lead to severely biased models. Lassarre and Thomas [29] point to the relevance of geographical disparities in epidemiological studies of road mortalities. In their study they demonstrate how spatial patterns of road mortalities in Europe change with the level of aggregation (NUTS0, NUTS1, and NUTS2). On the scale of a city, Loidl et al. [30] made the high spatial variability and temporal dynamic of bicycle crash locations visible. Their study calls for risk calculations on the local scale that account for the high degree of spatial heterogeneity. Investigating spatial patterns of road crashes, Anderson [31] found distinct spatial clusters within the city of London. This means that an even distribution of crash locations on a local scale cannot be assumed. While the cluster detection algorithm in Anderson [31] is designed for the planar space, Okabe et al. [32] considered the network-bound character of road crashes. Their kernel density estimation of crash locations is network-based. However, spatial clusters of crashes in a test area in Tokyo become evident as well. Xie and Yan [33] extended this approach and introduced a significance test for spatial clusters, based on completely random and conditional Monte Carlo simulations. For both methods they found significant spatial clusters of road crashes in Bowling Green, Kentucky. Depending on the purpose, risk calculations that are used as evidence basis for informed decisions on infrastructure improvements, road surveillance, and other targeted measures for better road safety, need to account for the spatial heterogeneity within the area under investigation. Therefore, disaggregated statistics with small reference units seem to be preferable. However, as it is demonstrated in Figure 1 for different spatial distribution patters, two aspects arise instead. Firstly, the number of reference units with 0 observations increases with the decrease of the reference unit size. Consequently the histogram is strongly skewed [27]. Secondly, the definition of arbitrary spatial reference units inevitably implies the modifiable areal unit problem (MAUP).

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(a)

(b)

Figure 1. Depending on the spatial distribution, the level of spatial aggregation implies spatial Figure 1. heterogeneity Depending the spatial distribution, level of spatialand aggregation implies spatial andon MAUP: (a) Aggregated statistics: the Spatial heterogeneity; (b) Dissaggregated heterogeneity and MAUP: (a) Aggregated statistics: Spatial heterogeneity; and (b) Dissaggregated statistics: Skewed histogram and MAUP.

(a) and MAUP. statistics: Skewed histogram

(b) 1.2. Definition of Spatial Reference Units Figure 1. Depending on the spatial distribution, the level of spatial aggregation implies spatial Generally, definition ofAggregated fixed spatial reference unitsheterogeneity; is a trade-off and between spatial details heterogeneity and MAUP: Units (a) statistics: Spatial (b) Dissaggregated 1.2. Definition of Spatialthe Reference (heterogeneity) andhistogram statistical of analyses that build upon these aggregates. statistics: Skewed and robustness MAUP. Independently from the level of aggregation, patterns might biased by between the MAUP. spatial The Generally, the definition of fixed spatial derived reference units is abetrade-off details MAUP effectof can be observed for regular (hex-, square-grid) andupon irregular (administrative 1.2. Definition Spatial Reference Units (heterogeneity) and statistical robustness of analyses that build these aggregates.units) Independently reference units. It describes the effect of scale or level of spatial aggregation (Figure 2a) and of zoning from the level of aggregation, derived patterns be biased the MAUP. The spatial MAUPdetails effect can be Generally, the definition of fixed spatialmight reference units isby a trade-off between (Figure 2b) [34]. Although the MAUP effect can be quite large, it is hardly ever explicitly addressed (heterogeneity) and statistical robustness of analyses that build upon these aggregates. observed for regular (hex-, square-grid) and irregular (administrative units) reference units. in risk calculations for bicycle crashes. Frequently spatial reference units are defined by pragmaticIt describes Independently from the level of aggregation, derived patterns might beInformation biased by 2b) the MAUP. The reasons, as the availability of statistical(Figure data. In2a) the and Geographical Systems for the effect of scale such or level of spatial aggregation of zoning (Figure [34]. Although the MAUP effect(GIS-T) can beliteratures observed[35,36], for regular (hex-,issquare-grid) and irregular (administrative units) Transport the MAUP primarily dealt with in the context of transport MAUP effect can be quite large, it is hardly ever explicitly addressed in risk calculations for bicycle reference units. It describes the effect scaleanalysis or level of spatial aggregation 2a) and zoning modelling, where the delineation ofof traffic zones (TAZ) raises the(Figure modifiable arealofunit crashes.(Figure Frequently spatial reference unitseffect are can defined by large, pragmatic reasons, such as the availability of 2b) Thomas [34]. Although MAUP beamong quite it studies is hardly ever problem. [37] andthe Abdel-Aty et al. [28] are the few that dealexplicitly with the addressed MAUP statistical data. In theofGeographical Information Systems for Transport (GIS-T) literatures in in risk for analysis bicycle crashes. Frequently spatial reference units are defined thecalculations context crash and modelling. However, to our current knowledge, there isbynopragmatic study[35,36], the bicycle riskas calculation and mapping, which the MAUP. MAUP reasons, ison primarily dealt in the context of explicitly transport where the delineation such the with availability of statistical data. In considers themodelling, Geographical Information Systems forof traffic

(GIS-T) literatures [35,36], the areal MAUPunit is primarily dealt with in[37] the and context of transport analysisTransport zones (TAZ) raises the modifiable problem. Thomas Abdel-Aty et al. [28] modelling, where the delineation of traffic analysis zones (TAZ) raises the modifiable areal unit are among the few studies that deal with the MAUP in the context of crash analysis and modelling. problem. Thomas [37] and Abdel-Aty et al. [28] are among the few studies that deal with the MAUP However, to our current knowledge, there is no study on bicycle risk calculation and mapping, which in the context of crash analysis and modelling. However, to our current knowledge, there is no study explicitly MAUP.and mapping, which explicitly considers the MAUP. on considers bicycle risk the calculation

Figure 2. MAUP effect. (a) scale effect; and (b) zoning effect.

