Predictive Modeling of Crash Frequency on Mountainous Highways: A Mixed-Effects Approach Applied to a Brazilian Road

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

First of all, I would like to thank the authors for their effort to conduct the present research. This paper presented a methodology for estimating the travel time on urban roads and expressways. I have listed the following comments to improve the quality of the paper and I believe the paper needs to be improved and needs more rounds of review and consideration before publishing.

 

General points:

1. Key words should be selected related to the content of the paper. Please choose more related words to improve.
2. References are not updated. Please use more recent references.

 

Technical points:

1. Please clarify how you have categorized the contributing factors you have used in this paper such as type of the roads, distance, timing etc. Are those based on previous research or you yourself classified them?
2. Was Table 1 classified by the authors or reference is needed to refer the content? How do levels represent conformity? For example, what level A represents? More explanation is needed.
3. Evaluation process may need to be explained more to clarify the matching procedure. I did not understand that procedure well enough.
4. What is the reason that you considered different factors including time and distance in highways and urban roads respectively for travel time estimation and calculating the accuracy of the model?
5. Also, the subject of the paper says the methodology estimates the travel time, however, there were no estimation details mentioned in the paper. It would be best if you explain more about that.
6. I am not sure if there is new contribution in the paper compared with similar researches conducted in this regard. However, please provide more details about the differences and the main reasons that your research stands strongly based on the true evidence.

Author Response

We thank the reviewer for their time and effort in providing feedback. However, upon a detailed review of the comments, we believe there may have been a significant misunderstanding, as the critiques appear to be directed at a different manuscript.

The comments from reviewer consistently refer to a study on "travel time estimation on urban roads and expressways," including:

• A methodology for "estimating travel time."
• An analysis of factors like "type of roads, distance, timing."
• A "Table 1" that classifies factors based on "levels" and "conformity."
• An "evaluation process" involving a "matching procedure."

In contrast, our manuscript, "Predictive modeling of crash frequency on mountainous highways: a mixed-effects approach applied to a Brazilian road," presents:

• A crash frequency prediction model, not a travel time estimation model.
• An analysis of a single, specific mountainous highway (BR-116/SP), not a network of urban roads and expressways.
• A Generalized Linear Mixed Model (GLMM) with a Negative Binomial distribution.
• A Table 1 that summarizes data sources and variable descriptions.

Given that reviewer's comments do not correspond to the content, methodology, or findings of our submitted work, we are unable to provide a point-by-point response.

We have, however, thoroughly and diligently addressed all comments from other reviewers, making substantial revisions to improve the manuscript as detailed in the previous sections. We hope these revisions meet with your approval.

Reviewer 2 Report

Comments and Suggestions for Authors

This manuscript presents a comprehensive study on crash frequency prediction along a 57-km mountainous segment of the BR-116/SP highway in Brazil. The research employs a Generalized Linear Mixed Model (GLMM) with Negative Binomial distribution to analyze the influence of roadway geometry, environmental conditions, and traffic exposure on crash occurrence. 

Specific comments:

1. While using segment-based analysis, the paper doesn't adequately address spatial autocorrelation effects or network connectivity patterns. The paper can be improved by incorporating spatial analysis techniques to examine crash clustering patterns.
2. The paper mentions sustainability primarily in road safety context but doesn't fully integrate broader sustainability concepts.
3. The paper relies on traditional data sources but doesn't explore opportunities from modern sensing technologies. Discuss how emerging technologies (connected vehicles, IoT sensors, smartphone data) could enhance crash prediction capabilities.
4. The paper includes meteorological variables but doesn't adequately address climate change impacts or extreme weather resilience.The following paper doi.org/10.1016/j.jtrangeo.2025.104420 may help improve the manuscript.
5. While high-risk locations are identified, policy recommendations could be more specific and actionable.

Author Response

Reviewer Comment 1: While using segment-based analysis, the paper doesn't adequately address spatial autocorrelation effects or network connectivity patterns. The paper can be improved by incorporating spatial analysis techniques to examine crash clustering patterns.

