PONE-D-20-08832

Urban scaling of opioid analgesic sales in the United States

PLOS ONE

Dear Dr. Mullachery,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

==============================

It is an important topic, and the results would deserve to have a nice publication.

However, the paper still misses a strong development of the state of the art and the reflexion (ofllowing also reviewer 1)

==============================

Please submit your revised manuscript by Dec 03 2020 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

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We look forward to receiving your revised manuscript.

Kind regards,

Celine Rozenblat

Academic Editor

PLOS ONE

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Additional Editor Comments (if provided):

It is an important topic, and the results would deserve to have a nice publication.

However, the paper misses in my point of view the theoretical hypotheses that would strengthen the interpretation. In particular, it does not contextualize the relation between medical treatments / deseases / medical infrastructure. It is argued that there are no studies on scaling and health that is not true: see for example L. E. C. Rocha, A. E. Thorson, R. Lambiotte (2015). The non-linear health consequences of living in larger cities, Journal of Urban Health 92 (5) and some others since that publication....

so please highly strength the state of the art and the reflexion (fllowing also reviewer 1)

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: Yes

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2. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: I Don't Know

**********

3. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: No

Reviewer #2: Yes

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4. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

**********

5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: The submission tackles a very interesting question but fails in several ways. (a) The choice of spatial unit is not sufficiently justified. (b) Scaling is not about size but about how interactions are affected by scale. Thus one would not expect similar scaling behavior across spatial units which might represent different interactions. (c) The methodological choice of a linear spline at thre population mean is not justified.

Reviewer #2: 1. The manuscript is technically sound. The content is informative, new and interesting to public health institutions and also individuals seen the huge problematics of opioide misuse in the US.

2. I am no statistics expert, so I can not really evaluate the statistics topic.

3. Neverthesless from my limited understanding of statistics the data seem to be complete.

4. The manuscript is understandable and written in standard English (I found only some small typos).

Due to my limited understanding of statistics I suggest a minor revision by a person with more statistical knowledge.

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6. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

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Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: No

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While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step.

PONE-D-20-08832R1

Urban scaling of opioid analgesic sales in the United States

PLOS ONE

Dear Dr. Mullachery,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

==============================

Thanks for the improvement of the paper. Please finalize this improvement following the recommendations of the Reviewer 3.

==============================

Please submit your revised manuscript by Feb 28 2021 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

Please include the following items when submitting your revised manuscript:

• A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'.
• A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'.
• An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'.

If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: http://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols

We look forward to receiving your revised manuscript.

Kind regards,

Celine Rozenblat

Academic Editor

PLOS ONE

Additional Editor Comments (if provided):

Thanks for the improvement of the paper. Please finalize this improvement following the recommendations of the Reviewer 3.

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #2: All comments have been addressed

Reviewer #3: (No Response)

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2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #2: Yes

Reviewer #3: Yes

**********

3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #2: I Don't Know

Reviewer #3: N/A

**********

4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #2: Yes

Reviewer #3: (No Response)

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5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #2: Yes

Reviewer #3: Yes

**********

6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #2: It seems that there has been a substantial improvement in content and, as mentioned by reviewer 1,

clearing of other available contextual literature and research. It also seems that all data are fully available and accesible on the gitHub platforme. In the abstract there is still a small typo (line 14: superlinear (not superliner). Soures / literature are added and also explained. The structure of the document is now much clearer. (All this under the precondition that I am not an expert in statistics neither in opioid/medical-social topics).

Reviewer #3: Report on “Urban scaling of opioid analgesic sales in the United States”

The authors analyze the prescription of opioid pills in commuting zones (CZ) in the USA. Analyzing the entire set of CZ they find super-linear scaling, ie in large cities more pills are prescribed. However, the authors find that the residuals exhibit a systematic deviation in a U-shape from which the authors infer two different scaling regimes. Separating the CZ into two groupd according to the median, a super-linear (below the median) and a super-linear (above the median) regime are found. The authors hypothesize reasons for this different scaling regimes.

Overall, this is a nice little paper. It is mostly well written and relevant to the urban scaling community and probably also for the opioid-crisis community. Accordingly, I recomment publication.

The only (non-mandatory) thing that the authors could consider is a better statistical treatment. They could automatically find a best division value for the two regimes (instead of the median), ie an optimization. In addition, colleagues with statistics background would appreciate seeing some test statistics that the model with two regimes fits better than the model with only one beta. In this context Akaike Information Criterion might be useful.

Specific comments:

- which location is use, address of patient, doctor, or pharmacy?