1.3. Exposure Data A major reason for why most risk calculations are based on highly aggregated statistics is the lack of adequate exposure data on a local scale [13]. A recent Organization for Economic Co-operation and Development (OECD) [38] report on this topic states, “The lack of exposure data is a real Figure 2. effect. (a) of scale effect;safety and (b)and zoning effect. the assessment of hindrance to understanding theMAUP current status cycling complicates Figure 2. MAUP effect. (a) scale effect; and (b) zoning effect. cycling policies” (p. 61). This statement is confirmed by virtually any study on bicycle risk 1.3. Exposure Data calculations. International comparisons of safety performance tend to be biased by the heterogeneous 1.3. Exposure Data quality of the exposure data.most Tracing the data are sources ofon such studies (e.g., [16,20]) reveals A major reason for why riskback calculations based highly aggregated statistics is the extensive variabilities in spatial and temporal coverage. In addition to compiled statistics based on lack of adequate exposure data on a local scale [13]. A recent Organization for Economic Co-operation A major reason for why most risk calculations are based on highly aggregated statistics is the lack multiple statistic agencies, exposure variables are commonly derived from household travel surveys and Development (OECD) [38] report on this topic states, “The lack of exposure data is a real of adequate exposure data on a local scale [13]. A recent Organization for Economic Co-operation and [21], census data [23,39], and travel diaries [14]. Data from these sources are samples that require hindrance to understanding the current status of cycling safety and complicates the assessment of model-based extrapolations in order to get full population data. Development (OECD) [38] report on this topic states, “The lack of exposure data is a real hindrance to cycling policies” (p. 61). This statement is confirmed by virtually any study on bicycle risk Alternative sources for exposure data are not exploited yet. To our current knowledge there are understanding the current status of cycling safetyperformance and complicates thebiased assessment of cycling policies” calculations. comparisons of safety to be by the heterogeneous no bicycle International risk analyses that rely on mobile phone, tracking tend or VGI data as exposure variables. (p. 61). quality This statement is confirmed by virtually any study on bicycle risk calculations. International of the exposure Tracingofback sources of such [16,20]) reveals However, studies revealdata. the potential thesethe datadata sources as proxies for studies collective(e.g., mobility [40–42].

extensive variabilities in spatial tend and temporal coverage. In heterogeneous addition to compiled statistics on comparisons of safety performance to be biased by the quality of thebased exposure data. agencies,ofexposure variables are [16,20]) commonly derived from household travel surveys Tracing multiple back thestatistic data sources such studies (e.g., reveals extensive variabilities in spatial and [21], census data [23,39], and travel diaries [14]. Data from these sources are samples that require temporal coverage. In addition to compiled statistics based on multiple statistic agencies, exposure model-based extrapolations in order to get full population data. variables are commonly derived from household surveys census data [23,39], Alternative sources for exposure data are not travel exploited yet. To [21], our current knowledge there and are travel diaries [14]. Data from these sources are samples that require model-based extrapolations in no bicycle risk analyses that rely on mobile phone, tracking or VGI data as exposure variables.order to get full However, population data. studies reveal the potential of these data sources as proxies for collective mobility [40–42]. Alternative sources for exposure data are not exploited yet. To our current knowledge there are no bicycle risk analyses that rely on mobile phone, tracking or VGI data as exposure variables. However, studies reveal the potential of these data sources as proxies for collective mobility [40–42].

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Together with the severe underreporting of bicycle crashes in general [43–45], the lack of adequate exposure data has, of course, far-reaching implications for the reliability and robustness of risk models. This holds especially true for models and analyses on the local scale, where hardly any of the existing approaches on the regional and national scale meet the demands in terms of accuracy and spatial resolution. 2. Method In order to provide reliable bicycle crash risk analyses on the local scale level, while considering the issues discussed in the previous section, we followed an iterative workflow which helps to identify adequate reference units and tests the robustness of crash rates for various unit sizes. We demonstrate the applicability of the workflow in a case study from Salzburg (Austria). 2.1. Study Site Located in the northern Alps of Austria, the city of Salzburg, capital of the homonymous province, has roughly 150,000 inhabitants. Another 150,000 people live in the larger agglomeration, within a radius of 15 km from the city center. Thus, the city has a catchment of approximately 300,000 inhabitants within cycling-distance. The road network of the study area (city of Salzburg), which is legally relevant for bicycle traffic has a total length of 1045 km. Within the city a total of 320 road km are equipped with some kind of bicycle infrastructure, ranging from separated bicycle ways to opened one-way roads with painted on-road cycle lanes. According to the latest available figures, Salzburg has a 20% share of the bicycle in the total modal split [46]. The reasons for the popularity of the bicycle as utilitarian mode of transport are manifold. The flat topography, high-quality bicycle infrastructure along main corridors, short distances and a good accessibility of central facilities are commonly regarded as major attractors. 2.2. Crash Data The crash data used for this study consists of over 3000 police crash reports and covers a time period of 10 years (2002–2011). The federal bureau of statistics (Statistik Austria) is responsible for crash data collection in Austria and publishes an annual national road crash report. Usually, the collected and processed police reports are reported back to the respective authorities. In the case of the city of Salzburg, the department of urban planning and transport maintains the crash database for all road incidents within the city. This authoritative dataset is exclusively fed by police reports. Hence, hospital records [47], insurance claims [48], crowdsourced information [49], or other alternative data sources are not included. No estimations for the underreporting rate of bicycle crashes exist for the city of Salzburg. However, indications for the dimension of the problem are available in the literature. Watson et al. [44] showed that two thirds of bicycle crashes that were reflected in hospital data could not be linked to police reports in Queensland (Australia). De Geus et al. [14] estimate a fraction of only 7% of all minor crashes are being reported to the police in Belgium. Similar underreporting rates are presented by Janstrup et al. [50] for the Danish province of Funen. Although these rates cannot be directly transferred to the city of Salzburg, we must be aware that the data used in this study might only cover a maximum of one third of all crashes. However, it can be assumed that regions with an increased crash risk can be identified with the proposed workflow, because crashes with severe injuries and high material damage tend to be captured more probably by police reports. For the purpose of this study crash reports, with at least one involved bicyclist and valid location information, were extracted from the database. A total of 3045 geolocated crash reports between January 2002 and December 2011 met both criteria and were thus considered for further analysis; 51 crash reports suffered from invalid location information. In the present case, only location information for the risk calculation was relevant. Thus, associated data about the involved parties, liabilities and crash details were not considered.

