category: literaturenote citekey: boneranetworkwideroadcrash2024 title: "Network-wide road crash risk screening: A new framework" authors: "Bonera, Michela; Barabino, Benedetto; Yannis, George; Maternini, Giulio" year: 2024 date: 2024-00-00 2024 doi: 10.1016/j.aap.2024.107502 publication: "Accident Analysis & Prevention" url: "https://doi.org/10.1016/j.aap.2024.107502" zotero_key: C2WJXVZV zotero_storage: 6N5UKQ28 collections: transpordi_planeerimine folder: 001_artiklid/Road Safety Indicators firstAuthor: "Bonera, Michela"

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Accident Analysis and Prevention

journal homepage: www.elsevier.com/locate/aap

Network-wide road crash risk screening: A new framework

Michela Bonera a,* , Benedetto Barabino b,* , George Yannis ^c , Giulio Maternini ^b

^a Ufficio Studi, Ricerca e Sviluppo Brescia Mobilita ` S.p.A., Brescia, Italy
^b Department of Civil, Environmental, Architectural Engineering and Mathematics (DICATAM), University of Brescia, Brescia, Italy
^c Department of Transportation Planning and Engineering of the School of Civil Engineering at the National Technical University of Athens (NTUA), Athens, Greece

ARTICLE INFO

Keywords: Network wide screening Road crash risk Road infrastructure safety management Crash probability Crash severity Crash exposure

ABSTRACT

Network-wide road crash risk screening is a crucial issue for road safety authorities in governing the impact of road infrastructures over road safety worldwide. Specifically, screening methods, which also enable a proactive approach (i.e., pinpointing critical segments before crashes occur), would be extremely beneficial. Existing literature provided valuable insights on road network screening and crash prediction models. However, no research tried to quantify the risk of crash on the road network by considering its main components together (i.e., probability, vulnerability, and exposure).

This study covers this gap by a new framework. It integrates road safety factors, prediction models and a riskbased method, and returns the risk value on each road segment as a function of the probability of a crash occurrence and the related severity as well as the exposure model. Next, road segments are ranked according to the risk value and classified by a five-level scale, to show the parts of road network with the highest crash risk.

Experiments show the capability of this framework by integrating base map data, context information, road traffic data and five years of real-world crash data records of the whole non-urban road network of the Province of Brescia (Lombardy Region - Italy).

This framework introduces a valid support for road safety authorities to help identify the most critical road segments on the network, prioritise interventions and, possibly, improve the safety performance. Finally, this framework can be incorporated in any safety managerial system.

1. Introduction

The European Commission has updated the EU 96/2008/CE with EU Directive 1936/2019, to support Road Safety Authorities (RSAs) in governing the impact of road infrastructures over road safety. Although RSAs generally have the responsibility of managing, maintaining, and monitoring vast and extensive road networks, they have limited resources available to carry out intensive and detailed analysis or act over the whole network. Therefore, RSAs urgently need even more decision support tools to a priori identify critical roads (or sections) and prioritise interventions to improve their safety performance. Likewise, the ISO 39001 (2012) (International Organization for Standardization – ISO, 2012) was developed to provide private and public organisations with a support tool to improve their road safety performances and reduce the risk of fatal or severe road crashes. However, it does not provide any technical requirements for its implementation, nor it strictly defines the overall structure of the system itself. Hence, further work is necessary to set up an effective still low-intensive methodology for a risk-based road infrastructure predictive safety analysis, which can (i) include the recommendations provided by EU Directive 1936/2019 (i.e., the risk-based proactive approach), (ii) accommodate the implementation of the ISO 39001:2012, and (iii) work as a valuable and effective decision support procedure for the wide scale. A risk-based Road Network Screening (RNS) procedure may be a valuable answer to such need and is investigated in this paper.

RNS is applied as the very first stage of the overall Road Infrastructure Safety Management (RISM) process to evaluate the safety performance of a whole road network - at a large scale - and identify its most critical segments (e.g., Elvik, 2010; Park & Sahaji, 2013; Stipancic et al., 2019). RNS is not a novelty in the scientific field, and the literature is quite rich of existing methods, which represent a baseline for the definition of the new Risk-Based Road Network-Wide Screening (RB-RNWS). Generally, RNS is organised in three main stages: (i) network segmentation (by e.g., fixed length, sliding windows, homogeneous segment, high crash risk profile), (ii) network evaluation (by e.g., composite indicators, Crash Prediction Models (CPMs) for frequency and

E-mail addresses: michela.bonera@gmail.com (M. Bonera), benedetto.barabino@unibs.it (B. Barabino).

^* Corresponding authors.

severity crash estimations), and (iii) network ranking (by e.g., scales, ranges). Many studies were conducted about it (e.g., Borghetti et al., 2021; Boroujerdian et al., 2014; Elyasi et al., 2016; Ghadi and Tor¨ ok, ¨ 2019; Stipancic et al., 2019; Viera Gomes et al., 2018; Wang et al., 2011; Yannis et al., 2013; Association and of State Highway and Trans portation Officials - AASHTO, 2010; Association and of State Highway and Transportation Officials - AASHTO, 2014; Elvik, 2007; European Road Assessment Program - EuroRAP, 2020; Gupta and Bansal, 2018). As for ii), which is the key of RNS, several methods are used (Bonera et al., 2022a). They range from reactive approaches based on the analysis of historical road crash data (e.g., Gupta & Bansal, 2018; European Road Assessment Program, 2020, Borghetti et al., 2021), to more proactive approaches, which rely on the inherent safety characteristics of the network instead (e.g., Viera Gomes et al., 2018; Yannis et al., 2013), or apply Crash Prediction Models (CPMs). The last ones are preferable compared to other methods as they enable both a quantitative and qualitative estimate of specific factors over the expected frequency or severity of crashes (Association and of State Highway and Trans portation Officials - AASHTO, (2010), Association and of State Highway and Transportation Officials - AASHTO, (2014); Wang et al., 2011; Stipancic et al., 2019). Moreover, CPMs enable to implement more targeted and cost-effective actions to fix potential safety drawbacks in advance (Yannis et al., 2016; Ambros et al., 2018). Despite this highquality literature, existing CPMs do not fully respond to the development of a RB-RNWS (i.e., EU Directive 1936/2019): as far as the authors know, a road crash risk model that complies with the definition of risk still misses from the literature. A handful of studies tried to formalise a risk-based analysis through the implementation of CPMs (Persaud et al., 2010; Persia et al., 2016; Ambros et al., 2018); however, they did not account for all the three risk components (i.e., crash occurrence, crash severity, and crash exposure), according to its the well-known definition nor model the exposure factor as a function of traffic-related predictors. In addition, just a handful of studies applied frequency-severity prediction models for RNS implementation (Miranda-Moreno et al., 2009; Aguero-Valverde and Jovanis, 2009; El-Basyouny and Sayed, 2009; Zeng et al., 2017; Yasmin and Eluru, 2018; Afghari et al., 2020). More precisely, among the few studies retrieved, in some cases, the results of the crash frequency-severity models have been generally included in a parameter, which served as an evaluation measure for the site ranking (e.g., a Weighted Risk Score or a crash rate, a total crash cost or excess of crash cost, or Total Risk score). Conversely, in other few cases, the results of the predictive models were directly applied in the RNS, to evaluate the safety performance of the network.

To bridge the previous gaps, this study proposes a new framework for a RB-RNWS. Specifically, it integrates a tri-variate multivariable (econometric) CPM to estimate the crash risk, that combines in an innovative way: (i) the likelihood of a crash to occur instead of its frequency, to be more consistent with the risk definition; (ii) an estimation of the exposure component (e.g., traffic volumes), to provide a viable solution when traffic data could be unavailable; (iii) the severity of a crash as a driver of consequences. In addition, it assures the 1936/2019 Directive requirements and complies with the ISO 39001 (2012).

The framework is tested over the main road network of the Province of Brescia (Lombardy Region - Italy), which represents an emblematic case study, being an important residential, industrial, commercial, and touristic hub, whose road network is interested in high traffic volumes.

This study aims at contributing to both theory and practice. On the theoretical side, this study expands the theoretical understanding and application of crash risk not much explored in the field of RNS approaches, to the authors' knowledge. From a practical perspective, it provides RSAs and practitioners with a decision support tool, which can help in (i) identifying most critical road segments, (ii) prioritising interventions, and (iii) defining the most appropriate measure to mitigate the effect of the crash risk components, according to a proactive approach. Moreover, this study makes possible to assess crash risk in the road infrastructure planning stage, i.e., to assess the expected impact

that a new (or restored) road may show, according to its characteristics.

The remaining paper is as follows: Section 2 provides a critical review of crash prediction models that simulate a risk-based formulation. Section 3 presents the framework for a RB-RNWS. Section 4 illustrates its application in an Italian case study, whilst section 5 discusses the results. Finally, some conclusive remarks and future perspectives are drawn in section 6.

2. Literature review

2.1. Crash prediction models for road network screening

CPMs find a relationship between the road safety performance of a site (e.g., crash frequency, crash severity) and a set of predictors, that stands for the inherent safety of a road (Yannis et al., 2016; Ambros et al., 2018). In doing so, they enable a proactive approach for road safety and a valid starting point for the development of a risk-based crash prediction model. According to such perspective, literature has expanded towards the development of modelling approaches, which integrate crash frequency and severity models in the evaluation of the overall road safety performance of a site (e.g., entire roads, road segments, intersections, areas). Such models have great potential, as they can (i) evaluate these components to return a comprehensive result and (ii) provide a cost-effective and reliable support for policy makers (Milton et al., 2008; Afghari et al., 2020). Although not exhaustive, Appendix A reports a summary of the literature that provided frequencyseverity prediction models for road safety analysis. It is argued in what follows.

