PONE-D-23-06211Archetypal analysis of COVID-19 in Montana, USA, March 13, 2020 to April 26, 2022PLOS ONE

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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: Partly

Reviewer #2: Yes

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

Reviewer #1: No

Reviewer #2: Yes

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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: No

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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: No

Reviewer #2: Yes

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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 paper describes an application of the archetypal analysis to study of COVID-19 epidemic in the state of Montana. While the application by itself is interesting from the methodological perspective, the manuscript has several important drawbacks:

1) The authors have not provided access to their data and code. This violates the community standards for data availability, which stipulates that data and code should be accessible to reviewers and readers of the paper for validation purposes.

2) The results are not clearly formulated, rendering the central message of the study unclear. The authors did not supply any quantitative or statistical evidence to substantiate the associations described in the Results section.

3) The rationale behind the abrupt shift from discussing COVID-19 pandemic results to flu on page 10 is unclear, as is the relevance of flu to the overall topic of the paper.

4) It is unclear why a significant portion of the results section (pages 5-6) is devoted to results acknowledged by the authors to be biased.

5) The decision to select 10 archetypes for the analysis (as stated on page 5) lacks a clear justification.

6) The paper is not well-written. For instance, the first paragraph of the introduction leaves readers questioning the essence of the "new implementations" that rendered spatio-temporal approaches tractable (implementations of what?), why these approaches were previously intractable, and the nature of the "patterns over time" mentioned. Furthermore, the sentence "the methods can detect spatial clustering could may reveal environmental causatives" is particularly opaque.

7) Table 1 is not cited in the paper.

Reviewer #2: The authors apply archival analysis (AA), an innovative tool similar to principal components analysis (PCA). The rationale for applying AA is convincing and the results are interesting.

Major Comment:

The subsection on the mathematical formulation has some problems. I believe these problems are in the explanation, not in any underlying issue with the method itself. The authors say “Given a specified value for k, AA identifies m-dimensional vectors z_1, z_2, … , z_k that best describe k characteristic patterns, or archetypes in the original data set … .” They go on to give some restrictions regarding these z’s, but they don’t say precisely what “best” means. The authors seem to make an attempt to make things precise at the bottom of p. 3 where they say

“The m x k matrix Z of k archetypes is defined by the matrix factorization problem:

min_{A,B} || X – XBA ||

where Z = XB.”

A couple of remarks on this statement. First, the authors don’t exactly say what the matrix factorization problem is. It actually looks like a minimization problem, not a matrix factorization problem. Is Z the minimum of || X – XBA || over all A and B? If so, they could write

Z = arg min_{A,B} || X – XBA ||.

I see no connection between Z and the minimization problem. Second, at the end of the sentence, they say Z = XB. So is Z the solution to the given minimization problem, or is it simply XB?

Minor Comments

1. The authors often talk about “observations” when they really mean “days.” It would help the reader to say there are data values for counties and days. Every time I saw “observations” I had to stop reading and think about what that means.

2. Near the bottom of p. 2, the authors talk about the AA algorithm. At this point of the paper, I didn’t have enough background to understand what any of this means. I’d suggest trimming this back, and then coming back to it later in the paper once the groundwork is laid.

3. It looks like the authors used Matlab, a package familiar to most mathematicians. Statisticians tend to use R because of its array of functions for doing data analysis. I believe there is an R package to do AA, which is called "archetypes". See the paper

Eugster, M., & Leisch, F. (2009). From spider-man to hero-archetypal analysis in R.

https://cran.r-project.org/web/packages/archetypes/vignettes/archetypes.pdf

4. On p. 3, first paragraph, the authors say “To account for differences in population size, we weighted the COVID-19 cases … .” “Weighted” could mean a lot of things in this context. Did the authors just look COVID rates on a per capita basis?

5. p. 3, just above equation (1). Should be “… coefficients that sum to unity …”

6. In equation (1) and thereafter, the betas are vectors and should be bold. This can be easily done in LaTeX using the amsmath package and the \\boldsymbol{} command.

7. p. 3, just after equation (1), Should be “Each archetype is either a convex combination of …”

8 p. 3, lines 84 and 90 (using numbering in the right margin). Write these matrices using brackets:

B = [ beta_1, … , beta_k ] and A = [ alpha_1 , … , alpha_n ]. These alphas and betas are themselves vectors and should be bold. Also use \\ldots for the ellipsis between commas; save \\cdots for the ellipsis between math operators like “+”.

9. In equation (1), the constraints must hold for all j. The “for all j” could be added a the end of (1).

10. The definition of mutual information at the bottom of p. 4 looked asymmetric to me. I got out some paper and tried to see whether it was symmetric, and of course it is. Then I turned the page and saw that the authors pointed out the symmetry. By the way, the description of MI at the top of p. 5 is very nice!

11. I couldn’t help but think that ten archetypes may be a bit much. I suspect that by the time you get past the first five or six, you get mostly noise. I’m not suggesting anything specific here, except maybe a statement that there will come a point beyond which we are observing noise.

12. p. 8, line 221. Shouldn’t “no flu” be “no COVID”? Same page, line 228, shouldn’t figure 8 be “Fig. 8”?

13. Throughout, I’d suggest not spelling out alpha. Just use $\\alpha$.

14. p. 13, lines 355-357. “A high (relative) MI indicates that a county’s time series can be better predicted by considering the other, and vice versa.” First, congratulations on getting “vice versa” correct; I always put a hyphen between the words, which is incorrect. I think the idea is that you can augment data from a county with other counties for which the MI is high. The way it is worded suggests that you ignore the data from the current county and just use the data from counties with a high MI.

15. The graphs are generally fuzzy. I know that PLOS ONE allows files in TIFF or EPS format only. EPS is a vector graphics format so the figures should be clear (no fuzziness at any level of magnification). I suspect the authors used TIFF files. The best strategy would be to render the graphs in EPS format. If this isn’t possible, then maybe saving the files at a higher TIFF resolution would make them clear.

16. In Figure 3, the axes are not needed. The legend on the right is, however, needed, but this can be given once (assuming the legend is the same for all archetypes). The figure will probably be set in a 5 by 2 array of maps so it fits on one page. The county names will not be readable at this scale. Similar comments apply to Figure 8. If the county names are needed, the authors might consider giving one map of Montana with just the county names. This figure could contain the map information (e.g., compass, scale in miles, surrounding topography, etc.) along with the county names.

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Reviewer #1: No

Reviewer #2: No

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Archetypal analysis of COVID-19 in Montana, USA, March 13, 2020 to April 26, 2022

PONE-D-23-06211R1

Dear Dr. Stone,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication.

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Kind regards,

Maurizio Fiaschetti

Academic Editor

PLOS ONE

Additional Editor Comments (optional):

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: All comments have been addressed

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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

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

Reviewer #2: Yes

Reviewer #3: Yes

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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: No

Reviewer #3: Yes

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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

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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 #2: (No Response)

Reviewer #3: The present study is interesting because it analyzes Archetypal to epidemiological data of COVID-19 from March 13, 2020 to April 26, 2022, for the counties of Montana, USA. The manuscript has already undergone an extensive review, with many details that have actually made the manuscript substantially improve its quality. The authors made the suggested adjustments appropriately and the manuscript can be accepted for publication.

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Reviewer #2: Yes: Steven E. Rigdon

Reviewer #3: No

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