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Safety 2016,Variable 2, 17 2.3. Exposure

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As 2.3. demonstrated Exposure Variablein Section 1.3, commonly employed exposure data is not suitable for the mapping of local risk patterns. Thus, we used the results from a spatial simulation of bicycle flows as As demonstrated in Section 1.3, commonly employed exposure data is not suitable for the the exposure variable for this study. For details concerning the agent-based simulation model itself we mapping of local risk patterns. Thus, we used the results from a spatial simulation of bicycle flows as refer the to Wallentin and Loidl exposure variable for [51]. this study. For details concerning the agent-based simulation model itself The agent-based model (ABM) simulated the total number of traverses per segment for one day we refer to Wallentin and Loidl [51]. (6 June 2014). Segments model are the(ABM) spatial increment of the digital of thefor road The agent-based simulated the total number of representation traverses per segment one network. day (6 case, June 2014). Segments are the spatial increment of undirected the digital representation of nodes the roadcorrespond network. In with In our the road network was modelled as an graph, where our case, road network was modelled as an undirected graph, where nodes junctions and the edges with segments. In accordance with Yiannakoulias et al. [23]correspond we did notwith employ junctions and edges with segments. In accordance with Yiannakoulias et al. [23] we did not employ the number of traverses (or trips) as the exposure variable, but the total distance travelled. Thus, the the number of traverses (or trips) as with the exposure variable, but theBased total distance Thus, number of traverses was multiplied the segment length. on the travelled. simulation of the a single number of traverses was multiplied with the segment length. Based on the simulation of a single day day and counting data for the whole year 2014 the flows (total distance travelled) were extrapolated and counting data for the whole year 2014 the flows (total distance travelled) were extrapolated accordingly (Figure 3). This extrapolation exhibits a certain degree of generalization, as the implicit accordingly (Figure 3). This extrapolation exhibits a certain degree of generalization, as the implicit assumption is that variabilities over distributedover overspace. space. assumption is that variabilities overtime timeare areevenly evenly distributed

(a)

(b)

Figure 3. The simulated flow for 6 June (a) is extrapolated according to averaged counting data from

Figure 3. The simulated flow for 6 June (a) is extrapolated according to averaged counting data from two central, permanently counting stations (induction loops) (b). two central, permanently counting stations (induction loops) (b).

The crash data covered the years from 2002 to 2011. Unfortunately no counting data was available entire the time period. we2011. multiplied the simulated annualdata flowwas byavailable 10, The crashfor datathe covered years fromThus, 2002 to Unfortunately no counting disregarding the change of bicycle traffic over time. For the current state of research this degree of the for the entire time period. Thus, we multiplied the simulated annual flow by 10, disregarding generalization was tolerated, since alternative exposure variables are by far less suitable for the change of bicycle traffic over time. For the current state of research this degree of generalization was purpose of local risk mapping and the focus of this study was on spatial patterns. tolerated, since alternative exposure variables are by far less suitable for the purpose of local risk mapping and the focus of this study was on spatial patterns. 2.4. Conceptual Workflow The aim of this study was to map bicycle risk patterns on the local scale, in order to account for 2.4. Conceptual Workflow spatial variabilities adequately (see Figure 4 for the overall workflow). Although the geolocated crash

The of simulated this studyflow waswould to map bicycle patternson onthe the local scale, in orderthe todata account data aim and the allow for riskrisk calculations level of road segments, for spatial variabilities adequately (see Figure 4 for the overall workflow). Although thesuitable geolocated was aggregated for the sake of statistical robustness. Consequently, the decision on the most crashspatial data and the simulated flow allow was for risk calculations on the of road segments, reference unit (level of would aggregation) a trade-off between the level amount of spatial heterogeneity and the size of the confidence interval of the risk calculation. Additionally, the MAUP the data was aggregated for the sake of statistical robustness. Consequently, the decision on the most was spatial to be considered. suitable reference unit (level of aggregation) was a trade-off between the amount of spatial In order testsize the of type reference unit and the of the unit size, Additionally, irregular and regular heterogeneity andtothe theofconfidence interval of effect the risk calculation. the MAUP reference units were defined. Additionally, network-based reference units were generated (for the was to be considered. algorithm for the delineation of network-based units we refer to Loidl et al. [30]). In order to test the type of reference unit and the effect of the unit size, irregular and regular reference units were defined. Additionally, network-based reference units were generated (for the algorithm for the delineation of network-based units we refer to Loidl et al. [30]).

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Each reference unit was overlaid with the geolocated crash reports and the total distance travelled. The high standard deviations for the number of crashes per reference unit in Table 1 Safetyindicate 2016, 2, 17that crash locations and bicycle flows are unevenly distributed over space, what is in line 6 of 16 with a previous study [30,31]. For the present study the following spatial reference units were tested.