First, the estimation of crash frequency and severity can be made by independent models or simultaneous models. The former aims at assessing the frequency and the severity levels of crashes by separated models; the latter aims at estimating both the frequency and the severity level of crashes by a unique model structure, thus at once.

Second, the most common independent models are univariate and two-steps; simultaneous models include multivariate and joint ones (Lord and Mannering, 2010; Savolainen et al., 2011; Viera Gomes et al., 2012; Mannering et al., 2020). While the simultaneous estimation of crash frequency and severity may help with prediction accuracy, it might compromise the inference quality, as consistency among variables is required, as opposed to the independent models (Anastasopoulos and Mannering, 2011). Indeed, simultaneous models are applied to investigate the frequency of different level of crash severity. As a result, crash-specific and post-crash data cannot be included as they are not applicable for frequency estimation (e.g., Ma and Kockelman, 2008; Yasmin and Eluru, 2018; Xie et al., 2019).

Third, independent models are more straightforward to develop and interpret. Indeed, the development of two separated models helps in better understanding the single estimation result, in terms of parameter estimates and significance magnitude understanding (Park and Lord, 2007). Moreover, this flexible structure helps apply more straightforward models for crash frequency (e.g., Negative Binomial) and severity (e.g., Binary, or multinomial logit). Simultaneous models are usually more computation-intensive because they are built on a more complex mathematical function that must account for a multivariate response variable. Moreover, the result is less straightforward to interpret, as they include two components in one estimation and so the effects of the predictors over frequency and severity may not be immediate.

Finally, a handful of studies implemented such models for screening purposes. Indeed, while extensive research has tried to outperform existing crash frequency and severity modelling, in the road network screening process few studies have integrated such models (Miranda-Moreno et al., 2009; Afghari et al., 2020). Among these studies, the results of the crash frequency-severity models have been generally transferred into a parameter, which served as an evaluation metric for the site ranking. Conversely, few studies directly applied the model's results in the RNS, to evaluate the safety performance of the network.

For instance, Yasmin and Eluru (2018) and Zeng et al. (2017) ranked sites: a crash count by severity levels and a crash rate by severity level was set as the response variable for their modelling, respectively.

2.2. Gaps in the literature

Overall, all the previous studies provided valuable insights in understanding road safety by adopting CPMs in different ways to estimate risk-components. However, some gaps persist.

First, besides e.g., Park and Sahaji (2013), Theofilatos et al. (2016), risk has always been computed as a combination of crash frequency and severity, thus, never considering the exposure factor, as a main response variable to be estimated.

Second, almost all previous studies have included the exposure factor (i.e., traffic volumes) as input among the set of explanatory variables to estimate the frequency (mainly) or severity. However, this may be questionable as road traffic volumes are not always available for the whole road network (Park and Sahaji, 2013). Moreover, the potential of a road site to register road crashes or generate severe consequences should be evaluated regardless of the extent of the exposure measure. In other words, when estimating the expected crash frequency or severity of a site, just the inherent characteristics of the site itself should be considered as risk factors (i.e., infrastructural, operational, context, etc.), while risk exposure should be treated separately.

Third, risk calls for the likelihood of crashes to occur, but crash occurrence has been mainly addressed in terms of crash frequency. This might occur because probability models rely on observation-specific data, so that building an appropriate dataset for crash occurrence probability may be unfeasible in many cases.

This study aims to cover all these gaps.

3. Methodology

This section presents the new analytic method for the implementation of an RB-RNWS according to EU Directive 1936/2019. The method expands and improves the one proposed by Bonera et al., (2022a). It consists of three main parts: (I) Data collection, (II) Data compliance with ISO 39001 (2012), and (III) RB-RNWS process. Those parts are further detailed in steps to make the implementation clearer and systematic. The overall method is shown in Fig. 1, and it is illustrated in what follows.

3.1. Part I - Data collection

Part I is devoted at collecting all the data required for processing the whole RB-RNWS method. Since crash occurrence, severity and exposure should be estimated, related data should be collected from specific sources and by specific type, according to the scope of the analysis and their availability. Data must be suitable for the wide-level investigation, consistent with the scale of the analysis, and specifically with the segmentation of the road network at hand. Annex III of the EU Directive 1936/2019 may be considered as a reference, as it contains a long list of parameters for a road safety assessment. However, if a whole road network is to be screened a compromise should be reached: then, less but available and easy-to-collect data are suggested, also to be gathered from official sources, to ensure greater attainability and standardisation. According to such issue, the main sources, and data type to be considered for the study area are the following: (i) base map data including e. g., the maps showing the physical and/or administrative partition of the territory into the several levels, the road network map and the related Nomenclature of the Territorial Units for Statistics (NUTS) for linking issues; (ii) context information including e.g., the characteristics of the study area such as socio-demographic and land use data; (iii) road traffic data including e.g., traffic demand, and road functional and operational characteristics etc.; (iv) road crash data referring to all road crash data included in related record tracking. Indeed, all the Police bodies involved in collecting road crash data fill a standardized form, with all the main crash data. For instance, data can include the number of people involved and the damage received (e.g., fatality, severe injury), crash location (e.g., road design characteristics, road name) and other data.

3.2. Part II – Data compliance with ISO 39001:2012 standard

Part II of the framework is devoted at arranging the collected data according to ISO 39001 ((International Organization for Standardization – ISO, 2012)), because a road crash results from the interaction of several factors e.g., the road context, the infrastructure design, and the operational characteristic. Specifically, the following factors need to be identified:

Intermediate outcome safety factors: they have the potential to generate conditions that can lead to a potential hazard event.
Risk exposure factors: they reflect the actual use of the network by road users of all categories.
Final safety outcome factors: they represent a break in the equilibrium between the previous ones and, therefore, affecting the occurrence and severity of the crash event.

One could not apply the ISO 39001-2012; however, such data organisation is key for two reasons at least: first, to guarantee that the method follows a standardised process, which is mandatory for safety certification according to ISO 39001-2012; second, to ease the computation of the road crash risk by mean of CPMs, as it helps identify the role of each element in the estimation process.

3.3. Part III – Risk-based road Network-Wide screening

3.3.1. A – Network segmentation

This step is devoted at dividing the whole road network into a set of unique spatial units (A.1) and their characterisation, according to the different infrastructural and operational attributes (A.2). According to Bonera et al., (2022a), the segmentation process provides enough flexibility to investigate the whole network in a deep manner, based on the several territorial levels (i.e., regional, provincial, local, etc.), and allows independency from spatial coordinates of both segments and crashes. However, different segmentation procedures may be applied to divide the road network into easy-to-manage segments (e.g., homogeneous segments, fixed length segments, etc.). Here, briefly, the road network is partitioned into a set of road network units (or RNU, or simply units – u), which are defined as the portion of a generic road encompassing the boundaries of a territorial jurisdiction considered at its lowest hierarchical level (for further detail refer to Bonera et al., 2022a). More formally, let:

J be the set of the territorial jurisdiction within the study area, and j ∈ J be a generic jurisdiction.
R(j) be the set of roads crossing jurisdiction j ∈ J, and r ∈ R(j) be a generic road.
S(r) be the set of road segments of route r ∈ R(j), and s ∈ S(r) be a generic segment.¹
Ur be the set of all the road network units and *ur,j*be a generic road network unit.

Specifically, the road network unit *ur,j*is defined as the set of all segments s ∈ S(r) of route r ∈ R(j) included in the jurisdiction j ∈ J and can be formalised as follows:

$$u_{r,j} = {s \in S(r) : r \in R(j) \text{ and } j \in J}$$ (1)

¹ A road segment is identified as the link between two intersection or a change in the infrastructural characteristics of the road.

Fig. 1. Methodological approach for a RBNWRS.

The definition of the RNU *ur,j*depends on the detail of the jurisdiction considered, thus its hierarchical level. Therefore, the more the territorial jurisdiction levels, the denser the network partition and the deeper the screening analysis. Specifically, if the road network segmentation is made by considering the lowest level of the jurisdiction hierarchy, then the road network units are defined at the lowest level. In this case, they can be defined as "minimum" RNU. Fig. 2 shows the definition of ur,j(or simply u).

As for the spatial unit characterisation (A.2), the link among the context, infrastructural, traffic and crash data and the RNU is required to associated related characteristics.

3.3.2. B – Network screening

This step applies a screening procedure to all the spatial units of the network to assess their safety performance, according to a Road Crash Risk Index. In this research, the widely recognised risk concept of Fine (1971) is adopted, which combines (i) the likelihood of crash occurrence, (ii) crash severity, and (iii) crash exposure. However, unlike Fine (1971) and Barabino et al. (2021), in this paper the risk index considers separately the three components, by formulating, calibrating, and validating three prediction models. More formally, let T be the time span for which each risk component is estimated. Next, let:

*PFur,j*be the probability factor over the road network unit ur,^j ∈ Ur.
*Eur,j*be the exposure factor over the road network unit ur,^j ∈ Ur.
*Cur,j*be the consequences over the road network unit ur,^j ∈ Ur.
*Pur,j*be the probability of a crash over the road network unit ur,^j ∈ Ur; it is intended as a proxy of the probability factor.
*Sur,j*be the metric of the severity of a crash over the road network unit ur,^j ∈ Ur; it is intended as a proxy of the potential consequences.

