Uncovering the behaviour of road accidents in urban areas

Different patterns in the incidence of road accidents are revealed when considering areas with increased levels of urbanization. To understand these patterns, road accident data from England and Wales is explored. In particular, the data are used to (i) generate time series for comparison of the incidence of road accidents in urban as opposed to rural areas, (ii) analyse the relationship between the number of road accidents and the population size of a set of urban areas, and (iii) model the likelihood of suffering an accident in an urban area and its dependence with population size. It is observed that minor and serious accidents are more frequent in urban areas, whereas fatal accidents are more likely in rural areas. It is also shown that, generally, the number of accidents in an urban area depends on population size superlinearly, with this superlinear behaviour becoming stronger for lower degrees of severity. Finally, given an accident in an urban area, the probability that the accident is fatal or serious decreases with population size and the probability that it is minor, increases sublinearly. These findings promote the question as to why such behaviours exist, the answer to which will lead to more sustainable urban policies.

paragraph) are based on the same source, please add it in more than one places (e.g. at the beginning and at the end of the paragraph). -In part (c) of the introduction, it is written "… the UK's participation in projects such as Vision Zero …". Vision Zero is not a project but a road safety strategy, which initiated in Sweden in the 90's and since then, has been adopted by numerous countries in the framework of the Safe System approach towards road safety. Please adjust the text accordingly.
-Data used in this paper refer to only one year (2017). This is not common in road safety research as the number of road accidents and casualties in one year may be strongly affected by local, temporare conditions (e.g. existing work zones, infrastructure projects, traffic arrangements or even one major accident with multiple casualties). Therefore, time-series analysis should use data from an at least 10-year period. Especially in the UK, where complete and reliable road safety data are available for several decades, this is possible and necessary.
-According to the text, data used refer to 2017. However, in the supplementary excel file available with this submission, it is written 2011. Please, clarify and correct as necessary. In addition, the data used in this work are not accessible through the website indicated in the text (data.gov.uk) (at least it is not clear how they could be accessed). Please provide the specific link to the used data. In addition, in the excel file, it is not clear what "Total" means in column titled "Rural urban". Please explain this.
-The text in Data and methods (b) presents a light repetition in comparison to (a). Please amend it to avoid that.
-The authors suggest that the increased number of fatalities in rural areas is due to the higher speed limits there. Indeed speed limits are the legislative "official" measure of behaviour however, road safety research has indicated that what is even more important are adopted / travelling speeds and these may differ significantly from speed limits. Thus, it is more appropriate to discuss about travel speeds than speed limits.
Decision letter (RSOS-191739.R0) 02-Jan-2020 Dear Professor Cabrera-Arnau, The editors assigned to your paper ("Uncovering the behaviour of road accidents in urban areas") have now received comments from reviewers. We would like you to revise your paper in accordance with the referee suggestions which can be found below (not including confidential reports to the Editor). Please note this decision does not guarantee eventual acceptance.
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If you wish to submit your supporting data or code to Dryad (http://datadryad.org/), or modify your current submission to dryad, please use the following link: http://datadryad.org/submit?journalID=RSOS&manu=RSOS-191739 • Competing interests Please declare any financial or non-financial competing interests, or state that you have no competing interests.
• Authors' contributions All submissions, other than those with a single author, must include an Authors' Contributions section which individually lists the specific contribution of each author. The list of Authors should meet all of the following criteria; 1) substantial contributions to conception and design, or acquisition of data, or analysis and interpretation of data; 2) drafting the article or revising it critically for important intellectual content; and 3) final approval of the version to be published.
All contributors who do not meet all of these criteria should be included in the acknowledgements.
We suggest the following format: AB carried out the molecular lab work, participated in data analysis, carried out sequence alignments, participated in the design of the study and drafted the manuscript; CD carried out the statistical analyses; EF collected field data; GH conceived of the study, designed the study, coordinated the study and helped draft the manuscript. All authors gave final approval for publication.
• Acknowledgements Please acknowledge anyone who contributed to the study but did not meet the authorship criteria.
• Funding statement Please list the source of funding for each author.
Once again, thank you for submitting your manuscript to Royal Society Open Science and I look forward to receiving your revision. If you have any questions at all, please do not hesitate to get in touch. Comments to the Author(s) This paper deals with the estimation of the incidence of a road accident injury in urban areas in England and Wales. The paper is well written with an adequate literature review. The presented methodology, while simplistic, is scientifically sound and successfully conveyed to the reader. Finally, the conclusions are valid and well supported by the data. Some issues should be addressed for the further improvement of the paper: -The objective of the paper should be written more clearly in both the abstract and the introduction of the paper. -In chapter 2a, the authors refer that data concern 2017. However, in the dataset provided in the supplementary files 2011 accident data are included. Please correct accordingly.
-The sub-chapter 1c does not offer extra value in the paper, while its title is not relevant as well. It is suggested that the related to paper information to be added in the sections 1a and 2a.
-The title of Table 2 should be corrected.