Figure 4. Conceptual workflow of the study. Figure 4. Conceptual workflow of the study. Table 1. Descriptive statistics of spatial reference units. Number of crashes and the total distance

Eachtravelled reference unitcovers was overlaid with geolocated crash reports and the total distance travelled. (in km) a time period of the 10 years. The high standard deviations for the number of crashes per reference unit in Table 1 indicate that Number of Mean Min-Max Number of Total Distance crash locations Type and bicycle flows are unevenly distributed over space, what is in line with a previous Units Size/Length Size/Length Crashes Travelled study [30,31]. For the present study the following spatial reference units were tested. City 3045 211,881,301.3 1 65.66 km2 boundary Table 1. Descriptive statistics of spatial reference units. Number of crashes and the total distance Census(in km) covers a time period of 10 years. xത = 6,621,290.67 xത = 95.16 travelled 0.32–9.41 km2 32 2.05 km2 σ = 59.58 σ = 4,480,156.25 districts Number of Mean Min-Max Number of Distance xത = 761.75 xത Total = 53,341,757.43 Type Units Size/Length Size/Length Crashes Travelled 4 29.74 km2 σ = 435.82 σ = 24,541,406.77 City boundary 1 3045 211,881,301.3 65.66 km2 xത = 15,240,502.12 xത = 199.44 16 7.44 km2 2 x = 95.16 x = 6,621,290.67 32 Census districts σ σσ==17,510,622.49 2.05 km 0.32–9.41 km2 σ= = 296.63 59.58 4,480,156.25 Square grid ത = 47.61 x ത = 4,183,667.25 x x = 761.75 x = 53,341,757.43 2 644 1.86 29.74km km2 σσ==435.82 σσ== 24,541,406.77 95.22 5,541,589.9 16 256

7.44km km2 2 0.46

--

64

1.86 km2 16.24 km2

-

256 37

0.46 km2 2.60 km2

-

9

16.24 km2 0.65 km2

-

Square grid

9

Hex grid

Hex grid

Network voronoi

130 37

11.90 xxത==199.44 σσ==296.63 27.08 47.61 = 338.56 xതx = σ = 95.22 σ = 493.56 x = 11.90 82.35 σxത == 27.08 132.82 xσ== 338.56 σxത==493.56 23.44

xത = 15,240,502.12 1,212,312.67 σ 17,510,622.49 σ= = 1,907,209.11 4,183,667.25 xത x==23,707,769.77 σ = 5,541,589.9 σ = 30,431,269.94 x = 1,212,312.67 xതσ ==5,766,754.81 1,907,209.11 σ = 7,407,292.35 x = 23,707,769.77 30,431,269.94 xതσ = 1,680,078.17

2.60 km2

-

447 130

0.16 km2 0.65 km2

-

2190 447

0.03 km2 2 0.16 km

--

25 2190

29.8 0.03km km2

- km 7.23–59.23

xതx ==119.32 1.39 σ = 3.41 σ = 121.17

5,766,754.81 σx ==2,442,302.80 σ = 7,407,292.35 xത = 484,887.14 x = 1,680,078.17 σ = 822,243.05 σ = 2,442,302.80 xത = 98,364.95 x = 484,887.14 σσ==203,197.45 822,243.05 xത =x108,489,485.02 = 98,364.95 = 203,197.45 σ =σ116,657,894.47

5025

14.9 29.8km km

0.96–38.94 km 7.23–59.23 km

xxത==119.32 59.82 σ = 121.17

108,489,485.02 xതx = = 54,245,335.48 σ = 116,657,894.47

50

14.9 km

0.96–38.94 km

x = 59.82 σ = 68.12

x = 54,245,335.48 σ = 97,581,581.05

75

9.93 km

0.27–22.66 km

x = 39.97 σ = 49.34

x = 36,162,789.35 σ = 64,971,853.35

100

7.45 km

0.56–25.45 km

x = 29.96 σ = 38.99

x = 27,122,440.62 σ = 62,068,620.58

Network voronoi

xσ== 82.35 43.46 σ = 132.82 xത = 6.82 x = 23.44 σ = 13.13 σ = 43.46 xത = 1.39 x = 6.82 3.41 σσ==13.13

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Based on the number of crashes and the simulated total distance travelled, the risk was calculated for each reference unit. These crash rates were only calculated for reference units where both crash data and simulated flows were available. When these risk calculations had been mapped, spatial patterns emerged. The problem with bicycle crashes is that they are rare events and it is decisive for any interpretation to identify random occurrences. Thus, a measure is required that determines the robustness of derived risk calculations (crash rate). In order to do so, a 95% confidence interval was calculated for each reference unit applying an exact binomial test [52] as implemented in the open source software package “R” (https://www.r-project.org/). The size of the confidence interval indicates the robustness of risk calculations and helps to interpret crash rates. The larger the confidence interval, the lower is the statistical robustness, and the higher is the chance that the calculated risk is the product of random processes or an artefact. In order to provide information about the quality of calculated crash rates, the risk map was complemented with mapped confidence interval sizes. With regard to the trade-off between spatial heterogeneity and statistical robustness we made use of a scatterplot with logarithmically scaled axes. With this, we were able to plot the calculated risk, the number of accidents and the size of the confidence interval. Based on this scatterplot, reference units with a maximum visual compactness could be identified. Together with the mapped crash rates and confidence intervals, the scatterplot served as a decision basis for the choice of appropriate reference units. MAUP effects could be identified through the link of map series and the scatterplot. 3. Results As it becomes obvious in Figure 5, crash locations are not evenly distributed over space, but clustered. This spatial heterogeneity cannot be captured when the city is investigated as a whole. On average 1.43 crashes per 100,000 km cycled (95% Confidence Interval (CI) [1.38 . . . 1.48]) occurred during the 10 years of investigation. Aggregating the data to census districts reveals distinct patterns of risk distribution. Interestingly the frequency of crash occurrences does not directly correspond with the crash rate. The highest crash rates emerge north of the city center and in the very east-most region. However, the high risk in the eastern district can be identified as an artifact by the mapped confidence interval. For this area a very low flow was simulated because the model concentrated on utilitarian trips. The statistical district in the east covers a mountainous area with lots of leisure cycling. Consequently, the number of crashes is disproportionately high in relation to the simulated total distance traveled. In contrast to this particularity, the comparable high risk in the districts around the city center is statistically more robust and should, thus, be subject to further analyses.