Author Response: We thank the reviewer for this critical methodological insight. We acknowledge that spatial autocorrelation is a key consideration in road safety modeling, as crashes in adjacent segments are often not independent. While our GLMM with a random intercept for segment (u_i) accounts for some unobserved, segment-specific heterogeneity, it does not explicitly model the spatial dependency between segments.

To address this, we have conducted a post-hoc spatial analysis of the model's residuals and have significantly expanded the discussion on this limitation and its implications for future work.

Reviewer Comment 2: The paper mentions sustainability primarily in the road safety context but doesn't fully integrate broader sustainability concepts.

Author Response: We agree with the reviewer and have expanded our discussion of sustainability to explicitly address the "triple bottom line": social, environmental, and economic dimensions, moving beyond the primary focus on social (safety) sustainability.

Reviewer Comment 3: The paper relies on traditional data sources but doesn't explore opportunities from modern sensing technologies. Discuss how emerging technologies (connected vehicles, IoT sensors, smartphone data) could enhance crash prediction capabilities.

Author Response: This is an excellent suggestion that points toward the future of road safety analytics. We have added a dedicated discussion point on this in the "Future Research" section.

Reviewer Comment 4: The paper includes meteorological variables but doesn't adequately address climate change impacts or extreme weather resilience. The following paper doi.org/10.1016/j.jtrangeo.2025.104420 may help improve the manuscript.

Author Response: We thank the reviewer for this crucial point and for the highly relevant reference. We have integrated this perspective to frame our findings within the context of a changing climate, which is critical for the long-term sustainability and resilience of highway infrastructure.

Reviewer Comment 5: While high-risk locations are identified, policy recommendations could be more specific and actionable.

Author Response: We have taken this advice to heart and have substantially revised the "Practical Implications" section in the Conclusion to provide a clear, tiered, and actionable set of recommendations for different stakeholders.

Reviewer 3 Report

Comments and Suggestions for Authors

The paper "Predictive modeling of crash frequency on mountainous highways: a mixed-effects approach applied to a Brazilian road" has a suitable methodology, a clear structure and is relevant to the field of sustainable traffic safety. The authors use adequate statistical methods (GLMM with negative binomial distribution). The results are clearly interpreted, and the discussion relates the findings to previous studies. However, there are aspects that can be improved to improve the work and I suggest a minor revision.

• The biggest objection to the work is the small number of literary units. In the introductory section, expand the view on traffic safety to create a bigger picture. I suggest citing some of the works: https://doi.org/10.3390/su16187903b and https://doi.org/10.18280/ijtdi.070406. In addition to the above, in the introductory part, but also in the discussion and where you can, list at least 10 more works of recent date, in order to improve and expand the now modest list of literature.
• I suggest that you define the research questions or hypotheses in the introductory section. This would make it easier for the reader to understand what specific problems the model focuses on.
• It is desirable to include a flowchart of the methodological procedure, which would visually show the steps from data collection to modeling.
• If possible, the data should be aggregated to a monthly level and consider daily or weekly aggregation, if the data is available. This would allow the inclusion of dynamic weather factors. If not possible, state this in the limitation of the work and/or future research directions.
• Additionally consider the inclusion of triple interactions (eg curvature × grade × rainfall), as they could better explain the complex driving conditions on mountain roads.
• If possible, add a table with descriptive statistics (means, standard deviations) of all main variables. Currently, it goes directly to the model, without displaying the basic characteristics of the data.
• The section on practical implications needs to be expanded, especially for decision makers and road managers (eg how exactly they can apply the findings in practice).
• It is necessary to highlight special recommendations for future research in a separate subheading in the conclusion.
• Considering the journal, it would be good to add a paragraph in the conclusion about the implications for sustainability, how the proposed approach contributes to emission reductions, energy efficiency and economic benefits.
• You can consider evaluating the costs and benefits of implementing the measures proposed by the model, which would give a practical dimension to sustainability or indicate future research directions.

Author Response

Reviewer Comment 1: The biggest objection to the work is the small number of literary units. In the introductory section, expand the view on traffic safety to create a bigger picture. I suggest citing some of the works: https://doi.org/10.3390/su16187903 and https://doi.org/10.18280/ijtdi.070406. In addition to the above, in the introductory part, but also in the discussion and where you can, list at least 10 more works of recent date, in order to improve and expand the now modest list of literature.