- “Scaling is the response of complex systems, such as cities, to changes in their size.” might be misleading. In most cases urban scaling is studied cross-sectionally (fixed year), but “changes” suggests change over time

- beginning of page.11: “For example” is just repeating what is already said in the previous sentence

- “disporportionally high number of social conections in large cities leads to an exponential increase in various outcomes such as economic productivity and number of patents”: the increase is probably not exponential

- why 607 CZ? Is this the total number? If not, how have they been chosen, why have others been omitted?

- “After visually exploring initial results, we detected a strong non-linear pattern” In log-log representation, I assume

- how do the authors deal with zero-values? Ie are there any CZ with no pills? If they, then the log-value cannot be shown

- why are the Figures in the SI?

- “we added a linear fit with a linear spline at the population median” spline is not visible, is the linear regressions are discontinuous

- Tab.1: it is not clear how adjustment and stratification has been done

- somehow the authors describe more Figures than were in my pdf

- to me the probable better availability of illegal drugs in large cities (the third reason mentioned by the authors) sounds most plausible for the sub-linear scaling of CZ above the median

- how do the years 2006-2014 go into the analysis? Is it that the values simply represent the total pills prescribed in this period?

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7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #2: No

Reviewer #3: No

[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.]

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step.

PONE-D-20-08832R2

Urban scaling of opioid analgesic sales in the United States

PLOS ONE

Dear Dr. Mullachery,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.  One reviewer noted a few minor suggestions which could further strengthen the manuscript.  

Please submit your revised manuscript by May 21, 2021. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

Please include the following items when submitting your revised manuscript:

• A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'.
• A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'.
• An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'.

If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: http://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols. Additionally, PLOS ONE offers an option for publishing peer-reviewed Lab Protocol articles, which describe protocols hosted on protocols.io. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols.

We look forward to receiving your revised manuscript.

Kind regards,

Nickolas D. Zaller

Academic Editor

PLOS ONE

Journal Requirements:

Please review your reference list to ensure that it is complete and correct. If you have cited papers that have been retracted, please include the rationale for doing so in the manuscript text, or remove these references and replace them with relevant current references. Any changes to the reference list should be mentioned in the rebuttal letter that accompanies your revised manuscript. If you need to cite a retracted article, indicate the article’s retracted status in the References list and also include a citation and full reference for the retraction notice.

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #2: All comments have been addressed

**********

2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #2: Yes

**********

3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #2: I Don't Know

**********

4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #2: Yes

**********

5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #2: Yes

**********

6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #2: It is visible see that you worked hard on the last version and answered to all comments of the reviewers. It seems to me (as already mentioned, I am not a statistics expert) that you did a lot of new research.

I found the discussion and explanations with the reviewer very interesting and helpful.

Maybe in general it is helpful to explain results in this way. It depends also on the target group how you formulate your text. Myself as a scientist with a backgroud in Geology/Paleontogy and Systems Scientist I am always working on making results easily understandable (also for "oursiders").

Therefore I very much appreciate your documentation of the discussion and review process.

Finally two small typos again in the downloaded Fig 2 & 3: I suppose the legend should be named "coefficient" (not "coefificient").

**********

7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #2: No

[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.]

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step.

PONE-D-20-08832R3

Urban scaling of opioid analgesic sales in the United States

PLOS ONE

Dear Dr. Mullachery,

Thank you for submitting your manuscript to PLOS ONE and for your patience during the review process. I am terribly sorry for the delay, it has been quite challenging securing reviewers during the current pandemic.  I have tried to do my due diligence in soliciting reviews for your revised manuscript after at least one prior reviewer was no longer available.  As you can see from the reviewer comments, there are still some points that need to be addressed in the revised manuscript.  I believe that these comments are addressable and therefore, I invite you to submit a revised manuscript. 

Please submit your revised manuscript by August 31, 2021. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

Please include the following items when submitting your revised manuscript:

• A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'.
• A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'.
• An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'.

If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: http://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols. Additionally, PLOS ONE offers an option for publishing peer-reviewed Lab Protocol articles, which describe protocols hosted on protocols.io. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols.

We look forward to receiving your revised manuscript.