According to Fine (1971), the risk index may be defined as follows:

$$R{u{r,j}} \stackrel{\text{def}}{=} PF{u{r,j}} * E{u{r,j}} * C{u{r,j}} \quad \forall u_{r,j} \in U_r$$ (2)

Conversely, in this paper, the Road Crash Risk Index *Rur,j*for each ur,^j ∈ Ur is computed as follows:

$$R{u{r,j}} = P{u{r,j}} \bullet E{u{r,j}} \bullet S{u{r,j}} \quad \forall u_{r,j} \in U_r$$

$$(3)$$

The choice of such formulation is due to specific reasons: first, the selection of the two probability models for both the crash occurrence and severity probability, plus the estimation of the exposure, was made to better reflect the definition of risk. Next, as suggested by e.g., Wang et al. (2011), Stipancic et al. (2019) and Afghari et al. (2020), it is worthy to account that road crash risk's components should be better studied separately, as they may require different mitigation strategies (prevention and/or protection) to reduce e.g., the number of crashes and their consequences respectively. Moreover, the choice of a straighfoward combination of such risk factors through a simple multiplication was made to provide an easier and more intuitive tool from the practitioners' viewpoint and according to extisting formulations (e.g., Miranda-Moreno et al., 2009; Afghari et al., 2020; Barabino et al., 2021).

The estimation by Eqn. (3) is straighforward, provided that the three risk components Pur,j, *Eur,j*and *Sur,j*are estimated. Nevertheless, according to the way the risk components are conceived, their estimation may vary. Specifically, whilst severity (or vulnerability) and exposure have been treated by the widely agreed definition,2 the likelihood of road crash occurrence may be more controversial to asses. Indeed, the

probability factor *PFur,jmay be interpreted by (i) the stricter statistical meaning of the probability of a road crash to occur or (ii) the wider sense of the frequency of the event (i.e.,* how many times crashes occur over a defined time-span). In this research, the former interpretation is adopted, for three main reasons: first, it better reflects the meaning and definition of the related risk component (i.e., the probability to occur); second, regardless the number of potential road crashes over a specific road unit, the foremost goal is to assess to what extent the segment has a potential to generate even a single crash, owing to its e.g., infrastructural, context characteristics. Indeed, the lower the probability of crash occurrence, the lower the potential number of crashes that can be registered. Third, the crash frequency is strongly influenced by exposure factors included in the modelling. Indeed, when all other conditions being equal, the greater the number of vehicles along a specific road, the greater the frequency. Conversely, the crash probability is not affected by this issue, because it is a dimensionless quantity. Thus, the crash probability can be intended as "normalized frequency" per unit of exposure factors (e.g., vehicles). To summarise, Eqn. (3) returns an index that could be interpreted as a crash frequency that quantifies how much exposed traffic is transformed into a severe crash. However, as opposed to e.g., Wang et al. (2011) and Hosseinpour et al. (2014) computing the probability of a crash instead of frequency enables more disaggregate analysis and makes easier to discern the effect each factor has on crash events.

The risk components are estimated by three separated econometric models and their mathematical formulations follows.

3.3.2.1. Road crash probability model. Road crash probability refers to the possibility for a crash to occur, given specific conditions. Hence, crash occurrence can be interpreted as a binary response variable that assumes only two options: occurrence or non-occurrence of the road crash. Therefore, a Logistic Regression Model can be adopted. More formally let:

qu be the number of crash occurred on ur(j) ∈ R(j) within j ∈ J.
K be the set of intermediate outcome factors and k ∈ K a single factor.
xk,r(j) be the intermediate outcome factor k ∈ K of r(j) ∈ R(j) within j ∈ J.
*θ0, θk*be the set of coefficients in the model with respect to factor k ∈ K.

The crash occurrence probability,3 i.e., Pur,j, ∀ur ∈ Ur is computed as follows:

$$P{u{rj}} = Prob\left(q{r(j)} \ge 1 \underset{k \in K}{|} \left{x{k,r(j)}\right}\right) = \frac{\exp(\theta0 + \sum{k \in K} \thetak x{k,r(j)})}{1 + \exp(\theta0 + \sum{k \in K} \thetak x{k,r(j)})} \ \forall u_{rj} \in U_r \quad \textbf{(4)}$$

The results may be interpreted by the odds ratio (OR), which returns the number of successes (to have a crash) against each failure (not to have a crash) and can be easily calculated by taking the exponent of the parameter estimated. In this study, when OR > 1 (*<*1), an increase (decrease) in the odds of the road crash is observed. The estimation of the model is based on a maximum likelihood procedure. To check the Goodness of Fit (GoF), the ratio between the regression deviance and the degree of freedom (i.e., the deviance ratio, d.r.) was considered, along with the overall statistical significance of the model shown by the χ² . In addition, the signs of the coefficients, the significance of each explanatory variable, and the OR were evaluated. For instance, a negative sign in the variable estimate implies a reduction in the probability for the crash to occur for each increase in the considered intermediate outcome

² Road crash severity can be intended as a surrogate measure of road crash vulnerability, thus the amount of damage or loss (in general, the expected road crash outcome) that can be generated by the road crash. Exposure is the measure of how much an object can be exposed to a defined risk or to a set of risk factors, which jointly interact and may lead to a crash (i.e., the potential hazardous event).

³ It is worth noting that to estimate the probability of a crash, the related dataset should be manipulated. According to the available crashes, a different crash to non-crash ratio could be observed. An example on how it is determined is shown in Appendix B.

Fig. 2. Conceptual scheme of the network partition and RNU definition (Adapted from Bonera et al., 2022b).

factor, and vice versa. Finally, the percentage of rights was computed. It represents the number of consistent responses between the observed and predicted values.

3.3.2.2. Road crash exposure model. The exposure factor could be evaluated in many ways. In this study, the exposure response was considered in terms of AADT*(length of the unit at hand), which is also converted in a passenger-car*km equivalent traffic volume. When dealing with an existing road network, the road length is a fully available factor. Conversely, the AADT is not, and it may be necessary to estimate it by mean of specific model structure (Bonera, 2022). Multiple Linear Regression (MLR) models have been largely used to estimate AADT as a relationship of context, socio-economic, infrastructural features, or other intermediate outcome factors (e.g., Zhao and Chung, 2001; Apronti et al., 2016; Das and Tsapakis, 2020; Sfyridis and Agno lucci, 2020). Let:

*zk,u*be the intermediate outcome factor k ∈ K of ur(j) ∈ U within j ∈ J
*ρ0, ρk*be the estimate coefficients of the linear regression.
*lr,j*be the length of each road unit ur(j) ∈ Ur

The exposure Eur,^j zk,^r ) to road crashes for each ur ^∈ Ur can be computed as follows:

$$E{u{r,j}}(z_{k,r}) = (\rho0 + \sum{j} \rhok z{k,r(j)})^* l{r,j} \ \forall u{r,j} \in U_r$$ (5)

To model the exposure factor, each minimum RNU is considered as a single observation, with the related characteristics. The ordinary least residuals were also performed.

3.3.2.3. Road crash severity model. In this research, road crash severity is defined as the highest degree of seriousness experienced among all the people involved in a crash. Crash severity should be evaluated according to a sorted level, e.g., from the most severe outcome (i.e., fatal crashes), to the lightest one (e.g., only property damage). Thus, a multivariate logistic regression with at least three response variables could be adopted to its modelling. However, as in many countries (e.g., Italy and other EU member states), official crash data only refers to fatalities and injuries (i.e., property damage crashes were not reported), the severity of crash is evaluated by assuming a fatal4 or non-fatal result. Therefore, the crash severity can be modelled as a binary variable that assumes 0 if the crash results in injury-only and 1 in case of fatal crash. As a result, a LRM can be adopted, which follows the same model structure explained for crash occurrence probability. More formally, let:

gu be the binary variable that assumes 1 if at least one fatal crash occurs on ur(j) ∈ U within j ∈ J; 0 otherwise.
*yk,u*be the intermediate outcome factor k ∈ K of r(j) ∈ R(j) within j ∈ J
*φ0, φk*be the set of coefficients to be estimated in the model with respect to factor k ∈ K

The crash severity probability, i.e., Sur yk,r(j) ∀ur ∈ Ur is computed as follows:

$$S{u{rj}} = Prob\left(g{r(j)} = 1, \left| \left{ y{k,r(j)} \right} && \left(P_{u_r} > 0\right) \right.\right) = \frac{\exp(\varphi0 + \sum{k \in K} \varphik y{k,r(j)})}{1 + \exp(\varphi0 + \sum{k \in K} \varphik y{k,r(j)})} \qquad \forall u_{rj} \in U_r$$

$$(6)$$

squares method was used to estimate the best possible coefficients of the multiple regression model. To check the GoF, *R*2 and R² adj were considered, along with the overall statistical significance of the model (p-value of the F-ratio). Then, the signs of the coefficients and the significance of each explanatory variable are evaluated. In addition, some checks on the

⁴ A road crash in which at least one person got killed at the crash location or by 30 days from the crash date.

Table 1 The ranking scale for the crash risk distribution.

Risk level	Risk ranges values
1 - Very low risk	(Q1-1.5 IQR) – Q1
2 - Low risk	Q1 – Q2
3 - Intermediate risk	Q2 – Q3
4 - High risk	Q3 - (Q3 + 1.5 IQR)
5 - Very high risk	(Q3 + 1.5 IQR) - Max

The estimation of the model is based on a maximum likelihood procedure. Noteworthy, alike crash occurrence probability model, the input data should be provided in a disaggregated way, thus observation per observation. In this case, no artificial manipulation of the crash dataset is required, as the binary nature of the response variable is simply returned by recoding the crash outcome variables as "fatal; non-fatal (injury-only)" crash.