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(a)

(b)

Figure Figure5.5.Crash Crashlocations locations(a); (a);Risk Riskcalculations calculationsfor forthe thewhole wholecity cityofofSalzburg Salzburgand andcensus censusdistricts districts(b). (b).

Different to census districts, regular reference units are equal in size. On the one hand this helps in the interpretation of results because there is no need to control for the area. On the other hand, underlying structures are not considered in the definition of the reference units and, thus, the MAUP becomes an eminent issue. In the present case regular reference units are primarily used to calculate crash rates for various levels of aggregation.

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Although natural barriers (river, railway, etc.) and population density are commonly considered in the definition of census districts, they are still hard to compare. Additionally, phenomena that are not constituted by a static population but by dynamic elements (e.g., bicycle traffic flows generated by commuters) are not fully captured by census districts. In our case major corridors with high volumes of in- and out-flux are relevant. This becomes evident when considering the statistical district in the very north-most region. It covers a large area and the calculated crash rate is relatively high. In fact, there is an important bicycle corridor, connecting the city center with the adjacent municipality along (a) (b) are hardly any other crash a primary road. The crashes are concentrated along this road, while there locations in 5.the whole district. the spatialfor heterogeneity this district is high and (b). calls for Figure Crash locations (a);Thus, Risk calculations the whole citywithin of Salzburg and census districts further disaggregation. Different Different to to census census districts, districts, regular regular reference reference units units are are equal equal in in size. size. On On the the one one hand hand this this helps helps in the interpretation of results because there is no need to control for the area. On the other hand, in the interpretation of results because there is no need to control for the area. On the other hand, underlying underlying structures structures are are not not considered considered in in the the definition definition of of the the reference reference units units and, and, thus, thus, the the MAUP MAUP becomes In the the present becomes an an eminent eminent issue. issue. In present case case regular regular reference reference units units are are primarily primarily used used to to calculate calculate crash crash rates rates for for various various levels levels of of aggregation. aggregation. Hex grids are arethe themost mostcompact compactunits units that cover entire planar space without Hex grids that cancan cover the the entire planar space without gaps.gaps. This This explains their popularity in domains that deal with continuous phenomena, such as ecology [53]. explains their popularity in domains that deal with continuous phenomena, such as ecology [53]. Apart from the type of the reference unit, the size strongly influences the patterns that emerge. Figure 6 Apart from the type of the reference unit, the size strongly influences the patterns that emerge. Figure maps thethe risk calculations forfor five different levels of aggregation. TheThe smaller the the reference units, the 6 maps risk calculations five different levels of aggregation. smaller reference units, better local particularities are mapped. However, as the reference units with the two lower levels of the better local particularities are mapped. However, as the reference units with the two lower levels aggregation cover onlyonly veryvery small areasareas each,each, they they are prone to extreme outliers (as the(as range values of aggregation cover small are prone to extreme outliers theof range of in the legend indicates) and artifacts. TheseThese valuesvalues can only be interpreted in conjunction withwith the values in the legend indicates) and artifacts. can only be interpreted in conjunction mapped confidence intervals. the mapped confidence intervals.

Figure 6. Risk calculations for regular hex grids (for cell sizes see Table 1). Figure 6. Risk calculations for regular hex grids (for cell sizes see Table 1).

Mapping the risk calculations based on square grids reveals patterns that are in some parts Mapping the hex riskgrid calculations based square grids reveals that are in Comparing some parts different from the (Figure 7). This on is due to the shape and topatterns the respective size. different from the hex grid (Figure 7). This is due to the shape and to the respective size. Comparing the two maps in the center nicely demonstrates the MAUP (scale effect). Whereas the map with the the two maps inof the center nicely demonstrates therisk MAUP theismap with at thea higher level aggregation shows a rather low level(scale in theeffect). north, Whereas the pattern different higher levelofofaggregation. aggregationHowever, shows a again, ratherthe low risk level in the north, pattern is lower level mapped confidence intervalthe is decisive fordifferent judging at a lower level of aggregation. However, again, the mapped confidence interval is decisive for judging on the quality (statistical robustness) of this local particularity. The square grid maps with different levels of aggregation (Figure 7) demonstrate the spatial heterogeneity within aggregated units. Decomposing the reference unit in the northwest of the map with the highest level of aggregation

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on the quality Safety 2016, 2, 17

(statistical robustness) of this local particularity. The square grid maps with different 9 of 16 on the of quality (statistical robustness) of this local particularity. The squarewithin grid maps with different levels aggregation (Figure 7) demonstrate the spatial heterogeneity aggregated units. levels of aggregation (Figure 7) in demonstrate theofspatial heterogeneity within aggregated units. Decomposing the reference unit the northwest the map with the highest level of aggregation reveals the variability within this aggregate. In the present case it becomes obvious that the areas with Decomposing the reference unit the northwest ofpresent the mapcase with highest level ofthat aggregation reveals the variability within thisinaggregate. In the it the becomes obvious the areas areveals high crash rate are concentrated along a corridor. the variability within this aggregate. the present case it becomes obvious that the areas with a high crash rate are concentrated along aIncorridor. with a high crash rate are concentrated along a corridor.

Figure 7. Risk calculations for regular square grids (for cell sizes see Table 1). Figure 7. Risk calculations for regular square grids (for cell sizes see Table 1). Figure 7. Risk calculations for regular square grids (for cell sizes see Table 1).