Reviewer: 2
Comments to the Author(s) This paper presents an effort to link road accidents to socioeconomic sizes i.e. population and urbanization. In the field of road safety, this is not something new. On the contrary, several studies have taken into account such metrics, in combination with others, to explore their impact on the number and the severity of road accidents. Based on international literature, it is well established that the number of road accidents increases in urban areas due to the increased number of traffic conflicts. Moreover, the severity of accidents increases in rural areas due to the higher travel speeds. The specific paper mathematically verifies existing road safety knowledge. Thus, it could be more appealing to mathematicians than to road safety scientists. It remains to the journal Editor to decide whether or not this paper is suitable for publication in the specific journal. In any case, the following points should be taken into consideration for the overall improvement of the paper: -In part (a) of the introduction, several statements are made without indicating the respective source. E.g. in the first paragraph a WHO reference is included only in the first sentence. Please indicate all used sources in the text and in the reference list. If several sentences (e.g. a whole paragraph) are based on the same source, please add it in more than one places (e.g. at the beginning and at the end of the paragraph).
-In part (c) of the introduction, it is written "… the UK's participation in projects such as Vision Zero …". Vision Zero is not a project but a road safety strategy, which initiated in Sweden in the 90's and since then, has been adopted by numerous countries in the framework of the Safe System approach towards road safety. Please adjust the text accordingly.
-Data used in this paper refer to only one year (2017). This is not common in road safety research as the number of road accidents and casualties in one year may be strongly affected by local, temporare conditions (e.g. existing work zones, infrastructure projects, traffic arrangements or even one major accident with multiple casualties). Therefore, time-series analysis should use data from an at least 10-year period. Especially in the UK, where complete and reliable road safety data are available for several decades, this is possible and necessary.
-According to the text, data used refer to 2017. However, in the supplementary excel file available with this submission, it is written 2011. Please, clarify and correct as necessary. In addition, the data used in this work are not accessible through the website indicated in the text (data.gov.uk) (at least it is not clear how they could be accessed). Please provide the specific link to the used data. In addition, in the excel file, it is not clear what "Total" means in column titled "Rural urban". Please explain this.
-The text in Data and methods (b) presents a light repetition in comparison to (a). Please amend it to avoid that.
-The authors suggest that the increased number of fatalities in rural areas is due to the higher speed limits there. Indeed speed limits are the legislative "official" measure of behaviour however, road safety research has indicated that what is even more important are adopted / travelling speeds and these may differ significantly from speed limits. Thus, it is more appropriate to discuss about travel speeds than speed limits.