3.3.3. C – risk ranking

Once the values of the crash risk index are computed for all the road units, they must be ranked according to a defined scale to identify the worst (or best) performing ones. Unless such scale could be selected among many, in this case the 5-level ranking scale based on the distribution of quartiles of risk is applied (Bonera et al., 2022b). It helps emphasizing the riskiest segments of the road network thanks to its structure. Table 1 shows the structure of the five-level ranking scale and reports the lower and upper limits for each range values. The ranking scale should be read as an unsafety scale, thus the lower the Road Crash Risk Index, the safer the road unit. Therefore, when defining strategies to improve road safety, roads that score a crash risk of 5th level should be considered as a priority. Conversely, roads that have a crash risk of 1st level are considered sufficiently and relatively safe.

The ranking results can be presented in different ways: a simple and clear dashboard of the screening, that represents the share of the whole network belonging to each risk level, also according to the risk value and the road class; or graduated maps, where each road network unit is represented with a colour corresponding to the related safety ranking level. It is worth noting that one does not have to obey to the previous scale to use the framework, which acknowledges the freedom to establish this scale in some other ways.

4. Real world experiment

4.1. Context description

The method was experimented over the main road network of the Province of Brescia (hereafter Brescia), located at the eastern side of the Lombardy Region (Italy) and represents its largest province, with a surface of more than 4,500 km² . It includes 205 municipalities and has a population of about 1.250 million people (the fifth in Italy, per inhabitants). Brescia represents one of the most important industrial, commercial, and residential areas in Italy, so that it originates/attracts major traffic flows daily (Martinelli et al., 2023; Regione Lombardia, 2016). The overall road network comprises 340 + km of highways, about 170 km of state roads, 1,700 + km of provincial roads and 200 + km of local roads (Faccin et al., 2011). As for road safety data, many road crashes occurred in Brescia over the last years, with an average of 3,000 + crashes, 4,000 + injuries and around 80 deaths per year (Polis-Lombardia, 2020). Most of road crashes occurred on urban roads (almost 74 %), but the greatest share of fatal crashes occurs on the nonurban main road network. A total of 482 road segments representing almost 2,000 + km of road network was considered, which is organised according to MIT (2001) and shown in Appendix C1. A total of 6,123 road crashes occurred on the main road network of Brescia over the fiveyear period 2014–2018 were included in the study.

4.2. Experimental setup (Parts I and II)

According to Part I of the framework, all the required data types were gathered from four main sources: *Geoportale Regione Lombardia*5 for base map data about context, land use, road network, etc.; the National Institute of Statistics (ISTAT)6 for the socio-demographic characteristics; the Regional General Directorate (RGD) for road traffic data and Polis-Lombardia7 (Regional Institute for Policy Support) for all the road crash datasets. Further details about the data retrieved for the case study can be found in Bonera (2022). As for road crash information, it is noteworthy to state that, as for crashes location, almost 33 % of the road crash observations lacked geographical/plane coordinates or reported them inaccurately and was impossible to find the accurate locations. This issue is crucial: if the analysis had relied on spatial coordinates, a large quota of road crashes would not have been included in the assessment, hence, affecting the overall results.

Further information was inferred from the available dataset such as seasons and time of the day, road type. For modelling purposes, all variables were coded as binary (e.g., urban/non-urban, day/night) or categorical. In this part, data were managed and processed by spreadsheet software (i.e., Microsoft Excel) and a geographical information system (GIS) software (i.e., QGis).

Next, according to Part II of the framework, all available variables and related data from the different datasets were associated with the three main risk factor categories according to the ISO 39001 (2012) and grouped by the list of factors included in the Annex III of the EU Directive 1936/2019, when applicable due to the Italian road crash standardised dataset. Table 2 reports the descriptive statistics related to the road crash dataset and it is self-explanatory.

4.3. Running the framework (Part III)

Once data were collected and prepared, Part III was implemented following the steps A.1, A.2, B, and C of the framework.

4.3.1. Network segmentation, RNU definition and attribute assignment

The segmentation of the road network was performed according to step A.1. Specially, the road names and the codes of territorial units (NUTs and Local Administrative Units – LAUs⁸ ) were considered as the reference road crash location data because they were available and common to all the datasets. Next, according to eqn. (1), RNU were built by aggregating the s-segments of each road of the road network with respect to the municipality level and the whole Province level, considering the RNU at the municipality level the minimum RNU. Moreover, a univocal identification code was created for each RNU, to be used as the primary key for the relational association among all the information from the different datasets. This code was built by merging the variable "Road code" and "NUTS code" because this information is provided in each dataset. Full details of the RNU definition are shown in Bonera et al. (2022b).

Next, according to step A.2, each minimum RNU was also associated with all the related attributes from the different datasets retrieved in Part I, such as traffic volumes, road infrastructure characteristics, land use, and socio- demographic attributes. As for land use characteristics (referred to the surrounding areas to each RNU of the road network), a buffer was created to define the area where the land use characteristics were to be analysed. The buffer width was set based on the road

⁵ Dataset accessible at the following link: https://www.geoportale.regione.lo

mbardia.it/download-dati. 6 Dataset accessible at the following link: https://dati.istat.it/Index.aspx. 7 Polis-Lombardia webpage available at: https://www.polis.lombardia.it/wps

^/portal/site/polis. 8 They represent the geographical subdivision of the territory based on administrative regulation.

Table 2 Road crash dataset descriptive statistics (Entries in italics are the reference category).

| CPM Components |-------------------| | | | Response variable | | | Predictors | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ISO 39,001 and Risk Components | EU 1936/2019 Annex III List of factors | | | | | -------------------------------------|----------------------------------------|---------------------------|-----------------------------------|---------------|--| | Level 1 | Level 2 | Description | | | | Final safety outcome | Crash data | Crash outcome | Fatal | 3.61 | | | | | Injury only | 96.39 | | | Intermediate safety outcome factors | Road Crash dynamic | Crash Type | Hit with obstacle | 5.54 | | | | | Head-on or sideswipe | 41.04 | | | | | Single vehicle collision | 17.26 | | | | | Pedestrian collision | 3.74 | | | | | Rear-end crash | 32.42 | | | | Violation | Violation by user A | 68.89 | | | | | No violation by user A | 31.11 | | | | | Violation by user B | 52.83 | | | | | No violation by user B | 47.17 | | | Users involved | Pedestrian | Pedestrian involved | 4.00 | | | | Cyclist | Cyclist involved | 6.21 | | | | Heavy vehicle | Heavy vehicle involved | 23.80 | | | | Powered Two-Wheeler | PTW involved | 19.29 | | | | Car | Car involved | 87.05 | | | Road infrastructure
design | Road type | Urban | 33.24 | | | | | Non-urban | 66.76 | | | | Road class | Primary | 25.09 | | | | | Non primary | 74.91 | | | | N. of lanes per direction | One lane | 74.54 | | | | | Two or three lanes | 25.46 | | | | Median presence | Divided carriageway | 20.46 | | | | | Undivided carriageway | 79.54 | | | | Site type | Segment | 65.80 | | | | | Intersection | 34.20 | | | | Pavement condition | Paved | 99.61 | | | | | Ruined | 0.39 | | | | Road signs type | Horizontal | 7.59 | | | | | Vertical | 3.97 | | | | | Horizontal and Vertical
Absent | 86.13
2.30 | | | Operational features | % Heavy Good Vehicle | < 15 % | 32.03 | | | | | 15 % − 30 % | 34.59 | | | | | >30 % | 33.38 | | | Environmental factors | Type of terrain | Flat | 70.98 | | | | | Rolling | 24.30 | | | | | Mountain | 4.72 | | | | Land Use | Built up areas | 31.36 | | | | | Rural areas | 51.66 | | | | | Forests and woods | 13.70 | | | | | Wet areas | 3.28 | | | Context conditions | Season | Spring - Summer | 45.06 | | | | | Winter-Fall | 54.94 | | | | Day type | Weekday | 67.79 | | | | | Festive | 32.21 | | | | Daytime | Day | 68.58 | | | | | Night | 31.42 | | | | Surface conditions | Dry | 80.53 | | | | | Not dry | 19.47 | |

functional classification (e.g., MIT, 2001; Zhao and Chung, 2001; Sfyr idis and Agnolucci, 2020; Pulugurtha and Mathew, 2021). Next, the most relevant land use category within each buffer was computed and associated to the related RNU. As for socio-demographic characteristics of each municipality of the province of Brescia, population size, municipality and urban areas extensions, and total network length were included as further information. Each minimum RNU was associated to the related characteristics by the road-code and, specifically, by associating each Municipality and the related NUTS code.

Finally, each minimum RNU was associated with the related number of crashes.

Table 3 provides some descriptive statistics of the road network of Brescia, after being enriched with all the features from the several datasets. According to e.g., Hosseinpour et al. (2014), RNUs showed a length ranging from 0.1 to 33 km, but 97 % present a length up to 7 km.

4.3.2. Crash risk prediction model estimations

According to step B of Part III, RB-NWS was performed.

For the development of the crash occurrence probability and severity models, the integrated road crash dataset was used as input. All the response variables were associated to crashes, i.e., occurred/notoccurred crash, and crash damage outcome (severity), respectively. Conversely, for the development of the crash exposure model, being the response variable related to a measure of the traffic volumes over each RNU, the dataset of the road network was used. All the models were estimated by the statistical software GenStat.9 For each risk component, two models were estimated: (i) a full model, defined as baseline model, that includes all the intermediate outcome safety factors available and

⁹ Genstat is a general statistics software package for education and research, developed by VSN International (https://www.vsni.co.uk/software/genstat).

Table 3 Road network segments descriptive statistics (entries in italics are the reference category).