As argued before, bicycle crashes are network-bound incidents. Thus, planar reference units As before, are incidents. Thus, planar reference units As argued argued before, bicycle bicycle crashes degree, are network-bound network-bound incidents. Thus, planarresults. reference units neglect this characteristic to a crashes certain which can lead to biased analysis Take for neglect this characteristic to a certain degree, which can lead to biased analysis results. Take for neglect this characteristic to a certain degree, which can lead to biased analysis results. Take for example two locations with a significantly high number of crashes. In reality these two locations are example two significantly high number of crashes. In two are example two locations locations with significantly highother, number of only crashes. In reality reality these these twoislocations locations are disconnected (e.g., by awith river)aa but close to each when the Euclidean distance considered. disconnected (e.g., by a river) but close to each other, when only the Euclidean distance is considered. disconnected (e.g., bythese a river) but close toare each other, when onlysame the Euclidean distanceunit, is considered. It might happen that two locations aggregated to the spatial reference indicating It happen that these two the spatial unit, It might happen that these two locations locations are aggregated to the same same spatial reference reference unit, indicating indicating anmight area with high risk, although there isare noaggregated relation in to reality. Considering this argument, we also an area with high risk, although there is no relation in reality. Considering this argument, an areadifferent with high risk, although there is units no relation in reality. Considering we also also tested network-based reference (for details refer to [30,54]). this argument, we tested different network-based units details refer testedFigure different network-based reference units (for (for detailsunits referto to[30,54]). [30,54]). 8 shows the effect ofreference network-based reference on the emerging patterns. Depending Figure shows the ofofnetwork-based reference onon thethe emerging patterns. Depending on Figure shows theeffect effectregions network-based reference emerging patterns. Depending on the level88of aggregation, in the network withunits aunits high crash rate become obvious that tend the level of aggregation, regions in the network with a high crash rate become obvious that tend to be on thehidden level ofinaggregation, regions in the network with a7,high crash rate become obvious that tend to be planar reference units. Similar to Figure the MAUP effect can also be observed in hidden in planar reference units. Similar to Figure 7, the MAUP effect can also be observed in this case to be hidden in planar reference units. Similar to Figure 7, the MAUP effect can also be observed in this case (see the reference units with high risk in the east). (see units withunits highwith risk high in therisk east). this the casereference (see the reference in the east).

Figure 8. Risk calculations network-based reference units (100, 75, 50, and 25 units from left to Figure right). 8. Risk calculations network-based reference units (100, 75, 50, and 25 units from left to Figure 8. Risk calculations network-based reference units (100, 75, 50, and 25 units from left to right). right).

Whereas spatial patterns become obvious from maps, the statistical distribution of crash rates Whereas spatial patterns become obvious from maps, thethe statistical distribution of crash ratesrates and Whereas spatial patterns become obvious from maps, statistical distribution offorcrash and confidence intervals remains hidden. Therefore, we link maps with a scatterplot each type confidence intervals remains hidden. Therefore, we link the maps with a scatterplot for each type of and confidence intervals Therefore, we link thereference maps with a scatterplot for each type of reference unit. Figure 9remains shows hidden. the result for the square grid units. reference unit. Figure 9 shows the result for the square grid reference units. of reference unit. Figure 9 shows the result for the square grid reference units.

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The scatterplot, together with the maps help to identify outliers and to decide on an optimal The scatterplot, together with purpose. the maps The help visual to identify outliers and optimal level level of aggregation for a given compactness of to thedecide pointsoninanthe scatterplot of aggregation for a given purpose. The visual compactness of the points in the scatterplot indicates indicates the similarity of the reference units. Generally there is a direct relation between the size of the the reference units. Generally there is a direct relation between the size ofinthe reference the similarity reference of units (generalization through aggregation) and the visual compactness scatterplot. units (generalization through aggregation) and the visual compactness in scatterplot. However, in less the However, in the case illustrated in Figure 9, the higher level of aggregation (orange dots) is case illustrated in Figure 9, the higher level of aggregation (orange dots) is less compact (higher range compact (higher range of values on both axes) than the finer grid (green dots). In this case one might of values on both finer (greenas dots). In this case one the might conclude thatstatistical the finer conclude that theaxes) finerthan grid the is to be grid preferred, it better represents spatial and the grid is to be preferred, as it better represents the spatial and the statistical distribution. distribution.

Figure 9. 9. Based Based on onemerging emergingpattern patternininthe thescatterplot scatterplotdecisions decisions size reference Figure onon thethe size of of thethe reference unitunit cancan be be made. Linked with map, outliers be identified located. made. Linked with thethe map, outliers cancan be identified andand located.