Kind regards,

Nickolas D. Zaller

Academic Editor

PLOS ONE

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #4: (No Response)

Reviewer #5: All comments have been addressed

**********

2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #4: No

Reviewer #5: Yes

**********

3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #4: No

Reviewer #5: Yes

**********

4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #4: Yes

Reviewer #5: Yes

**********

5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #4: Yes

Reviewer #5: Yes

**********

6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #4: 1. It would help to better justify the research approach. All prescription opioid counts from 2006 to 2014 were aggregated for each county over a period of increasing prescriptions. Why isn’t the outcome of interest the growth of prescriptions over the time period rather than the total amount? (It seems like from a policy perspective, you would want to know where prescriptions increased substantially given the introduction section.) Do any of the CZs grow substantially over the time period? If so, then this seems like information you would want to examine (if not, it justifies the averaging of population size and should be stated). That is, do fast growing populations correlate with fast growing prescriptions? Is this a confounder to worry about? What I’m getting at is the paper reads as if a couple variables were chosen without much thought to see if they were or weren’t correlated. Why is the chosen correlation the one to focus on rather than a different one? Explaining this would help justify the statistical approach.

2. It’s not clear why Alaska and Hawaii were excluded. Are they weird outliers for some reason? At a minimum the authors should explain more clearly why they should be excluded and test whether the estimates change in any meaningful way if Alaska and Hawaii are included. If there is no real difference, this should be stated. If the estimates do change in meaningful ways, then omitting them really needs a stronger justification.

3. The U-shaped pattern in Fig S1 seems largely driven by the three outlier residuals in the lower left of the figure. Indeed, when omitted in Table S1, the coefficient for beta1 falls a large amount. Although the “findings are robust” to this, meaning the signs of the coefficients and statistical significance presumably don’t change, the magnitude of the coefficient changes and needs to be discussed. Does the U-shape disappear? Does the optimal spline change? Are the outliers located in a particular region, perhaps explaining some of the stratification results?

4. In Table 1, what does “adjusted for region” mean? Does it mean a dummy variable was included for each region in the estimates? Or something else? This can be clarified in the text or Table 1 notes.

5. There is no interpretation of the coefficients. What does a beta1 of 1.42 vs 1.17 mean from a practical perspective? Both are superlinear, but does the difference of magnitude mean anything? How should they be interpreted? Why should we care about these specific numbers? Does a beta1 of 1.01 and a beta2 of 0.99 have any real meaning? If not, what level of these coefficients should matter? Or does it not matter and only the superlinear or not question is what matters (if so why?)?

6. If it is really a U-shaped relationship, why not use a quadratic estimation equation (add a population squared term)? Does it fit the data better? If so, how would you interpret the results?

7. The discussion needs work. The first sentence of the second paragraph is “Our results highlight the importance of exploring nonlinear scaling”, but nowhere is the “importance” explained. That it is detected in the estimates does not mean it is “important”. More care needs to be taken in explaining the importance of the results if this is the goal. (PLOS ONE does not judge things based on importance, so the highlighting of the importance could be removed if the author does not want to justify the importance of the results.)

8. Discussion says “One potential explanation [that below a threshold, higher populations are more strongly correlated with more opioid prescriptions, and above it, less] is that increases in potential matches beyond a certain threshold no longer translate into higher rates of successful matches.” But isn’t it that beyond some threshold, the higher rates of successful matches slows down, not that it disappears? Or am I missing something? It’s not like there is a sharp break at a threshold, but a (very) gradual flattening of the curve.

9. Several potential explanations are given in the discussion, but it would be helpful if it was explained why these (or other confounders) were not included in the analysis. Can you control for number of pharmacies/prescribers or not? Levels of prescription opioid vs heroin deaths in a CZ? It seems there are a potential long list of confounders that the limitations should highlight (poverty rates, unemployment, demographic profile, number of physicians, income level, existence of PDMP programs, opioid treatment availability, etc.). In addition, since PLOS ONE requires "appropriate controls", the lack of any controls needs justification.

Small typo: “42th” is used instead of 42nd.

Reviewer #5: The authors did a great job addressing previous reviewers comments. The revisions helped to clarify the methods and results.

On page 5, line 6, "maybe" should be "may be"

On page 10, line 7, "Last" should be "Lastly"

On page 11, line 3, insert "be" between "could" and "the"

On page 12, line 12, insert a reference for the statement about patients filling prescriptions close to home or work.

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Reviewer #4: No

Reviewer #5: No

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Urban scaling of opioid analgesic sales in the United States

PONE-D-20-08832R4

Dear Dr. Mullachery,

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Reviewer #4: All comments have been addressed

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Reviewer #4: Yes

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Reviewer #4: Yes

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Reviewer #4: Yes

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Reviewer #4: Yes

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6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #4: The authors have addressed all of my comments. The authors have clarified their statistical approach and discussion.

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Reviewer #4: No