CPM Components	ISO 39001 and Risk Components	EU 1936/2019 Annex III List of factors
		Level 1	Level 2		Description		Freq. [%]
Predictors	Intermediate safety outcome factors	Road Infrastructure	Road type		Urban		18.05
					Non-urban Primary A		81.95
			Road class				9.80
							7.14
					B		2.66
					Non primary		90.20
					C		36.54
					E		5.48
			F	48.17
			N. of lanes per direction		One lane		90.37
			Type of terrain		Two or three lanes Flat Rolling		9.63
		Environmental factors					66.94
							18.60
			Land Use		Mountain Built up areas Agricultural zone Forests and woods		14.45
							18.11
							60.63
							19.93
					Wet areas		1.33
CPM Components	ISO 39,001 and Risk Components	EU 1936/2019	U.M.	Mean	Min	Max	Std
Response variable	Exposure factors	Segment length	[km]	3.67	0.10	33.33	3.61
		Average Annual Daily Traffic (AADT)	[veh]	3,642,209	24,338	25,860,250	3,836,075
		Average km travelled	[veh*km]	17,076,954	32,273	507,587,490	44,131,945
Predictors	Intermediate safety outcome factors	% of Heavy Vehicles	[%]	23	1	100	17
		< 15 %	[%]	42.19
		15 – 30 %	[%]	32.06
		> 30 %	[%]	25.75
	Demographic context	Urban area density	[km2 /km2 ]	0.14	0.01	0.60	0.11
		Population density	[ab/km2 ]	404	4.86	2,154	327.95
	Road Network provision	Network density	[km/km2 ]	4.10	0.16	11.84	2.53

	Road crashes		[n crash]	3	1	38	3

(ii) an enhanced (if any) model, defined as best-fit model, that includes a sub-set of the most promising variables selected by the stepwise regression: if more performing models can be returned with less predictors, then this will gain in simpler interpretability of the results, higher replicability, and updateability of the process over time and over other context. In what follows, the results of both the baseline and bestfit models are presented for each risk's components estimations and a brief comment is provided. Each model reports the prediction coefficient (i.e., estimates) and its p-value (significance level). In addition, the summary statistics section is reported at bottom of each table, to show the parameter used to evaluate the GoF.

Next, once models have been estimated the risk crash index RSur is computed.

4.3.2.1. Crash occurrence probability model estimation. As introduced in section 3.3.2.1, the crash occurrence probability was estimated according to eqn. (4). Table 4 shows the results.

Overall, this model fits the data well, as the statistical test (χ2) on d.r. returns a small p-value for goodness-of-fit (*<*0.001), and the d.r. factor registered a very high value. Therefore, strong evidence exists for a regression effect, so that the null hypothesis can be rejected (i.e., that at least one regression coefficient is not zero). Thus, by a huge dataset, the model performances were enhanced. The percentage of rights shows almost the 99 % of the predicted response was consistent to the related observed result. All the observation related to a non-occurred crash were correctly estimated, while those of occurred crashes were estimated correctly at almost the 16 %. As for the explanatory variables included in the model, all of them resulted to be strongly significant, thus with a pvalue at the 0.001. Indeed, it was not deemed necessary to apply stepwise regression to further improve the model performances (a very slight improvement of the d.r. was registered doing so). Noteworthy, as a summary of results, Table 8 shows that the likelihood of having a crash is highest in paved road (OR = 104.7) as opposed to unpaved ones.

Moreover, it increases in areas that are classified as Agricultural zone (OR = 12.76) and in build up (OR = 11.94) as opposed to wet areas. Conversely, in dry pavement conditions, the likelihood of having a crash is higher 2.52 (OR = 1/0.3966) times as opposed to not dry conditions.

4.3.2.2. Crash exposure model estimation. Crash exposure was evaluated by VKM (km travelled) from vehicles. It was obtained by multiplying the AADT on each RNU, which was estimated by mean of the MLRM, by the length of each RNU. Hence, because RNU length is easy to collect or compute (see eqn. (2)) and is always an available variable, the sole AADT was included in the model estimation by MLRMs. Table 5 shows the results.

Overall, the best fit model clearly fitted the data better than the baseline model. Indeed, F-test returned a small p-value (*<*0.001) with a larger F-ratio. Moreover, also the R² adj increased, so that the best-fit model was able to explain at least the 68 % of AADT's variance by the selected predictors. Specifically, it was not completely able to model greater AADT volumes. However, this might not be considered as a limitation. Indeed, on the one hand, road that records highest traffic volumes belong to the highest hierarchy level of the road network, such as highways or major roads (MIT, 2001). Such roads are regularly and widely monitored by automatic traffic detection systems, so that traffic data may be largely available and complete. On the other hand, AADT can help in optimising resources when it comes to decide where to install traffic monitoring devices to have complete information about road network traffic data. Indeed, AADT volumes *<*6 million are usually observed in minor of intermediate road classes (MIT, 2001). Then, if traffic volumes can be well estimated by the model up to such AADT levels, then traffic monitoring devices may be primarily assigned to midhigh road classes, which are generally not constantly monitored (MIT, 2001).

As for the predictors, most of them were found to be very significant

Table 4 Crash occurrence probability model results (baseline model and best-fit).

	Baseline model			Best fit model
Intermediate safety factor	Estimate	P-value	OR	Estiate	P-value	OR

Road type
						1.665

						5.804

						5.522

						6.853

						1.866

						104.7

						2.610
						1.697
						14.80

						1.464
						1.464

						8.717
						4.244

						11.94
						12.76
						6.354

						0.3966

						–

						1.548

						1.793

						Mean deviance
						422.3075
						0.07166
						0.12607



						Rights [%]
						98.97 %
						15.61 % 99.95 %
	Non-urban Road class Non primary Lanes per direction One lane Median presence Undivided carriageway Site type Segment Pavement condition Paved Road signs type Horizontal Vertical Horizontal and Vertical % Heavy Vehicle < 15 % 15 % − 30 % Type of terrain Flat Rolling Land Use Built up areas Agricultural zone Forests and woods Surface conditions Not dry Season Winter-Fall Day type Weekday Daytime Day Observed 147,456 1,7041	− 18.207 0.5100 1.7585 1.7087 1.9248 0.6240 4.652 0.959 0.529 2.695 0.3813 0.3813 2.1653 1.4454 2.480 2.546 1.849 − 0.9249 0.0120 0.4366 0.5838 Baseline model Degree of freedom 20 147,435 147,455 401.19 <0.001 Rights 145,943 266	* * * * * * * * * * * * * * * * * * – * * Deviance 8,024 10,566 18,590	1.665 5.804 5.522 6.853 1.866 104.7 2.610 1.697 14.80 1.464 1.464 8.717 4.244 11.94 12.76 6.354 0.3966 1.012 1.548 1.793 Mean deviance 401.19452 0.07166 0.12607 Rights [%]1 98.97 % 15.61 %	− 18.201 0.5100 1.7585 1.7087 1.9248 0.6240 4.652 0.959 0.529 2.695 0.3813 0.3813 2.1653 1.4454 2.480 2.546 1.849 − 0.9249 – 0.4366 0.5838 Best fit model Degree of freedom 19 147,436 147,436 Rights 145,943 266	* * * * * * * * * * * * * * * * * * – * * Deviance 8,024 10,566 18,590

(i.e., up to the 0.001), thus quite similar results compared to the baseline model. To summarise, the AADT increases in flat and rolling terrains, when the population density increases and when the % of heavy vehicle increases as well. Conversely, it decreases in not primary roads and in those having only one lane per direction.

4.3.2.3. Crash severity probability model estimation. For crash severity estimation, individual crashes were considered to build the input dataset. The crash severity probability model was estimated according to eqn. (6). Table 6 shows the results.

Overall, the best-fit model fitted the data better than the baseline model. Indeed, the statistical test (χ2) on d.r. still returned a small pvalue for goodness-of-fit (*<*0.001), while the d.r. value increased by almost 62 %. The percentage of rights is over 96 % of the predicted response and was consistent to the related observed result. However, the model responded better to the estimation of non-fatal crashes than fatal crashes. This may be due to the limited number of fatal crashes included in the dataset, which – fortunately – may be considered as rare events among rare events. As for the explanatory variables included in the model, few were found to be significant (i.e., up to at least 0.1). Specifically, the results showed that crash involving Pedestrian increase the severity 8.187 times as opposed to car, as expected. Moreover, crashes involving Heavy Good Vehicle increase the severity 3.455 times as well.

4.3.3. Risk estimation

According to part C), the Road Crash Risk Index *Rur,j*was computed for each RNU over the whole road network both at provincial and municipality level by the application of eqn. (2) using the results of eqns. (4), (5) and (6). Next, all the RNUs were ranked based on their crash risk index value and assigned with the related risk level. More precisely, when considering the municipality level, RNU were defined considering the municipality boundaries; while when considering the provincial level, RNU were defined considering the provincial level (i.e., the whole roads over the Province of Brescia). With reference to Table 7, the

P-value legend: ****: *<*0.001; ***: *<0.005; **<0.010; *<0.1; -:^>*0.1. 11To model the crash occurrence probability, the original dataset was manipulated: once all the possible combinations of intermediate factors causing at least a crash (i. e., 1,704), all the other combinations of factor with no crash were included in the dataset. Therefore, the expanded dataset reached 147,456 combinations that registered "at least one crash" or "no crash". 1

This value is computed as the ratio between Rights and Observed.

Table 5 Exposure estimation model results (baseline and best fit models).

