PGENETICS-D-25-01372

FEMA-Long: Modeling unstructured covariances for discovery of time-dependent effects in large-scale longitudinal datasets

PLOS Genetics

Dear Dr. Parekh,

Thank you for submitting your manuscript to PLOS Genetics. The editorial board and three reviewers have read the work. The reviewers provided some detailed suggestions.  We invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

Please submit your revised manuscript by Mar 30 2026 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosgenetics@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pgenetics/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

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If you would like to make changes to your financial disclosure, competing interests statement, or data availability statement, please make these updates within the submission form at the time of resubmission. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

We look forward to receiving your revised manuscript.

Kind regards,

Lin S. Chen, Ph.D.

Academic Editor

PLOS Genetics

Xiaofeng Zhu

Section Editor

PLOS Genetics

Aimée Dudley

Editor-in-Chief

PLOS Genetics

Anne Goriely

Editor-in-Chief

PLOS Genetics

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Authors:

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

Reviewer #1: In this manuscript, the authors extended their previous FEMA method to allow unstructured longitudinal covariance, multiple random effects, spline interactions, and GWAS-scale testing. The proposed algorithm is computationally efficient and addresses an important gap in longitudinal GWAS methodology. I suggest the acceptance for publication after resolving the following issues:

Major comments:

1. Notations. I suggest using boldface consistently for vector and matrices to avoid confusion and avoid reusing the same symbols for different objects. For example, in equation 12, the coefficient of fixed effects in the first term is denoted by beta, which is a vector, and the coefficient of the effect on spline basis functions is by denoted beta_s, which is a scalar. This creates ambiguity, because beta_1 can be interpreted as either the effect of the first fixed effect or the first spline basis. In the following Omnibus Wald test (equation 13), beta is used again. But here it appears to refer only to coefficients for the spline basis functions, that is, beta_s in equation 12, because the degree of freedom is S.

2. In the GWAS-like scaling, Vhat is estimated from a genotype-free stage-1 model and then reused for genotype residualization and SNP testing (equations 9, 15, 17). The authors are implicitly assuming that omitting g when estimating variance components introduces negligible error in Vhat, and that uncertainty in Vhat is ignored in stage-2 inference. Please clarify this assumption explicitly. It would help to add a brief justification and a sensitivity check for a few large-effect loci showing that refitting Vhat does not change inference much.

3. The proposed algorithm estimates unstructured visit-by-visit covariance matrices using pairwise method-of-moments estimates (equation 11), with each covariance term estimated independently. This approach does not guarantee that the assembled covariance matrix is positive semidefinite. Since the GLS inference requires inversion of Vhat, please clarify whether any regularization, eigenvalue correction, or nearest positive-definite projection is applied in practice. If not, a short discussion of numerical stability and why this issue does not materially affect the simulations or GWAS results would be helpful.

4. Pairwise estimation uses only observations that have both visits v and v'. Real longitudinal cohorts usually have irregular visit attendance (later visits may have fewer subjects), leading to substantially different pairwise sample sizes. As a result, some Omega_vv' are estimated from many subjects and others from very few. This may lead to unstable inverse of V_hat in GLS. Please provide justification for this approach and consider a sensitivity check in simulations that explicitly reflects uneven visit overlap.

5. Please make it clear that the proposed method is designed for only continuous, approximately Gaussian outcomes, and does not apply to binary traits.

6. In simulation 1, the description "Var ∈ [0.1, 0.9]" is ambiguous and suggests a continuous interval. The authors appear to use a discrete grid with step size 0.1, which obtains in total 84 combinations. Please clarify that variance components take values in {0.1, 0.2, …, 0.9}, or otherwise explicitly describe the discretization.

7. Simulation 1 is an unbalanced longitudinal design (5,000 subjects with up to five repeated measurements but only 20,000 total observations). However, the manuscript does not specify how observations are allocated across visits. Similarly, the procedure for assigning family membership and the resulting family size distribution are not mentioned. Please clarify these aspects of the data-generating mechanism.

8. In Figure 2, the boxplots show small absolute differences in the average number of false positives between covariance models. The QQ plot suggests separation in the extreme tail (around p < 1e-4), but the boxplots of counts have limited resolution in that regime given only 1000 tests per iteration. Consider increasing the number of null tests per iteration and reporting false-positive counts at smaller alpha. Alternatively, providing a tail summary statistics such as extreme quantiles. This will better reflect GWAS-scale settings.

9. The reported runtimes and carbon footprints are informative. Reproducibility will be enhanced by providing additional computational details, including hardware configuration (number of cores, memory), the exact number of parallel workers used, and whether runtime was dominated by model fitting or genotype I/O.

10. In real data application, the omnibus Wald tests identified substantially more genome-wide significant SNPs than the main-effect-only analysis. To clarify whether these represent genuinely new loci or additional LD-correlated variants within the same region, please report LD-clumped locus counts for each phenotype and summarize overlap between the two approaches.

11. Although simulation results show good type-I error control, the manuscript can benefit from explicit calibration summaries in the real data, especially given that a stage-1 covariance estimate is reused across millions of SNP tests. Please report QQ plots and a genomic inflation factor for the omnibus Wald test and compare with the main-effect-only test.

