Note- response to the reviewer comments were also provided in a Word document in the Cover Letter.

Editor Comments:

Dear Author,

Thank you for your contribution. We continue to assert that your work is important, though the reviewers and I believe that it would be stronger with some further thoughts and considerations as well as some qualification in your claims. Please see both reviewers' comments and address.

[Note: HTML markup is below. Please do not edit.]

Response: Thank you for the opportunity to revise the manuscript. We have addressed the reviewers comments as outlined below.

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: I Don't Know

Reviewer #2: Yes

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

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Reviewer #1: Yes

Reviewer #2: No

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

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Reviewer #1: Yes

Reviewer #2: No

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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: In this study Authors constructed a new model for predicting fetal growth, The subject is of interest, the ms well written so I would like to congratulate with Authors for their effort

My comments are

1) since many of the reader are not familirar with heteroscedastic model I suggest to add an explanation of the rationale of using this approach and how it was constructed

Response: The Gardosi method constructs the percentile cutpoints to define SGA and LGA, namely, 10th and 90th, in a specific way. The method is based on the assumption that the coefficient of variation (CV) is constant. Our first objective was to investigate this assumption. For the second objective, the advantage of creating a new method for customization using a heteroscedastic model is that it directly calculates the CV based on the empiric data without making such assumption. Therefore, the heteroscedastic model allows for more flexibility. We have clarified this description in the Introduction (new text underlined) (Pages 4-5):

“Second, we developed an expanded, alternative TOW customization method for estimating we created a new customization method that has more flexibility in calculating customized percentiles using a heteroscedastic regression that customizes both customized mean TOW (and hence EFW by extrapolation) and customized standard deviation, leading to customized percentiles, using a heteroscedastic regression.[16] To be precise, the heteroscedastic model customizes a transformed value of the standard deviation but because that makes the standard deviation depend on the customizing factors, hereafter we refer to it as a model for customizing the standard deviation.”

2) of interest it should be the % variation at each gestational age in the comparison of the 3 models and if differences are significant

Response: Thank you for this suggestion. We revised Figure 3 to add confidence bands for the 10th and 90th percentiles for each week. (new Fig 3) We also provide the percentiles by week to present the absolute differences and calculated the relative differences in the Table below:

GA Range of 90th and 10th in Gardosi Range of 90th and 10th in Hetero Range of 90th and 10th in Quantile Relative difference between Gardosi and Heteroscedastic a

% Relative difference between Gardosi and Quantile b

%

37 959 982 962 -2.4 -0.3

38 1042 969 963 7.0 7.5

39 1116 962 948 13.8 15.1

40 1147 949 918 17.3 19.9

41 1176 937 903 20.3 23.2

42 1216 921 921 24.2 24.3

GA, gestational age; Hetero, heteroscedastic

a Relative difference was calculated using the range as [(Gardosi–Hetero)/Gardosi] *100%

b Relative difference was calculated using the range as [(Gardosi–Quantile)/Gardosi] *100%

3) i will consider in the reference list and in the discussion the paper of Ghi et al JUM 2016 that similarly also used father characteristics in the construction of the customized mode

Response: We originally omitted this study because it didn’t report EFW or birthweight which was the focus of our study; however, we have now added this reference to the discussion. Page 25, new text underlined:

“These findings are similar to findings from the Generation R cohort of EFW in the Netherlands [34] and fetal biometric measurements in an Italian cohort [new reference 35] although…”

Reviewer #2: The authors use longitudinal fetal weight measurements they obtained in the NICHD Fetal Growth Studies to assess some of the assumptions of the Gardosi’s customized chart which assumes that i) standard deviation is a fixed proportion of the mean, and that ii) the effect of maternal characteristics is proportional throughout gestation and affects all percentiles of the distribution. Specifically, the authors evaluated the normality and constant coefficient of variation (CV) assumptions and propose the hetroscedastic and quantile regressions based percentiles as an alternative.

Major:

1) Although the attention to the non-normality of the fetal growth data is warranted, the WHO and PRB/NICHD standards already proposed the use of quantile regression. Moreover, the PRB/NICHD standard questioned the proportionality of the effects of maternal characteristics and showed differential effects on specific percentiles. The paper should put these results in perspective and perhaps somehow tone down claims of novelty.

Response: We agree with the reviewer that others have used quantile regression and questioned the proportionality assumption of the Gardosi customization method. The novelty of our analysis is the in-depth examination and explaining whether Gardosi assumptions hold. We have clarified this point in the paper and added the WHO and PRB references (new text underlined):

“We performed an in-depth examination of the statistical assumptions of the Gardosi customization method.” (p. 23)

“ Quantile regression was used to create the WHO fetal growth charts and also for a customized fetal growth reference in an African-American population. (new references 30, 31; p. 24)

2) Comparison of customized and non-customized standards were also evaluated for prediction of adverse outcomes and the authors miss to acknowledge and discuss previous work (https://pubmed.ncbi.nlm.nih.gov/31006913/).

Response: While we do recognize the important contribution of the Kabiri paper, our goal was not to compare customized and non-customized standards, as we agree that this subject has been extensively studied. Our goal was to compare the statistical methods of customization. We have now added the Kabiri reference to the discussion (new reference 30) as outlined in response to Reviewer 2, Comment 1 above and edited the Discussion as follows (p. 24, new text underlined):

“In the study by Kabiri et al, a customized fetal growth reference based on quantile regression did not improve prediction of perinatal morbidity compared with ultrasound references. While in the present cohort the model also did not show significant improvement in terms of birthweight prediction, it is expected that as more data from controlled studies become available, the merits of flexible models compared to linear regression-based models could be better evaluated in the context of birthweight customization.”

