Tumor Volume Distributions Based on Weibull Distributions of Maximum Tumor Diameters

Round 1

Reviewer 1 Report

This manuscript describes a method to derive the distribution of tumor volume from the Weibull distribution of tumor diameter under the assumptions that tumor is ellipsoidal in shape. The proposed methods were validated on a three-dimensional dataset of segmented tumor volume and then applied to tumor diameter data from the SEER database. Information on tumor volume could be of relevant value for several fields in cancer research. However, they were rarely registered in available database. Therefore, the reviewer believes this manuscript could be of significant interest for the audiences of Applied Science. However, several weaknesses should be addressed before this manuscript can be considered acceptable for publication.

General aspects:

-                  The manuscript is focus on the derivation of tumor volume distributions from distributions of tumor diameters but nowhere in the paper it is specified what this distribution refers to. In the Methods section the authors distinguish between the “intrinsic distribution of tumor volume” i.e., the actual distribution of tumor size in patients, and the distribution of actually diagnosed tumor size in a cohort of tumor patients. However, it is not specified if patients are affected by the same cancer type, if they are treated or not, if the treatment is the same, if only tumor size at diagnosis is considered or more measurements in the same patients are taken in account. This is a fundamental aspect to be clarify.

-                  References are very few (n=7) and some of them are also dated. Please improved.

Introduction:

-                  Lines: 29-32: “it has been shown that tumor control in individual patients can be predicted from the tumor control probability of the corresponding patient cohorts, assuming that tumor volumes in these patient cohorts are exponentially distributed”. The reviewer believes that it is important to empathize and further deeper this aspect as it should represent a possible relevant application of the method presented in this manuscript.

Methods – 2.1 Maximum tumor diameter distribution

-                  Line 52: Please clarify that f(d) is a probability density function.

-                  How is selected the diagnostic limit function? Did the authors consider other functions as well?

-                  Lines: 69-72: Is this sentence a typo?

-                  Eq.3 – Line 80: The reviewer suppose that the parameter k is the same parameter of the Weibull distribution. If yes, please clarify.

-                  Lines: 89-91: The authors state that the shape of tumor depends on the volume. It is not always true. Indeed, for k=3, tumor mass is always spherical independently on the tumor volume.

-                  Eq.4: Please addthe mathematical derivation of Eq.4.

Methods – 2.2 Verification using real lung tumor volumes

-                  Line 126-129: Typo

Methods – 2.2 Tumor volume distributions determined from SEER for breast, NSCLC and liver

-                  See previous comment. Are the data in the SEER database related to patients under anticancer treatments? If yes, is the treatment the same for all the patients? Are the data relating only to tumor mass at diagnosis? These are important aspects to consider as treatment should relevantly affected the tumor mass dimensions.

-                  Table 1: are the data counts?

Results

-                  Figure 2 – lines 170-171: There is a mismatch between the estimate of the parameter k reported in the label of Figure 2 and at line 171.

-                  Figure 3: What do the vertical bars represent?

-                  When three-dimensional data relating to NSCL cancer were used, the value of the Weibull distribution were estimated to be k=2.14, lambda= 0.13 and dc=1.5. In particular, the value of k was consistent with estimate found using Eq.3. However, there were significant differences between parameters found on the three-dimensional dataset and the data from the SEER database. These differences are present also for the NSCLC case. What is the possible cause? This dependency of parameter values on the dataset could prevent the use of this methos to make extrapolation. Please discuss this limitation.

The written English has some typos and odd sentences. Please rectify during revision.

Author Response

Please see the attachment

Author Response File: Author Response.docx

Reviewer 2 Report

Summary 

In this work the authors demonstrate that the tumor volume can be derived from its maximum diameter assuming it to be a spheroid and applying a parameter that is derived from a Weibull distribution fitted to the maximum diameters for a given tumor type. The authors support their approach with a given data set of NSCLC tumors with documented maximum diameters and tumor volumes. The tumor volume distributions are then also predicted for some additional tumor types based on the distribution of maximum diameters. 