4. Discussion 4. Discussion The results results confirm confirm the the assumption assumption of of aa high high degree degree of of spatial spatial heterogeneity heterogeneity within within highly highly The aggregated reference units. However, the MAUP and random crash occurrences can bias the aggregated reference units. However, the MAUP and random crash occurrences can bias the emerging emerging examples significantly. In the following we want to discuss this trade-off referring to examples significantly. In the following we want to discuss this trade-off referring to selected results. selected results. 4.1. Spatial Heterogeneity and Local Particularities 4.1. Spatial Heterogeneity and Local Particularities Figure 10 demonstrates the additional insight that is gained from risk mapping on a local scale. Figure 10 demonstrates the of additional insight that iscaptured gained from mapping on a local scale. It reveals distinct spatial patterns risk, which are neither in therisk analysis of absolute numbers It reveals distinct spatial patterns of risk, which are neither captured in the analysis of absolute of crashes [30] nor in aggregated statistics. numbers crashes nortraffic in aggregated statistics. By farofthe most [30] bicycle occurs along the Salzach River in a north-south direction. From the By far the most bicycle traffic occurs along thealthough Salzach most River crashes in a north-south direction. From analysis on the local scale it can be concluded that occur along this corridor the analysis onrisk the is local scale it can be concluded thatisalthough most crashes occurand along corridor (Figure 5), the comparably low. The situation quite different in the north in this the south of (Figure 5), the risk is comparably low. The situation is quite different in the north and in the south of the city centre (the corridors are indicated in Figure 10). Here, the number of crashes is high in relation the city centre (the corridors are indicated in Figure 10). Here, the number of crashes is high in relation to the simulated volume. In both areas bicycle infrastructure (mixed cycle-/pedestrian way and to the simulated volume. In both areasroads bicycle infrastructure (mixedload. cycle-/pedestrian way and onon-road cycle lanes) runs along primary with a very high traffic Thus, dangerous situations road cycle lanes) runs along primary roads with a very high traffic load. Thus, dangerous situations inevitably occur at intersections where connector roads cross the bicycle infrastructure. In sum, it can inevitably occur at intersections where connector roads cross the bicycle infrastructure. sum,risk it can be concluded from this particular example, but also from the maps in Figures 5–8 thatInhigh is be concluded from this particular example, but also from the maps in Figures 5–8 that high risk is not not primarily a function of bicycle traffic volume (although the bias in the crash reports, namely the primarily a function bicycle traffic volume (although the bias inbut themore crashofreports, namely the overrepresentation of of bicycle-car collisions, need to be considered!), the combination of overrepresentation bicycle-car collisions, need to be considered!), but more of the combination of different modes andof infrastructure types. different modesthe andmapping infrastructure types. Generally, of crash risks on the local scale facilitates additional insights and Generally, the mapping of crash risks on the local scale additional insights and contributes to a better understanding of spatial variabilities of facilitates risk patterns. However, outliers contributes tothese a better understanding spatial of risk patterns. outliers might might distort emerging patterns.ofFrom thevariabilities example, mapped in FigureHowever, 10, one might conclude distort these emerging patterns. From the example, mapped in Figure 10, one might conclude that an extremely dangerous hot spot exists in the northeast of the study area. In fact, the high risk is due to

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the small population (total distance travelled). Therefore the confidence interval is very large; the single crash recorded in this reference unit can be regarded as random. In accordance with the maps Safety 2016, 2, 17 11 of 16 in Figures 5–8 the necessity for a statistical measure to judge on the robustness of the results becomes obvious. For independent events, which occur at rare intervals, the confidence interval determined Safety 2016, 2, 17 11 of 16 by an binomial test [52] is spot proven to in bethe an northeast adequate of measure, independent the type that anexact extremely dangerous hot exists the study area. In fact,from the high risk of is reference unit. Providing a(total measure fortravelled). the robustness of calculated crash rates is is very especially due to the small population distance Therefore the confidence interval large; the small population (total distance travelled). Therefore the confidence interval is very large; the important for small reference units and for areas atbethe periphery of the area under investigation, the single crash recorded in this reference canregarded regarded as random. In accordance with the single crash recorded in this reference unit unit can be as random. In accordance with the maps since the probability of artefacts is higher here than in more central areas. maps in Figures 5–8 the necessity for a statistical measure to judge on the robustness of the results in Figures 5–8 the necessity for a statistical measure to judge on the robustness of the results becomes becomes For independent events, which occur at rarethe intervals, the interval confidence interval obvious. obvious. For independent events, which occur at rare intervals, confidence determined determined an exacttest binomial [52] is to be an adequate independent by an exactby binomial [52] is test proven toproven be an adequate measure,measure, independent from thefrom typethe of type of reference unit. Providing a measure for the robustness of calculated crash rates is especially reference unit. Providing a measure for the robustness of calculated crash rates is especially important units and forfor areas at the periphery of the investigation, since importantfor forsmall smallreference reference units and areas at the periphery ofarea the under area under investigation, the probability of artefacts is higher here than in more central areas. since the probability of artefacts is higher here than in more central areas.

Figure 10. Spatial patterns, local particularities, and outlier detection.

4.2. Scaling and Zoning Effects (Modifiable Areal Unit Problem, MAUP) As conceptually discussed in Section 1.1, the MAUP affects the emerging patterns on the risk maps. Independently from the large confidence interval (Figure 7) for the reference unit mapped in Figure 11, the map Figure series illustrates both thelocal scaling and zoning effect. 10. Spatial Spatial patterns, patterns, particularities, and outlier detection. detection. Figure 10. local particularities, and outlier The mapped region is located at the periphery of the study area. This is why for some reference units no flows are simulated (in grey). Depending on the MAUP) level of aggregation and the size of the 4.2. Scaling Scaling and Zoning Zoning Effects (Modifiable (Modifiable ArealUnit UnitProblem, Problem, 4.2. and Effects Areal MAUP) reference unit respectively, the risk that is communicated by the map tends to be spatially As conceptually conceptually discussed discussed in in Section Section 1.1, 1.1, the the MAUP MAUP affects affects the the emerging emerging patterns patterns on on the the risk As overestimated. In fact, only 1/16 of the largest grid data is available. Therefore, the levelrisk of maps. Independently Independently from from the the large large confidence confidence interval interval (Figure 7) 7) for for the the reference reference unit unit mapped in in maps. aggregation (scaling) heavily influences the conclusion(Figure that might be drawn from themapped emerging Figure 11, the map series illustrates both the scaling and zoning effect. Figure the map series illustrates both the scaling and zoning effect. spatial11, pattern. The mapped region is located at the periphery of the study area. This is why for some reference units no flows are simulated (in grey). Depending on the level of aggregation and the size of the reference unit respectively, the risk that is communicated by the map tends to be spatially overestimated. In fact, only 1/16 of the largest grid data is available. Therefore, the level of aggregation (scaling) heavily influences the conclusion that might be drawn from the emerging spatial pattern.

(a)

(b)

Figure 11. 11. Simulated Simulated flows flows for for 10 10 years years (a) (a) and and example example for for MAUP MAUP effect effect (b). (b). Crash Crash locations locations are are Figure mapped as black dots. mapped as black dots.