		Baseline model			Best fit model
Category	Intermediate safety factors		Estimate	P-value		Estimate	P-value
Model constant			8,169,471			4,511,957
Road Infrastructure	Road class
	Non primary		− 3823563	***		− 2659782	****
	N. of lanes per direction
	One lane		− 2986408	*		− 1831778	****
Context conditions	Type of terrain
	Flat		1,747,545	****		1,097,157	****
	Rolling		2,169,713	****		1,802,150	****
	Land Use
	Agricultural zone		− 809038	*		–297838	*
Socio-demographic	Network density
	Roads per km2		− 125546	–		− 31550	–
	Population density		2850	****		2046	****
	Inhabitants per km2
Operational	% of HGV
	% of heavy good vehicles		6,748,691	****		3,524,487	****
Summary Statistics		Baseline Model			Best fit model
		Degree of freedom	Sum of Squares	Mean Squares	Degree of freedom	Sum of Squares	Mean Squares
	Regression	9	4.60E + 18	5.11E + 17	9	1.21E + 18	1.34E + 17
	Residual	472	3.34E + 18	7.08E + 15	406	5.38E + 17	1.33E + 15
	Total	481	7.94E + 18	1.65E + 16	415	1.74E + 18	4.20E + 15
		R2	0.58		R2	0.69
		R2 adj	0.57		R2 adj	0.68
		F-ratio	72.09		F-ratio	101.08
		P-value	<0.001		P-value	<0.001

P-value legend: ****: *<*0.001; ***: *<0.005; **<0.010; *<0.1; -:>*0.1.

specific risk levels and the related ranges value were computed for both the provincial and municipality level, to provide the road network ranking for each LAU considered.

Additionally, the variability of the scale in Table 7 is contingent upon the delineation of acceptable ranges. It is worth noting that strict adherence to these ranges for framework utilisation is not obligatory. This is attributable to the fact that these ranges can be ascertained through alternative methodologies and/or scales.

As shown in Appendix C2 and C3, crash risk maps were also produced, as they provide a more direct and clearer picture of the RB-RNWS by showing on maps the risk level of each RNU. Appendix C2 provides the map of the RB-RNWS at the municipal level while Appendix C3 provides the map of the RB-RNWS at the provincial level. The graphical representation of the risk ranking clearly show the potential of the proposed method, that enables a multiple level investigation of the road network, by implementing the RB-RNWS. Indeed, comparing provincial and municipality level maps, it emerges that some RNUs considered at the municipality level may show high level of risk while other lower level of risk, although belonging to the same road r at the provincial level. First, it clearly emphasises how local condition can affect the safety level of the road, so that adjacent RNU may present different level of risk. Second, the possibility to down-grading from the provincial level to the municipality level, enable the identification of the most critical RNU of, e.g., the riskiest road, so that priority can be assigned clearly.

Finally, Appendix D shows the ranking scale for the crash risk and the crash risk estimation at very small portion of the road network, as an example.

5. Discussion

Present findings show that the proposed methodology can potentially provide a tool for estimating the crash risk index value for each road segment of a network. While in the current case study, non-crashes were predicted with a much higher accuracy than crashes, the scope and focus of the present paper lies more in creating a proof-of-concept for the process, and in identifying a set of statistically influential variables rather than achieving exceptional results. Nonetheless, the overall

performance of the general framework is high because both models return a percentage of right larger than 95 %.

In what follows, some discussion is presented about the impact of the several intermediate factors over the risk components, the modelling results, and the comparison with other existing methods.

5.1. Impact of the intermediate factors over the risk components

The method enables the identification of proactive measure to reduce road unsafety. Therefore, this section discusses the impact of the several intermediate safety factors over the risk components and compares the findings of previous research. In addition, recommendations will be provided about potential measures to be implemented to mitigate road crash risk, as the follow-up that is required by the RISM procedure after the network-screening. The discussion will focus on those factors that resulted significant (up to 0.1) for at least one of the risk components. Table 8 summarises the significant factors in the case of the best-fit models. Overall, the same factors could have different effects on crash risk components. For instance, as for land-use factors, the agricultural zone may boost crash occurrence but reduce either the consequences in terms of severity or even the extent of the exposure factor. Likewise, travelling during weekdays and daytime increase the probability of a crash while reducing the severity outcome. Therefore, depending on the characteristics of each road (i.e., the presence/absence of a safety factor), the extent to which each factor defines the road (e.g., for which length extent it is registered), and the magnitude of the relative coefficient estimate, different values of crash occurrence probability, severity, and exposure can be returned. As a result, different combinations of risk components (which, in turn, depends on the coefficient estimates for each intermediate factor included in the prediction model) may result in the same risk range (score). This fact pinpointed that differences persist among the wide set of roads for e.g., road infrastructural, context, land use feature and exposure factors (i.e., traffic volumes), even in the same risk range. Therefore, as also argued by Barabino et al. (2021), at this stage of the analysis, crash risk ranges cannot be defined based on a specific set of intermediate factors.

Table 6 Crash severity model results (baseline model and best fit models).

		Baseline model			Best fit model
Category	Intermediate safety factors	Estimate	P-value	OR	Estimate	P-value	OR
Model constant		− 5.54			− 5.45
Users involved	Pedestrian	2.332	****	10.29	2.103	****	8.187
	Cyclist	0.851	**	2.341	0.651	*	1.917
	Heavy Good Vehicle	1.389	****	4.010	1.240	****	3.455

	Powered Two-Wheeler	0.951	****	2.589	0.746	****	2.109
Crash Type	Hit with obstacles	0.689	–	1.991	0.464		1.591
	Head-on or sideswipe	0.933	–	2.542	0.856		2.353
	Single vehicle collision	1.293	*	3.643	0.997		2.710
	Rear-end crash	0.112	–	1.118
Violation	Violation by user A (Yes)	0.130	–	1.139	0.183	–	1.201
	Violation by user B (Yes)	− 0.084	–	0.9192
Road Infrastructure	Road type
	Non-urban	0.761	****	2.140	0.744	****	2.105
	Road class
	Non primary	0.087	–	1.091
	Lanes per direction
	One lane	0.267	–	1.306	0.252	–	1.287
	Median presence

	Undivided carriageway	0.031	–	1.032
	Site type
	Segment	− 0.194	–	0.8237	− 0.210	–	0.8107
	Pavement condition		–
	Paved	− 0.32		0.7236
	Road signs type
	Horizontal	2.21	*	9.093	2.20	*	9.012
	Vertical	1.47	–	4.356	1.45	–	4.275
	Horizontal and Vertical	1.980	*	7.242	1.980	*	7.243
Operational	% Heavy Vehicle
	< 15 %	− 0.169	–	0.8441
	15 % − 30 %	− 0.026	–	0.9740

Environment	Type of terrain
	Flat	− 0.052	–	0.9497
	Rolling	− 0.088	–	0.9161
	Land Use
	Built up areas	− 0.262	–	0.7692
	Agricultural zone	− 0.658	*	0.5181	− 0.378	*	0.6855
	Forests and woods	− 0.339	–	0.7123
Socio-demographic	Population density
	Inhabitants per km2	− 0.00111	****	0.9989
	Network density
	Roads per km2	− 0.106	–	0.8998
Context conditions	Surface conditions
	Dry	− 0.118	–	0.8885

	Season
	Winter-Fall	− 0.024	–	0.9763
	Day type
	Weekday	− 0.390	**	0.6770	− 0.388	**	0.6782
	Daytime
	Day	− 0.770	****	0.4628	− 0.772	****	0.4623
Summary Statistics of the Model Fit		Baseline model			Best fit model
		Degree of freedom	Deviance	Mean deviance	Degree of freedom	Deviance	Mean deviance
	Regression	33	217	65.899	20	213	106.670
	Residual	6089	1685	0.2767	6102	1689	0.2768
	Total	6122	1902	0.3107	6122	1902	0.3107
Deviance Ratio (d.r.)	6.59				10.67

χ2	<0.001				<0.001
	Observed	Rights		Rights [%]1	Rights		Rights [%]
Total	6123	5902		96.39 %	5902		96.39 %
Fatal	221	0		0 %	0		0.00 %
Non– fatal	5902	5902		100.00 %	5902		100.00 %

P-value legend: ****: *<*0.001; ***: *<0.005; **<0.010; *<0.1; -:^>*0.1. 1

5.2. Crash probability

As for the road infrastructure, non-urban roads were found to increase the probability of crashes. This result is consistent with Ma and Kockelman (2008). However, it differs from Afghari et al. (2020), where urban roads were found to positively affect road crashes. Indeed, urban roads are characterised by a high level of interference among the several road users' categories (Bonera and Maternini, 2020). Nevertheless, this result is expected, because most of the road network considered in this study is made by non-urban roads.

Non-primary roads (i.e., those classified as F or C according to MIT, 2001) were found to have almost 6 times higher probability to register crashes as opposed to primary as in Yasmin and Eluru (2018) and Anarkooli et al. (2019). Indeed, compared to primary roads, nonprimary roads may be affected by lacking design properties or low maintenance that can lead to higher likelihood for crash to occur. In

This value is computed as the ratio between Rights and Observed.

Table 7 The ranking scale for the crash risk distribution of the road network of Brescia at the provincial and municipality level.

| Level | Crash Risk Index values | | | | | | | | |-------|-------------------------|---|---------|--------------------|---|-----------|--|--| | | Provincial level | | | Municipality level | | | | | | 1 | 0,00000 | - | 0,00203 | 0,0000000 | - | 0,0000001 | | | | 2 | 0,00203 | – | 0,01632 | 0,0000001 | – | 0,00085 | | | | 3 | 0,01632 | – | 0,06792 | 0,00085 | – | 0,02594 | | | | 4 | 0,06792 | – | 0,16676 | 0,02594 | – | 0,06485 | | | | 5 | 0,16676 | – | 0,54076 | 0,06485 | – | 0,81691 | | |

Table 8 Comparison of the effects of significant intermediate safety factors over the crash risk components.

