Dear Mr Bracher,

Thank you very much for submitting your manuscript "Why are different estimates of the effective reproductive number so different? A case study on COVID-19 in Germany" for consideration at PLOS Computational Biology.

As with all papers reviewed by the journal, your manuscript was reviewed by members of the editorial board and by several independent reviewers. In light of the reviews (below this email), we would like to invite the resubmission of a significantly-revised version that takes into account the reviewers' comments.

The Authors are expected to address all the criticisms by all Reviewers. In particular, include the results for HZI in Figure 5A & B (Reviewer #1), further elaborate the qualitative difference in Rt (e.g. Rt < or > 1) between different methods, provide (if possible) some insights on under what situations or methodological characteristics that would lead to most reliable estimates (Reviewer #2), further consider the generalizability of the study findings (Reviewer #3), such as when there is a much higher variability in Rt for Omicron or other situations, while it is understood that the study didn’t adopt a simulation approach which may give an advantage to methods most consistent with the data generating model. In additional to the above comments, please address,

1. Table 2, please avoid abbreviations, or provide the full terms in the footnote

We cannot make any decision about publication until we have seen the revised manuscript and your response to the reviewers' comments. Your revised manuscript is also likely to be sent to reviewers for further evaluation.

When you are ready to resubmit, please upload the following:

[1] A letter containing a detailed list of your responses to the review comments and a description of the changes you have made in the manuscript. Please note while forming your response, if your article is accepted, you may have the opportunity to make the peer review history publicly available. The record will include editor decision letters (with reviews) and your responses to reviewer comments. If eligible, we will contact you to opt in or out.

[2] Two versions of the revised manuscript: one with either highlights or tracked changes denoting where the text has been changed; the other a clean version (uploaded as the manuscript file).

Important additional instructions are given below your reviewer comments.

Please prepare and submit your revised manuscript within 60 days. If you anticipate any delay, please let us know the expected resubmission date by replying to this email. Please note that revised manuscripts received after the 60-day due date may require evaluation and peer review similar to newly submitted manuscripts.

Thank you again for your submission. We hope that our editorial process has been constructive so far, and we welcome your feedback at any time. Please don't hesitate to contact us if you have any questions or comments.

Sincerely,

Eric HY Lau, Ph.D.

Academic Editor

PLOS Computational Biology

Virginia Pitzer

Section Editor

PLOS Computational Biology

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The Authors are expected to address all the criticisms by all Reviewers. In particular, include the results for HZI in Figure 5A & B (Reviewer #1), further elaborate the qualitative difference in Rt (e.g. Rt < or > 1) between different methods, provide (if possible) some insights on under what situations or methodological characteristics that would lead to most reliable estimates (Reviewer #2), further consider the generalizability of the study findings (Reviewer #3), such as when there is a much higher variability in Rt for Omicron or other situations, while it is understood that the study didn’t adopt a simulation approach which may give an advantage to methods most consistent with the data generating model. In additional to the above comments, please address,

1. Table 2, please avoid abbreviations, or provide the full terms in the footnote

Reviewer's Responses to Questions

Comments to the Authors:

Please note here if the review is uploaded as an attachment.

Reviewer #1: I think the paper can be interesting to read and it can be helpful for understanding that different models with different assumptions can provide quite different results. Then we may wonder on how to align them and look if they are really incorrect or correct. In my opinion, the analysis was well-conceived and has logic. I recommend it for publication in PLoS CompBio. Some of my remarks, which are not critical, are below. However, my main concern is about keeping the analysis reliable in the "far" future. I am very unsure that many of those github repos listed in the Appendix would stay alive in two or in five years. So it would nice somehow to preserve links to stay working. Probably, by forking the original repos?

- the name for Section 2: I wonder why the authors called it "the agony of choice"? In my opinion, it is just about estimating the Rt by different methods. For example, when the meta-analysis performed, people do not usually give their personal assessment for analyzed studies. Here, when the authors called comparing all other studies as being in agony, they unintentionally become subjective.