Do you have any ethical concerns with this paper? No
Have you any concerns about statistical analyses in this paper? No

Recommendation?
Accept with minor revision (please list in comments)

Comments to the Author(s)
This is a revised paper dealing with the estimation of the incidence of a road accident injury in urban areas in England and Wales. The authors have addressed successfuly all comments. A minor issue is suggested to be tackled before the publication of the paper: -The adoption of the vision zero by the UK is not relevant with the description of the accident data in the section 2a. The authors are suggested either to add this paragraph in the introduction or delete it.

Review form: Reviewer 2
Is the manuscript scientifically sound in its present form? Yes

Do you have any ethical concerns with this paper? No
Have you any concerns about statistical analyses in this paper? No

Recommendation?
Accept as is

Comments to the Author(s)
The current version of the paper shows a significant effort on behalf of the authors to address all reviewers' comments. The objective and the intended audience of this work are now clearer. All in all, the paper is now more cohesive and comprehensive and it is considered appropriate for publication. One last suggestion to the authors is to use the following link as a reference to Vision Zero: https://www.trafikverket.se/en/startpage/operations/Operations-road/vision-zero-academy/ The link currently included in the text does not refer to the initial concept of Vision Zero but to the Vision Zero Network which is a collaborative campaign helping communities reach their goals of Vision Zero.

06-Mar-2020
Dear Professor Cabrera-Arnau: On behalf of the Editors, I am pleased to inform you that your Manuscript RSOS-191739.R1 entitled "Uncovering the behaviour of road accidents in urban areas" has been accepted for publication in Royal Society Open Science subject to minor revision in accordance with the referee suggestions. Please find the referees' comments at the end of this email.
The reviewers and Subject Editor have recommended publication, but also suggest some minor revisions to your manuscript. Therefore, I invite you to respond to the comments and revise your manuscript.
• Ethics statement If your study uses humans or animals please include details of the ethical approval received, including the name of the committee that granted approval. For human studies please also detail whether informed consent was obtained. For field studies on animals please include details of all permissions, licences and/or approvals granted to carry out the fieldwork.
• Data accessibility It is a condition of publication that all supporting data are made available either as supplementary information or preferably in a suitable permanent repository. The data accessibility section should state where the article's supporting data can be accessed. This section should also include details, where possible of where to access other relevant research materials such as statistical tools, protocols, software etc can be accessed. If the data has been deposited in an external repository this section should list the database, accession number and link to the DOI for all data from the article that has been made publicly available. Data sets that have been deposited in an external repository and have a DOI should also be appropriately cited in the manuscript and included in the reference list.
If you wish to submit your supporting data or code to Dryad (http://datadryad.org/), or modify your current submission to dryad, please use the following link: http://datadryad.org/submit?journalID=RSOS&manu=RSOS-191739.R1 • Competing interests Please declare any financial or non-financial competing interests, or state that you have no competing interests.
• Authors' contributions All submissions, other than those with a single author, must include an Authors' Contributions section which individually lists the specific contribution of each author. The list of Authors should meet all of the following criteria; 1) substantial contributions to conception and design, or acquisition of data, or analysis and interpretation of data; 2) drafting the article or revising it critically for important intellectual content; and 3) final approval of the version to be published.
All contributors who do not meet all of these criteria should be included in the acknowledgements.
We suggest the following format: AB carried out the molecular lab work, participated in data analysis, carried out sequence alignments, participated in the design of the study and drafted the manuscript; CD carried out the statistical analyses; EF collected field data; GH conceived of the study, designed the study, coordinated the study and helped draft the manuscript. All authors gave final approval for publication.
• Acknowledgements Please acknowledge anyone who contributed to the study but did not meet the authorship criteria.
• Funding statement Please list the source of funding for each author.
Please note that we cannot publish your manuscript without these end statements included. We have included a screenshot example of the end statements for reference. If you feel that a given heading is not relevant to your paper, please nevertheless include the heading and explicitly state that it is not relevant to your work.
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Once again, thank you for submitting your manuscript to Royal Society Open Science and I look forward to receiving your revision. If you have any questions at all, please do not hesitate to get in touch. Comments to the Author(s) This is a revised paper dealing with the estimation of the incidence of a road accident injury in urban areas in England and Wales. The authors have addressed successfuly all comments. A minor issue is suggested to be tackled before the publication of the paper: -The adoption of the vision zero by the UK is not relevant with the description of the accident data in the section 2a. The authors are suggested either to add this paragraph in the introduction or delete it.