Category	Intermediate safety factor	Crash Probability	Crash Exposure	Crash Severity
Road infrastructure
Non-urban road		▴		▴
Non-primary road		▴	▾
One-lane per direction		▴	▾
	Undivided carriageway	▴
Segment		▴
Paved surface		▴
Wet surface		▾
	Horizontal and vertical signs	▴		▴
Operational
< 15 % HGV		▴
15 % − 30 % HGV		▴	▴
> 30 %			▴
Environment
Flat terrain		▴	▴
Rolling terrain		▴	▴
Land Use
Built up areas		▴
Agricultural zones		▴	▾	▾
Forest and woods		▴
Context conditions
Winter-Fall season		▴
Weekdays		▴		▾
Daytime		▴		▾
Socio-demographic
Population density			▴
Users involved
Pedestrian				▴
Cyclist				▴
HGV				▴
PTW				▴
Crash dynamics
Single Vehicle crash				▴
Head-on or sideswipe				▴

▴indicates factors that help increasing the extent of the risk component; ▾ indicates factors that help decreasing the extent of the risk component.

addition, as opposed to primary roads, non-primary roads are generally managed by local authorities (e.g., Province), which may not have sufficient resources to adjust infrastructural and functional features to the required standard for the road classes.

Unlike Ma and Kockelman (2008), one-lane roads were found to increase crash occurrence probability as in Wang et al (2011) and Afghari et al. (2020).

Similarly, undivided carriageways were associated with a higher probability of crashes as opposed to divided. This may contribute to a greater share of head-on or sideswipe crashes, as no separation is provided among the two travel directions (Viera Gomes and Cardoso, 2012; Papadimitriou et al., 2019).

Segments were found to be prone crash-sites, compared to intersections. This represents a novel result because, all previous studies just focused on one of the two types of road location, and specifically analysed the effect of the related design characteristics instead. The increasing of the probability of crash on segments might be explained, by a higher degree of safety that intersection may have in this road network (e.g., not at-grade, so that flows are kept separated, MIT, 2001). Moreover, over the last years, many roundabouts were built over the main road network of Brescia so that intersection conflict points were reduced.

Unpaved roads are safer than paved roads. This result is unexpected. Nevertheless, as most of the roads are paved, this may be interpreted as a sign of lacking maintenance of road pavement conditions that may lead to unsafe conditions (Papadimitriou et al., 2019).

Wet pavement decreases the likelihood of a crash as opposed to dry. Although this result could seem unexpected, dry road surface, which may be related to good weather condition, e.g., no rain, or snow, may contribute to making drivers more confident and drive at higher speeds, as they perceive e.g., no slip is possible.

The presence of both vertical and horizontal signs increased the likelihood of a crash. Although it might be a counterintuitive finding, scares maintenance (e.g., ruined of colour-faded signs) may prevent drivers from adequately seeing road signs; or even an abuse of road signs may lead drivers to pay less attention to the warnings that they are meant to give, and maintain less safe driving behaviour while travelling. This was also confirmed by Yasmin and Eluru (2018), who found that higher road sign density increased the crash frequency.

As for operational factors, a 15–30 % of heavy good vehicles in the traffic flows contributed to higher crash occurrence probability. This is a controversial result. Pei et al. (2011) and Hosseinpour et al. (2014) find similar results, while Afghari et al. (2020) registered an opposite trend. However, it may be possible that with a limited number of HGV leads to less carefulness when driving, as HGV generally represent a critical element to deal with.

Built up areas, agricultural zones and forest and woods were found to increase the probability of crash as opposed to wet areas. Build-up areas are, indeed, characterised by greater traffic volumes and denser zone, which may contribute to the occurrence of interferences among road users. In addition, flat and rolling terrain are generally characterised by a higher likelihood of crash occurrence than mountain terrain. Indeed, agricultural zones are generally related to wide and flat terrain, which may induce drivers to travel at higher speed. Conversely, as for the latter case, wood areas may be more appropriate in mountainous and rolling environment, which may induce drivers to pay more attention. Conversely, a land use characterised by forest and woods seemed to still increase the occurrence of crashes. However, compared to flat terrain, the odds were lower (8.7 and 4.2, respectively).

Travelling by day and during weekdays increases the probability of crashes: greater traffic volumes are generally registered in daytime and during weekdays (due to systematic trips), than night and weekend. Moreover, travelling during winter and/or fall season increasing the probability of a crash occurring as opposed to other seasons. Finally, the population density does not affect the crash probability.

5.3. Crash exposure

As opposed to the crash probability, few factors affect the exposure model. Non-primary and one-lane roads showed a negative impact on the traffic volume estimation. Generally, non-primary roads have lower traffic volumes compared to primary roads, due to their functional role. In addition, road sections characterised by one-lane per direction are generally applied to minor roads (MIT, 2001). This was also confirmed by previous studies that showed that the more the number of lanes, the greater the traffic volumes (Zhao and Chung, 2001; Yang et al., 2014; Shojaeshafiei et al., 2017).

Higher presence of heavy vehicles (up to 30 %) on roads may be associated to great industrial or commercial areas. Hence, as also found by Pulugurtha and Mathew (2021), this may be related to the presence of traffic generating hubs so that greater AADT volume can be registered.

Novel results were the impacts of flat and rolling terrain on exposure.

Specifically, they both increased the traffic volumes. Presumably, flat and rolling terrain are associated with more regular vertical (but also horizontal) alignment, so that roads on such terrain type may be preferred by drivers. In addition, in this specific case, most of major roads are in the plain area of Brescia, where the surrounding is mainly characterised by flat or slight rolling terrain. Agricultural areas were found to decrease traffic volumes, instead. This may be intuitively related to the low attractiveness of such areas, and the lack of major hub which may generate greater traffic volumes. Population density increased the AADT estimation as in Zhao and Chung (2001) and Das and Tsapakis (2020). This result is intuitive as the greater the population density, the more traffic attractive/generating the area is.

5.4. Crash severity

Not many factors affect the severity. Non-urban roads were found to increase the odds of severe outcomes, confirming Afghari et al. (2020). Non-urban roads are characterised by higher speeds which may lead to greater damage and consequences in case of crash. The presence of both vertical and horizontal signs increased the severity of crashes. Again, this may be due to bad maintained road signs, which cannot be perceived anymore by road users. Indeed, as road signs are mainly aimed at alerting road users about road hazards and aware them towards careful driving behaviour, if no advice can be seen less protection is provided. In addition, two-lane roads have higher odd to record more severe road crash, as also found by Hosseinpour et al (2014).

If the most vulnerable road users (i.e., pedestrians, cyclists, and powered two-wheelers) were involved in a road crash, more severe consequences were registered (the severity odds increased by 8.187, 1.917, and 4.230 times). Indeed, being such users' categories those with less protection, they suffer more from road crash. In addition, also when HGV were involved in a crash, the severity odds increased by 3.455 times as opposed to crashes involving cars.

Head-on and single vehicle crashes increase the severity. As for headon crashes, that may be due to a hazardous manoeuvre that leads two vehicles one against the other, greater damage can result from the stronger hit between the two vehicles involved. According to Wang et al. (2011), single vehicle crashes can result in more severe consequences as this specific type of crash dynamic may be due to the health condition of drivers.

Travelling by day and during weekdays reduced the odds of severe road crashes compared to night-time and festive days, respectively. Travelling by day may secure higher lighting and visibility, so that drivers can have greater control over the surrounding road environment. However, this contrasted with Wang et al. (2011), who found that driving in darkness decrease the odds of severe crashes. Perhaps, the lower visibility at night (i.e., dark) that might reduce travel speed. As for safer driving at weekdays, this might still be related to time with greater traffic congestions (weekdays are working days) and lower speeds and confirms Wang et al. (2011) and Yasmin and Eluru (2018).

5.5. Comparison with existing methods

The proposed framework differs from existing methods of RNS.

Specifically, El-Basyouny and Sayed (2009), European Road Assess ment Program - EuroRAP (2020) applies a traditional method to evaluate the performance of road safety of a network. It relies on historical crash data and computes a ratio between the number of crashes and the billions of vehicles*km travelled for each road segment. Then, such ratio is compared against a gradual scale with fixed thresholds to identify black spots needing priority. Although the EuroRAP is a well-known and adopted method, it belongs to the category of reactive methods, as it does not predict the occurrence/frequency nor the severity of future crashes. In addition, severity is considered apart, and a gradual fixed value ranking scale is used to rank road segments. Moreover, a proprietary software is required to use the official EuroRAP method.

The European Union has recently updated the EU 96/2008/CE Directive on Road Infrastructure Safety Management (RISM) with the new EU Directive 1936/2019, by upgrading related procedures to provide safer roads and roadsides (European Commission, 2008; European Commission, 2019). Specifically, a risk-based network-wide mapping and safety ratings have been included as proactive assessments in place to the more traditional (and reactive) high crash concentration sites identification approach. Recently, the EU Directorate-General for Mobility and Transport has released the Network Wide Road Safety Assessment (NWA) Methodology and Implementation Handbook, to provide Member States with a methodological reference to perform effective road safety assessment at a network level (European Commis sion et al., 2023). The proposed methodology comprises both a reactive (statistical analysis of crash data) and a proactive (in-built safety evaluation) assessment procedure, whose results are then integrated to obtain an overall network wide assessment of the network, according to a 5-level ranking scale. However, although effective, the proposed NWA does not account for a full-developed risk formulation and still requires a quite time and resource consuming data input step, as for each segment specific and quantitative data are required to compute the included accident density/rates and reduction factors.