3) Studying the behavior of the mean and SD only answers questions about the constant CV, but not about the normality. This should better emphasized the paper.

Response: The reviewer is correct that the reported evidence based on the mean and the SD and the bin-specific percentiles do not provide sufficient evidence toward normality as the reason for departure could be due to the violation of constant CV assumption. We further investigated the assumption of normality by checking the residuals from the model fits for the Gardosi and the heteroscedastic models. The quantile regression does not assume normality and hence it is not included in the investigation. The residuals do not show any glaring departure from normality. We have now added this information to the results (p. 18) and in a new s2 Fig.

4) For the assessment of normality, the authors compare the Gardosi percentile with the percentiles generated empirically (for each sub-interval). This does not really answer the question, as the difference between the two values may also be the result of violation of the constant CV (proportionality) assumption. Other contributing factors could be the different datasets involved (Gardosi uses all the avalble data set; empirical uses a dataset in a given sub-interval).

Response: Our goal was not really to assess normal or abnormal. Rather, we wanted to examine how robust the Gardosi estimates were. We agree that it doesn’t say anything conclusive about normality which is why we checked the residuals and have now added to the paper as outlined in response to Reviewer 2, comment 3 above.

5) In Fig 1, we the black line (and dots) for Gardosi model are missing but shown in the legend.

Response: That part of the legend was indicating that the lines are from the models while the dots are the empirical observations. We have removed that information from the figure itself to avoid confusion and added to the figure description. (p. 13)

“The lines are from the models while the points are empirical observations.”

6) The authors noted that “In Fig 2…. If the Gardosi assumption of constant CV was satisfied the standard deviation would fall on the line with constant slope.” This can be true provided that data points in each interval are sufficiently large. It’s important that the authors also give number of data points in each interval.

Response: We have now added the sample size in each group in a footnote. (p. 13)

”The sample size of each group is 5, 25, 85, 292, 668, 822, 350, and 41 for the point representing the grouped bins from smallest to largest predicted birthweight, respectively.” Some of the points on either edge are based on fewer sample points so we also added a new line (red line) illustrating the constant coefficient variation assumption per the Gardosi model. As you can see, the bulk of the points do not fall where one would expect them to be under the Gardosi assumption. (revised Fig 2; revised legend p. 13)

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Reviewer #1: Yes: Giuseppe Rizzo

Reviewer #2: No

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Response: IRB approval was received before the study began. The Methods section has been edited with the information in the ethics statement (p. 5, new text underlined):

“Institutional review board approval was obtained at all participating sites as well as the NIH (IRB approval #09-CH-N152) on December 2009 prior to the study beginning. All participants provided informed consent prior to data collection.”

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This research was supported, in part, by the Division of Population Health Research, Division of Intramural Research, Eunice Kennedy Shriver National Institute of Child Health and Human Development (NICHD), National Institutes of Health; and, in part, with Federal funds for the NICHD Fetal Growth Studies – Singletons (Contract Numbers: HHSN275200800013C; HHSN275200800002I; HHSN27500006; HHSN275200800003IC; HHSN275200800014C; HHSN275200800012C; HHSN275200800028C; HHSN275201000009C); and in part, with Federal funds for the Consortium on Safe Labor (Contract Number HHSN267200603425C). KLG has contributed to this work as part of her official duties as an employee of the United States Federal Government.

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Response: The Role of Funder statement has been added to the cover letter.

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Please remove any funding-related text from the manuscript and let us know how you would like to update your Funding Statement. Currently, your Funding Statement reads as follows: This research was supported, in part, by the Division of Population Health Research, Division of Intramural Research, Eunice Kennedy Shriver National Institute of Child Health and Human Development (NICHD), National Institutes of Health; and, in part, with Federal funds for the NICHD Fetal Growth Studies – Singletons (Contract Numbers: HHSN275200800013C; HHSN275200800002I; HHSN27500006; HHSN275200800003IC; HHSN275200800014C; HHSN275200800012C; HHSN275200800028C; HHSN275201000009C); and in part, with Federal funds for the Consortium on Safe Labor (Contract Number HHSN267200603425C). KLG has contributed to this work as part of her official duties as an employee of the United States Federal Government. Please include your amended statements within your cover letter; we will change the online submission form on your behalf.

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Response: To clarify, there was no abstract formally published for this conference proceeding.

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Response: We have submitted the data and accompanying files to NICHD BRADS: https://brads.nichd.nih.gov/

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Response: We have submitted the data and accompanying files to NICHD BRADS. The administrators will notify me when the work is complete (estimated mid-January) and I will notify you when the data is available.

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Response: As the data are not a core part of the research being presented in our study, we have removed this statement from the methods (p. 18).

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Response: This information has been added to the Methods section (p. 5):

“Institutional review board approval was obtained at all participating sites as well as the NIH (IRB approval #09-CH-N152) on December 2009 prior to the study beginning. All participants provided written informed consent prior to data collection.”

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Response: Captions for our Supporting Information files have been added at the end of our manuscript. We have also updated in-text citations to match accordingly.

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