Reviewer: 2
Comments to the Author(s) The current version of the paper shows a significant effort on behalf of the authors to address all reviewers' comments. The objective and the intended audience of this work are now clearer. All in all, the paper is now more cohesive and comprehensive and it is considered appropriate for publication. One last suggestion to the authors is to use the following link as a reference to Vision Zero: https://www.trafikverket.se/en/startpage/operations/Operations-road/vision-zero-academy/ The link currently included in the text does not refer to the initial concept of Vision Zero but to the Vision Zero Network which is a collaborative campaign helping communities reach their goals of Vision Zero.
Author's Response to Decision Letter for (RSOS-191739 Decision letter (RSOS-191739.R2) 19-Mar-2020 Dear Professor Cabrera-Arnau, It is a pleasure to accept your manuscript entitled "Uncovering the behaviour of road accidents in urban areas" in its current form for publication in Royal Society Open Science.
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Reviewer 2
R: This paper presents an effort to link road accidents to socioeconomic sizes i.e. population and urbanization. In the field of road safety, this is not something new. On the contrary, several studies have taken into account such metrics, in combination with others, to explore their impact on the number and the severity of road accidents. Based on international literature, it is well established that the number of road accidents increases in urban areas due to the increased number of traffic conflicts. Moreover, the severity of accidents increases in rural areas due to the higher travel speeds. The specific paper mathematically verifies existing road safety knowledge. Thus, it could be more appealing to mathematicians than to road safety scientists. It remains to the journal Editor to decide whether or not this paper is suitable for publication in the specific journal.
A: The abstract (page 1) and introduction (last two paragraphs of section 1a and last paragraph of section 1b; pages 2 and 3) have been rephrased to express the aims and value of this paper with greater clarity. In the first paragraph of the discussion (page 8) and the first paragraph of the conclusion (page 9), the authors now acknowledge that, indeed, some of the results presented in the paper have been already explored by previous researchers. R: In any case, the following points should be taken into consideration for the overall improvement of the paper: in part (a) of the introduction, several statements are made without indicating the respective source. E.g. in the first paragraph a WHO reference is included only in the first sentence. Please indicate all used sources in the text and in the reference list. If several sentences (e.g. a whole paragraph) are based on the same source, please add it in more than one places (e.g. at the beginning and at the end of the paragraph).
A: The locations of the citations have been updated following the suggestions given in the reviewer's comment. R: In part (c) of the introduction, it is written ". . . the UK's participation in projects such as Vision Zero . . . ". Vision Zero is not a project but a road safety strategy, which initiated in Sweden in the 90's and since then, has been adopted by numerous countries in the framework of the Safe System approach towards road safety. Please adjust the text accordingly.
A: Thank you for the clarification. This information has been incorporated and it is now located in section 2a (page 3), according to the other reviewer's suggestion. R: Data used in this paper refer to only one year (2017). This is not common in road safety research as the number of road accidents and casualties in one year may be strongly affected by local, temporary conditions (e.g. existing work zones, infrastructure projects, traffic arrangements or even one major accident with multiple casualties). Therefore, time-series analysis should use data from an at least 10-year period. Especially in the UK, where complete and reliable road safety data are available for several decades, this is possible and necessary.
A: The authors appreciate the need to use data from a longer period. The results for the time-series analysis have now been obtained for the time period spanning from the year 2008 to the year 2018 (since the first submission, the dataset corresponding to 2018 was released). Similarly, the results for the scaling analysis have been recomputed with the larger data set; the values of the scaling exponents for each individual year have also been included in the