The mapped region is located at the periphery of the study area. This is why for some reference units no flows are(a)simulated (in grey). Depending on the level (b) of aggregation and the size of the reference unit the risk is communicated by the map tends to (b). be spatially overestimated. Figure 11.respectively, Simulated flows for that 10 years (a) and example for MAUP effect Crash locations are mapped as black dots.

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In fact, only 1/16 of the largest grid data is available. Therefore, the level of aggregation (scaling) heavily influences the conclusion that might be drawn from the emerging spatial pattern. In addition to the scaling effect, Figure 11 also illustrates the zoning effect. The single crash location in the highlighted reference unit is located close to the boundary. Grid cells are, of course, an arbitrary decomposition of a continuous space. Shifting the whole grid, for example in south direction, would impact the mapped result in this case significantly. The risk for the respective cells would be 0 for all levels of aggregation. 4.3. Results and Limitations of the Proposed Workflow Producing map series with various types of reference units and different levels of spatial aggregation makes the influence of these parameters on the emerging spatial patterns visible. From the hex grid maps continuous corridors can be derived best and MAUP effects are minor. However, the result for the lowest level of aggregation exhibits a large degree of uncertainty. For the maps based on square grids we showed the effect of the reference unit’s size. Additionally, MAUP effects tend to occur often, due to the less compact shape compared to hex grids. The network-based reference units are valuable and provide additional insights, as the connectivity of locations is considered. Although the algorithm for generating these units aims to produce units of equal size, they are hard to compare. Hence MAUP effects impact the emerging patterns considerably. In sum, the case study demonstrates that, for a final decision on most optimal reference units, information on the robustness of the results and an overview of alternatives is necessary. Additionally, the purpose of the map (e.g., city overview versus in-depth investigation of a specific corridor) ultimately decides the type and size of the spatial reference units. As our approach heavily relies on models, the results exhibit a certain degree of generalization. This holds especially true for the agent-based simulation model and the extrapolation of the total distance travelled for the entire period from 2002 to 2011. However, there are no studies yet, which draw exposure data from full population surveys (see e.g., [13,14,21,23]). In addition to the quality of the exposure variable the crash data directly impacts the emerging patterns. We assume that more complete crash data would lead to slightly different results. For example, along the Salzach River the calculated risk is comparable low (Figure 10). This might be due to the severe underreporting of single-bike-crashes (SBC, [55]) and bicycle-bicycle collisions. Dealing with risk, not only de facto crashes, but also near misses are considered as relevant. Here additional data sources, such as the BikeMaps.org project [49], would complement conventional data sources. 5. Conclusions We have shown that mapping bicycle risk patterns on the local scale reveals relevant information, which aggregated approaches would not have been able to uncover. To our current knowledge this is the first study, which calculates crash rates on the local scale. The lack of adequate exposure data on this scale level has been the restricting factor up to recently. This can be overcome through the utilization of simulated bicycle flows as exposure variable. With the calculation of risk on the very local scale, the spatial heterogeneity is directly accounted for. On the other hand the issue of statistical robustness and the MAUP effect become eminent. In order to assess the quality of calculated crash rates, we calculated the 95% confidence interval for each spatial reference unit. These two information layers can be visually linked (as in Figures 5–8), overlaid (as in Figure 10, where the units are extruded proportionally to the size of the confidence interval) or plotted in a scatterplot (Figure 9). This way, we were able to identify outliers and artifacts and to facilitate valid interpretations of emerging spatial patterns. With regard to the MAUP effect we provided map series with different types of reference units (shape) and levels of spatial aggregation (size). This way we were able to make MAUP effects for bicycle risk patterns explicit. Although the results presented in this paper are specific for the city of Salzburg, the conceptual workflow is transferable to any city as long as geolocated crash reports and exposure data are available.

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The proposed workflow for mapping bicycle risk patterns on the local scale extends existing approaches in spatial risk analysis. In addition to methodological improvements that stem directly from the limitations discussed in the previous section, further research should focus on the following aspects:

•

•

•

•

Temporal dynamics: it is generally known from literature that crash occurrences depend on a number of influential variables. Among the most relevant is time. Future risk mappings on the local scale should consider temporal dynamics, such as weekday-weekend patterns or seasonality [30]. In conjunction with the spatial dimension this might help to launch effective and adaptable interventions for increased bicycle safety. Subgroups: existing studies suggest different behavior depending on gender, age or trip purpose [17–19]. It is to be investigated to which degree these differences are reflected in distinct spatial patterns. Crash types: in this study all crashes were considered equally. In order to allow for an adequate design and a prioritization of interventions, areas of high risk must be identified, considering the crash type and severity. Explanatory analyses: once the risk is estimated for particular areas, it is of greatest interest to reveal causal factors, which contribute to the risk. Current studies (for instance [47,56]) consider the spatial configuration mostly implicitly or neglect it at all. However, geographical information systems (GIS) provide a platform to relate multiple perspectives on the road space [57]. Consequently, findings from studies on risk patterns on the local scale level can be related to information on infrastructure, crowd-sourced user feedback, or results from traffic flow models in further analyses.

Acknowledgments: This research was conducted without external funding. The authors want to thank the city’s department of urban planning and transport for making the crash data available for research purposes. Wolfgang Trutschnig’s (Department of Mathematics, University of Salzburg) advice for testing the statistical robustness with an exact binomial test is greatly acknowledged. The discussions with our colleague Christoph Traun substantially helped to sharpen our line of argumentation. Our thanks also go to Julia Stepan for proof reading the manuscript. Author Contributions: Martin Loidl has designed the analysis workflow, conducted the analyses, mapped the results and wrote the manuscript, Gudrun Wallentin contributed the simulated flows of bicycle traffic, Robin Wendel was involved in data management and processing, Bernhard Zagel contributed to the study design. Conflicts of Interest: The authors declare no conflict of interest.

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