- L197: the authors assess the importance of the generation time on estimation of Rt and risk assessment (L190-196), but write nothing about the incubation period. Why exactly do we need IP? Why changing the IP shifts Rt? (L199) This is not clear from the text.

- L139-L155 and further: could the authors indicate what all those acronyms mean? I understood RKI, but what's about ETH, SDSC, Ilmenau, etc.?

- Figure 5, panel AB: I wonder why I can't see HZI in the plots? If the width of 95% CI is zero, then there should be a line at zero, no?

- L339: I think it is "Cori et al." method.

- L403: Could the authors explain why they write "typically" lags? Does it mean that sometimes it may not be lagged by one generation time period? Could they expain more carefully the lagging issue?

Reviewer #2: The review is uploaded as an attachment.

Reviewer #3: In this study, the authors investigated why different estimates of estimates of the effective reproductive number are so different. The article presents an interesting perspective, but there are still some issues that need to be addressed urgently.

1. The authors used Germany as an example and found that many parameters will ultimately affect the estimation results. However, using only one example seems somewhat insufficient. We are very curious as to whether these results can be validated using simple and controllable simulation data. Modifying parameters (data source, data pre-processing, assumed generation time distribution, statistical tuning parameters and various delay distributions) to generate simulated data and then using these methods for estimation can help evaluate within-method temporal coherence and between-method agreement of retrospective estimates.

2. Page 5. The authors should summarize these methods in a table, listing the requirements for input data, the form of output results, and the calculation principles, etc.

3. The authors should organize the results in a clear and concise manner for better understanding, rather than presenting them in a large block of text, such as section 4.2.

4. The authors should explain what is meant by a "consolidated point" and further elaborate on the important role of the four indicators.

5. Figures 6 and 7 are difficult to understand. Besides the consistency among the methods, what does the mean absolute differences between point estimates represent?

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Have the authors made all data and (if applicable) computational code underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data and code 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 and code 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 or code —e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: None

Reviewer #3: None

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Reviewer #1: No

Reviewer #2: No

Reviewer #3: No

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Attachments

Attachment

Submitted filename: Review_Report.pdf

Dear Mr Bracher,

We are pleased to inform you that your manuscript 'Why are different estimates of the effective reproductive number so different? A case study on COVID-19 in Germany' has been provisionally accepted for publication in PLOS Computational Biology.

Before your manuscript can be formally accepted you will need to complete some formatting changes, which you will receive in a follow up email. A member of our team will be in touch with a set of requests.

Please note that your manuscript will not be scheduled for publication until you have made the required changes, so a swift response is appreciated.

IMPORTANT: The editorial review process is now complete. PLOS will only permit corrections to spelling, formatting or significant scientific errors from this point onwards. Requests for major changes, or any which affect the scientific understanding of your work, will cause delays to the publication date of your manuscript.

Should you, your institution's press office or the journal office choose to press release your paper, you will automatically be opted out of early publication. We ask that you notify us now if you or your institution is planning to press release the article. All press must be co-ordinated with PLOS.

Thank you again for supporting Open Access publishing; we are looking forward to publishing your work in PLOS Computational Biology. 

Best regards,

Eric HY Lau, Ph.D.

Academic Editor

PLOS Computational Biology

Virginia Pitzer

Section Editor

PLOS Computational Biology

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Thanks for addressing all the editor’s and reviewers' comments. Congratulations on the excellent work!

Reviewer's Responses to Questions

Comments to the Authors:

Please note here if the review is uploaded as an attachment.

Reviewer #2: I appreciate the authors' efforts in addressing my comments. I am satisfied with this revised version of the manuscript.

Reviewer #3: The revised version of the manuscript has been improved and I recommend it for publication.

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Have the authors made all data and (if applicable) computational code underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data and code 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 and code 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 or code —e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #2: None

Reviewer #3: None

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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