General Comments 

The structure of the manuscript as well as the presentation of the results is clear and appropriate. While some sentences may be improved in their style, the language is fine and comprehensible with no major issues. The abstract is well written for most parts but could benefit from some changes to improve clarity (cp. Specific Comments).  The intro and discussion are definitely on the shorter side in comparison to the majority of publications, which is not necessarily a shortcoming. The introduction touches briefly upon the significance of the tumor volume for cancer research and the discussion does nicely describe the shortcomings of the study design. However, I believe that the authors may be able to improve in the communication of the originality and significance of their work by reworking some parts of these sections (cp. Specific Comments). In addition a number of smaller issues can be found throughout the manuscript, which can be found in the section below. 

Specific Comments 

This list includes more detailed explanations to some of the comments above and the associated recommendations for changes. Furthermore, the list contains a number of smaller issues. The order of the comments roughly follows their position in the manuscript.

• A redundant comma appears to be included in the authors list 

• In the abstract, the dk parameter appears to be accidentally put into subscript instead of superscript. 

• The “Methods” Section of the abstract may be confusing in its current form. As the first sentence ends with “... it is shown that tumor volumes follow an exponential distribution.” and the following sentence starts with “The method is tested…”, the reader may be inclined to think that the focus of the work and its method may lay on the exponential distribution of the volume. However, if I understood correctly, the exponential distribution is a consequence of the derivations however not the core concept that is being tested. What is being tested in the manuscript is the assumption that the k value taken from the Weibull distribution of d is the same k value that could describe the connection between the volume and d. This aspect should be clearly emphasized. My own recommendation would be to completely kick the mentioning of the exponential distribution of relocate it to a later point of the abstract as it may be misleading at the current position and write something similar to: “Methods: The hypothesis is made, that tumor maximum diameters d are Weibull distributed and tumor volume is proportional to d^k, where k is a parameter from the Weibull distribution of d. The assumption is tested by using a test dataset of 176 segmented tumor volumes and comparing the k obtained by fitting the Weibull distribution of d and from a direct fit of the volumes. Finally, tumor volume distributions are calculated from the maximum diameters of the SEER database for breast, NSCLC and liver. (3) Results: For the test dataset, the k values obtained from the two separate methods were found to be k=xx (from Weibull distribution of d) and k = xx (from tumor volume). The tumor diameter data ….”.  

• While it is not a pressing need, I believe it would be beneficial for the manuscript to add a bit more statements of significance to the prediction/knowledge of the tumor volume. In its current version it only refers to one other reference and two of the authors themselves. To emphasize a broader significance of this work only a couple more references to the literature may already go a long way. 

• I have a similar issue with the originality of the study. While I do not doubt it, it would be highly recommended to at least state in some sort of way if there have been any other studies trying to achieve the same or similar goals. If it would be the case, how do they differ from the presented approach? If the presented study is the first to attempt such a conversion from maximum diameter and the volume it also should be clearly stated as it would strengthen the originality and significance of the manuscript. 

• In Line 69/70 a statement on interventionary studies seems to have been included by accident. 

• To me it is unclear how the authors arrive at equation 7. Specifically I do not understand how they obtain the middle factor in the equation (vbar + v_c / vbar²). Wouldn't it be simply 1/Vbar? 

• In Line 128/129 a sentence is double. 

• It may improve clarity to insert “Paritent Numbers in Time Period” instead of “Time Period” in Table 1. 

• The wording in line 164 might be a bit strong (“A match would verify the methodology”). As the authors point out themselves, the study has several limitations including the benchmark to only one tumor type. I would rather use a phrase such as “support” instead of “verify”. 

• Line 175: “is applicable” instead of “works” appears stylistically more appropriate. 

• In the second paragraph of the discussion, the authors mention “other work”. Please add concrete references. 

• Line 235 “besides” instead of “despite”. “Despite” has a similar meaning to “although”.

• The discussion section ends very abruptly. At the end of the manuscript, the reader should at least be reminded of what the study ultimately achieved, its potential impact on the field and what may come next. I recommend adding some corresponding conclusive remarks. 

• Within the author contributions the software section was left at X.X.    

Conclusion and Final Recommendation 

The study and its presentation are clearly structured and no scientific issues were found. While the manuscript is generally of good quality it has some smaller shortcomings here and there that should be fixed before publication. As these are predominantly connected to the manuscript itself and should thus be resolvable in a limited amount of time I ultimately recommend a acceptance after minor revision.

Author Response

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Author Response File: Author Response.docx