Cumulative Histograms under Uncertainty: An Application to Dose–Volume Histograms in Radiotherapy Treatment Planning

Round 1

Reviewer 1 Report

The authors present a study evaluating alternative distributions in an uncertainty propagation method for radiological dosing that is more efficient than Monte Carlo.

The paper is well-written and generally clear in its intent and findings. However, I feel that the discussion of the degree of success of the methods and the place of the paper in the larger effort to build efficient frameworks for computing with uncertain quantities both need significantly more attention. The discussion section of the paper is almost without reference, an indication that there is still an opportunity to relate the present findings to other research in the field. Though not absolutely required, some coverage of related approaches in fields other than radiology would also broaden the paper's importance.

In the discussion, I would encourage the authors to acknowledge that the study demonstrates that the distributional approach will not be a practical tool without further improvements. No distribution worked very well. Some success is claimed in describing a bimodal distribution, but the distribution was actually tri-modal and as such not described well at all. Moreover, it is not clear that the choice of distribution, or mixture of distributions, can be made on general principles. My thought is that a physical model is required that can help to define the interdependence of distribution of dosage at each voxel. This or something like it is a logical idea extending from the observation beginning on Line 390 that interdependence complicates the modeling process.

My only other general comments is that I expected to see a comparison of the computation time between the Monte Carlo sampling and the APM methods.

Detailed comments:

58: Awkward wording (is... histograms)

75: The list of distributions is never really given a justification. Something as simple as "we tried a variety of positive continuous distributions" or a more detailed rationale for each one. Given that this is just the introduction, it might be better just to say "a variety of positive distributions" and then give the list in the Methods.

81: The remainder of the introduction is either Methods or unnecessary structural foreshadowing. I would remove these last two paragraphs.

170: Still no reasons given for this list of distributions

Figs 2 and 4: Some curves seem to be missing from some panels. Please explain in the captions.

288: Delete "have"

291: Do not introduce a new methodological component of the study in the middle of the results section.

Fig. 5 caption: Too narrative. Eliminate "we show," etc. Additionally, please explain the abbreviated labels used in the figure.

314: To say that the Gaussian "may not be an optimal representation" is a very soft way of saying it was not the right representation. I think it's really important to come out and say this. None of the distributions here are right. You may want to go further with some kind of metric that is more practical than chi-sq to address whether any of them is good enough to be useful.

329: The distribution referred to here as bimodal had a third mode.

340: I needed more explanation around the use of copulas. And would the authors expect that the improvement seen in this particular combination of distribution and copula also show itself superior in other case studies? That is, how generalizable is this result?

357: Quotes are used several times in this portion of the ms as if to convey rhetorical meaning in the absence of precise terminology. No quotes are needed.

384: I suggest moving the rationale for choice of distribution from the second-to-last paragraph to somewhere earlier in the ms.

397: Describing the performance of the beta distribution as "not perfect" suggests perfection is near at hand. It is not. The discussion comes close a few lines above to identifying the exact challenge that will prevent this approach from working: that the interdependence of voxels is important. The authors would do well to use that as a launching point to describe what research steps are likely necessary to incorporate interdependence into the framework.

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Reviewer 2 Report

The work is interesting

Suggestions

1. in section 2.1 must be presented the model and more informations about the penalized least-squares

2. section 2.2 grphical presentation of the distribution

3. section 2.4 results of the comparison (table of the values)

4. The section 2.4 must be re-writen with more results about the goodness-of-fit tests include formulas

5. section 3.2 more image results

6. Figure 5 except the figure it would be interesting to be included the values for every distribution as well as the measure for comparison between them, so the best distribution to be presented

Author Response

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Author Response File: Author Response.docx

Reviewer 3 Report

Comments on the manuscript: stats-2868320
"Cumulative histograms under uncertainty: An application to dose-volume histograms in radiotherapy treatment planning"


    The manuscript is very well written, in clear, simple, and scientifically reliable language. It is a manuscript that is pleasant to read and even interesting but there are some comments that need to be taken into consideration:

1.The authors must start strong and clearly state the main idea of the work in the first few paragraphs. The abstract is too long and should be in the introduction section.
2.The scope of the current literature review is inadequate. The study would be much more thorough if it included more recent works about cumulative histograms under uncertainty, especially in the years 2021, 2022, 2023, and 2024.
3.A supporting references must be added to the Equations (2) and (8).
4.The manuscript's authors should refrain from using the pronoun "we" as much. Moreover, a few of the basic methods are used repeatedly in the manuscript.
5.It's intriguing and concerning that all of the references are so out of date, but it's also a crucial necessity that necessitates researching and learning more about the subject and earlier studies, at least from the last five years.

Comments for author File: Comments.pdf

Author Response

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Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

Accept as it is now