Author Response: We sincerely thank the reviewer for this crucial suggestion. We fully agree that a more comprehensive literature review strengthens the paper's foundation. We have expanded the literature review in the Introduction and Discussion sections by incorporating 10 more recent and relevant works, including one specifically suggested. The new citations cover a wider spectrum, including global safety studies, advanced modeling techniques, human factors, and the direct link between safety and sustainability, which perfectly aligns with the journal's scope.

Reviewer Comment 2: I suggest that you define the research questions or hypotheses in the introductory section. This would make it easier for the reader to understand what specific problems the model focuses on.

Author Response: We thank the reviewer for this excellent suggestion. We have now added a dedicated paragraph at the end of the Introduction that clearly states the research questions guiding this study. This provides a clear roadmap for the reader.

Reviewer Comment 3: It is desirable to include a flowchart of the methodological procedure, which would visually show the steps from data collection to modeling.

Author Response: We agree that a visual representation of the methodology will greatly enhance clarity. We have created a new figure (now Figure 1) illustrating the entire methodological workflow and have referenced it in the "Methodology" section.

Reviewer Comment 4: If possible, the data should be aggregated to a monthly level and consider daily or weekly aggregation, if the data is available. This would allow the inclusion of dynamic weather factors. If not possible, state this in the limitation of the work and/or future research directions.

Author Response: We thank the reviewer for this suggestion. Our data was already aggregated at the monthly level, as stated in Sections 2.2 and 2.3.1. Unfortunately, daily or weekly traffic volume and crash data were not available for the entire 10-year study period from the concessionaire, which precluded a higher-resolution analysis. We have now explicitly acknowledged this as a key limitation and a direction for future research.

Reviewer Comment 5: Additionally consider the inclusion of triple interactions (eg curvature × grade × rainfall), as they could better explain the complex driving conditions on mountain roads.

Author Response: This is a very insightful suggestion. We tested the triple interaction between curve radius, longitudinal grade, and precipitation. However, this interaction term was not statistically significant (p > 0.05) and did not improve the model fit. We believe this is likely due to the monthly weather data aggregation, as suggested by the reviewer in point #4, which dilutes the immediate, high-risk effect of rainfall on specific curves and grades. We have addressed this in the manuscript.

Reviewer Comment 6: If possible, add a table with descriptive statistics (means, standard deviations) of all main variables. Currently, it goes directly to the model, without displaying the basic characteristics of the data.

Author Response: We agree that this is a crucial addition for transparency. We have created a new Table 2 with descriptive statistics and renamed the subsequent tables.

Reviewer Comment 7: The section on practical implications needs to be expanded, especially for decision makers and road managers (eg how exactly they can apply the findings in practice).

Author Response: We have thoroughly expanded the practical implications in the Conclusion section to provide a clear, actionable guide for road managers and decision-makers.

Reviewer Comment 8: It is necessary to highlight special recommendations for future research in a separate subheading in the conclusion.

Author Response: We have restructured the conclusion to include a dedicated subsection for future research, as requested.

Reviewer Comment 9: Considering the journal, it would be good to add a paragraph in the conclusion about the implications for sustainability, how the proposed approach contributes to emission reductions, energy efficiency and economic benefits.

Author Response: This is a vital point for aligning with the journal's scope. We have added a dedicated paragraph in the conclusion that explicitly links our findings to the triple bottom line of sustainability (Environmental, Economic, Social).

Reviewer Comment 10: You can consider evaluating the costs and benefits of implementing the measures proposed by the model, which would give a practical dimension to sustainability or indicate future research directions.

Author Response: We agree that a cost-benefit analysis (CBA) would be a valuable addition. However, conducting a rigorous CBA requires detailed, localized cost data for countermeasures (e.g., cost of realigning a curve, installing a variable message sign) and reliable estimates of the economic value of preventing crashes of different severity levels, which is beyond the scope of this current modeling paper. We have added this as a specific and highly relevant recommendation for future work.

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

All my comments have been addressed