As for the modelling results, it is interesting to discuss the main difference with Bonera (2022), where a CPM was also applied to the same road network, which – however – computed the crash risk as the product of frequency and severity models. In terms of results, less than 30 % of the Risk Scores obtained for the several road segments included in the analysis at the provincial level got the same risk level. As a matter of fact, the main difference lies on the modelling technique adopted for the crash occurrence estimation: in this paper, a probability model (i.e., logit model) for crash occurrence is used and the exposure estimated separately; in the previous paper, a frequency model for crash counts is used, which also includes the exposure factor. As for the severity, the same modelling technique was used, so that results for the severity component are the same.

Therefore, the response variable for the crash occurrence represented the foremost dissimilarity, which strongly affected the overall road crash risk outcome. Indeed, based on a set of explanatory variables, the model here proposed estimates the probability of "even-a-single" crash, with no reference on "how many". Hence, e.g., infrastructural, context, environmental conditions for which one or more than one crash can be registered are treated at the same level. Conversely, when considering crash frequency, conditions that may lead to one, two, or more expected crashes are considered at different levels. As a result, the identification of roads that can register even a single crash should be accounted for and treated evenly to roads that, according to a frequency approach, can register a higher number of crashes. Indeed, if just a single crash can be avoided by reducing the probability of the crash to occur, then the analysis achieved its objective: it may be reasonable to think that, given specific conditions, the greater the probability of crash occurrence, also the greater the number of crashes that can be registered.

5.6. Recommendations

Some measures oriented to the most critical roads are proposed because of the previous discussion. They may help in reducing the overall road crash risk. Clearly, such measures are intended to provide proactive actions according to road crash risk formulation.

As for road Infrastructure features, ordinary and extra-ordinary maintenance may be suggested for non-urban roads. As for ordinary maintenance, yet paved, roads with uneven or battered road surface may lead to a loss of control by the driver or still dangerous manoeuvres. Hence, keeping the road surface in good condition is key. In addition, a revision of vertical and horizontal road signs will help enhance the readability of the road. Less but clearer and more effective road signs should be installed only, while avoiding the abuse of too many

indications, that may be also ignored by drivers. As for extra-ordinary maintenance, more invasive interventions can be proposed. For instance, if divided carriageway can help keeping separated the two travel directions and so the share of head-on or sideswipe crashes, median barriers can be introduced especially where higher level of traffic is registered, and the cross-section provides enough space. Separated facilities on the roadside would be advisable for the most vulnerable road users such as cyclists. In this way, beside avoiding conflicts between motorised and non-motorised road users' categories, it would also help in preventing more severe crashes involving the most vulnerable users. Furthermore, to prevent single vehicle crashes lower speed limits can be set/revised, and speed control devices can be installed. Overall, nonurban roads should be set according to the concept of the forgiving road and roadside and self-explaining road. In this way, road should be redesigned in a way that drivers immediately can understand which the most appropriate driving behaviour is to be held on the. However, in case of errors while driving, the road is set in a way it compensates for it.

As for operational features, the presence of heavy good vehicles turned to be a critical aspect. In that sense, it may be reasonable to first, equip roads with specific road signs to alert other users about the presence of HGV. Otherwise, when possible, it may be advisable to impose HGV specific itinerary that may follow safer and more adapted routes.

As for environment and land use features, both flat and rolling terrain may contribute to a higher probability of crashes and higher traffic volumes. Flat surface (along with straight segments) may be related to higher speed and to preferable itineraries by road users, due to the ease of driving. Rolling surface may be related to an uneven vertical (but also horizontal) alignment of the road that may contribute to driving difficulties. Hence, greater traffic control measures should be adopted to limit the driving speed but also some modification in the road alignment (e.g., traffic calming measures) may help in mitigating those effect.

Finally, as for context conditions, weekday and daytime travelling was found to positively increase crash probability, while reducing crash severity. However, over these time spans also greater traffic volumes may circulate on the road network. Hence, once again measures and intervention that can limit traffic conflicts, driving speeds and enhance road readability may help mitigate the road crash risk.

6. Conclusions and future perspectives

The contributions of this study are:

In recent years, the European Union has put a lot of effort and dedication into improving road safety. It has provided Road Safety Authorities (RSAs) with guidelines to manage the impact of road infrastructure on safety. However, further decision support tools are needed to help RSA enhance safety performance of their road networks: a proactive approach based on risk may efficiently meet this need. Despite existing literature provides valuable insights on Road Network Screening and Crash Prediction Models, an overall road crash risk model that complies with its definition is still missing from the research result.

The proposal of a new framework to perform a Risk-Based Network-Wide Road Safety Screening to estimate safety performance on a road network and identify the most critical segments. This framework: (i) integrates basemap, context, road traffic and crash data from different sources; (ii) systematises these data according to EU Directive 1936/2019 and EN 39001:2012; (iii) sets a tri-variate road crash risk prediction model to provide safety performance ranking
for each segment (of road) at hand, which is classified accordingly. • The setting of the crash occurrence model in terms of probability rather than frequency to estimate its amount; the crash exposure model to estimate traffic volumes in case of data unavailability; and the crash severity model as a driver of vulnerability.
The illustration of this framework in a real-world experiment to evaluate its effectiveness. Easy-to-read control dashboards based on

charts and maps help diagnosticate the safety performance on each segment and drive for prioritising interventions on the high-risk safety roads and segments.

This framework results in the following implications. It can be adopted to:

Systematise the overall dataset relying on the most common data obtained from official sources (e.g., official statistics bodies, Governments) to be consistent and standardized for all roads considered. Too detailed information may not be available for all roads, nor their recognition may be feasible or possible.
Assess the safety risk on each road segment for possible prioritise actions, allocate resources better and enhance safety performance of road networks. This study showed that the measure of crash risk could help develop a program to increase road safety performance for RASs.
Assign higher importance to those conditions that represented a major hazard, regardless of the number of crashes that could be recorded adopting the probability of occurrence instead of the frequency. As a result, roads that can register "even-a-single crash" are treated equally to roads that, according to a frequency approach, can register a higher number of crashes. However, it may be reasonable assume that, given specific conditions, the higher the probability of crash occurrence, the higher the number of crashes that can be recorded.
Calculate and control each risk component (model) separately and independently from each other, so that targeted measures can be better identified.

This framework was tested over the main road network of the Province of Brescia (Lombardy Region – Italy), and results can identify critical (risky) segments (and roads) of the network at hand. To the best of our knowledge, this framework provides the first empirical contribution towards the detailed understanding of road network screening, according to a complete road crash risk model. It is worth noting that the peculiarity of the context investigated will not affect the framework, but it will influence the overall results. Indeed, the framework is flexible and can be generalised, because if one aims at applying it, some calibration of coefficients could be required if the context at hand strongly differ from the original one (i.e., northern Italy).

Despite these interesting results, this study has some limitations and could be improved.

First, it would be interesting to consider more levels of the response variable in the probability computation, i.e., to return the probability that n number of crashes will occur. The same may be suggested also for severity estimation. The application of the method over time or to other contexts may be useful, to further test the predictive capabilities. Indeed, this could help in strengthening the results obtained and specifically confirm the effect of the explanatory variables over the several response variables. Testing additional risk factors to further improve the modelling prediction capabilities and assess their effect.

Second, this study provided RSAs with a risk prediction framework recommending effective management actions to enhance road safety performance. Consequently, econometric models were employed due to the straightforward interpretability of the effect each factor has on road crash risk. Nevertheless, from a modelling viewpoint, improvements can be made to outperform the prediction capabilities:

• the dataset was unbalanced between non crashes (high numbers) and crashes (low numbers). As a result, the model was better at predicting non crashes than crashes. Therefore, in future research, the analysis on the impact of a lower share of non-crashes or a higher share of crashes in the evaluation of the performance model and the significance of each predictor might help enhance the overall understanding of it. For instance, zero-inflated models might be more

suitable for count data that have many zero counts (e.g. models such as those described by Lambert, 1992). The zero-inflated Poisson distribution could be employed to represent count data where the percentage of zero counts exceeds what would be anticipated based on the average of the non-zero counts.
novel models could be specified, calibrated, and validated. Specifically, incorporating imbalanced Machine Learning (ML) approaches within the framework to increase the performance on crash prediction, incorporating solutions such as oversampling or random oversampling/under sampling with synthetic data generation to generate more artificial crash cases for model training (e.g. see Ziakopoulos et al., 2023). These models can capture the intricate (often nonlinear) relationship between the frequency and the severity of crashes and its influencing factors. Since several variables have already been identified as informative, they can be explicitly provided to the ML models as inputs. More resources can then be diverted to explicitly fine-tuning machine learning hyperparameters and internal model configurations/structures.

Third, the framework was based on the context at hand and the available crash data and included only fatal and not fatal crashes. It calls for two novel research avenues. On the one hand, if data on property damage only crashes will be available, the severity model could be enhanced by multivariate logistic regression. On the other hand, if crash data were not available, the model should be adjusted to include like response variables the probability of "misses crashes" and the severity of "misses crashes". Moreover, exploring alternative datasets in other areas or with different explanatory variables is always a valid option as well.

To conclude, the evaluation of quantitative performance using other methodologies e.g., iRAP, EuroRAP, Network Wide Road Safety Assessment Methodology will be included in the research agenda to possibly demonstrate the reliability of the proposed framework.

CRediT authorship contribution statement

Michela Bonera: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Visualization, Writing – original draft, Writing – review & editing. Benedetto Barabino: Conceptualization, Investigation, Methodology, Supervision, Writing – original draft, Writing – review & editing. George Yannis: Conceptualization, Methodology, Supervision, Writing – review & editing. Giulio Maternini: Conceptualization, Methodology, Supervision, Writing – review & editing.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability

The authors do not have permission to share data.

Appendices A–D. Supplementary material

Supplementary data to this article can be found online at https://doi. org/10.1016/j.aap.2024.107502.

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