12. In Figure 5d, the curves represent age-dependent SNP effects, but it is unclear how these lines are constructed from the fitted model. In particular, the y-axis is labeled eta, yet eta is not defined elsewhere in the manuscript or introduced in the model notation. Please clarify how these trajectories are computed, explicitly define eta, and state the scale (whether centered or normalized) of the effect shown in the figure.

Minor comments:

1. There are repeated texts describing the features of the proposed algorithm in the Abstract, the last paragraph of the Introduction, and the Methods (Page 3, last paragraph). Consider reducing redundancy.

2. Page 6, lines 19-20, equation 11, Omega_hat should be used instead of sigma_hat.

3. Page 9, lines 3-4. My understanding is that the residuals yhat-res,GLS_i,g from (18) are the residualized phenotype for (14), estimated using the residualized genotype. Please check.

4. In equations 21 and 22, use g_i instead of g.

Reviewer #2: The reviewer report has been uploaded as an attachment.

Reviewer #3: The authors introduced FEMA-Long to model unstructured covariances for discovery of time-dependent effects in longitudinal datasets. They demonstrated the effectiveness and efficiency of FEMA-Long through extensive simulations. They also applied FEMA-Long to several GWAS datasets, highlighting the importance of modeling the time-dependent effects and revealing how the SNP effects change over time. Overall, the paper is well written, and the experimental results are solid. I have some comments as follows.

1. Nomenclature: fixed effects refer to the coefficients ($\beta$) of covariates ($X$), rather than the covariates themselves. Please correct this throughout the manuscript.

2. Page 4 Line 9: $X_i$ should be a number if $p = 1$ and a vector if $p > 1$.

3. In the GWAS analysis, the dynamic patterns of the variance components are interesting. However, current findings remain largely descriptive and lack rigorous statistical validation. It would significantly strengthen the conclusions by performing formal statistical tests for the dynamic changes of the variance components.

4. When scaling FEMA for GWAS-like analyses, do you perform two separate statistical tests for each SNP—one to determine if the main effect is non-zero, and another to assess the presence of time-dependent effects? Please describe it clearly in the method section.

5. Can your method be extended to handle binary traits? In GWAS, many clinical outcomes and diseases are recorded as binary rather than continuous.

6. One notable advantage of FEMA-Long is its computational efficiency, as mentioned in the manuscript. However, this point has not been sufficiently demonstrated. Please include more competing methods for a more comprehensive comparison and highlight the novelty of your algorithm.

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Have all data underlying the figures and results presented in the manuscript been provided?

Large-scale datasets should be made available via a public repository as described in the PLOS Genetics       data availability policy, and numerical data that underlies graphs or summary statistics should be provided in spreadsheet form as supporting information.

Reviewer #1: None

Reviewer #2: None

Reviewer #3: None

**********

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Reviewer #1: No

Reviewer #2: No

Reviewer #3: No

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Submitted filename: Reviews.pdf

PGENETICS-D-25-01372R1

FEMA-Long: Modeling unstructured covariances for discovery of time-dependent effects in large-scale longitudinal datasets

PLOS Genetics

Dear Dr. Parekh,

Thank you for submitting your manuscript to PLOS Genetics. The three reviewers were largely satisfied with the revision, though a few questions and suggestions remain. We therefore invite you to submit a revised version of the manuscript that addresses the points.

Please submit your revised manuscript within by May 15 2026 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosgenetics@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pgenetics/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

Please include the following items when submitting your revised manuscript:

* A letter that responds to each point raised by the editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'. This file does not need to include responses to formatting updates and technical items listed in the 'Journal Requirements' section below.

* A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'.

* An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'.

If you would like to make changes to your financial disclosure, competing interests statement, or data availability statement, please make these updates within the submission form at the time of resubmission. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

We look forward to receiving your revised manuscript.

Kind regards,

Lin S. Chen, Ph.D.

Academic Editor

PLOS Genetics

Xiaofeng Zhu

Section Editor

PLOS Genetics

Aimée Dudley

Editor-in-Chief

PLOS Genetics

Anne Goriely

Editor-in-Chief

PLOS Genetics

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Authors:

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

Reviewer #1: The authors have addressed all my comments. The manuscript has been significantly strengthened and I have no further major concerns.

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

Reviewer #3: The authors have addressed all of my concerns.

**********

Have all data underlying the figures and results presented in the manuscript been provided?

Large-scale datasets should be made available via a public repository as described in the PLOS Genetics       data availability policy, and numerical data that underlies graphs or summary statistics should be provided in spreadsheet form as supporting information.

Reviewer #1: None

Reviewer #2: None

Reviewer #3: None

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Reviewer #1: No

Reviewer #2: No

Reviewer #3: No

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While revising your submission, we strongly recommend that you use PLOS’s NAAS tool (https://ngplosjournals.pagemajik.ai/artanalysis) to test your figure files. NAAS can convert your figure files to the TIFF file type and meet basic requirements (such as print size, resolution), or provide you with a report on issues that do not meet our requirements and that NAAS cannot fix.

After uploading your figures to PLOS’s NAAS tool - https://ngplosjournals.pagemajik.ai/artanalysis, NAAS will process the files provided and display the results in the "Uploaded Files" section of the page as the processing is complete. If the uploaded figures meet our requirements (or NAAS is able to fix the files to meet our requirements), the figure will be marked as "fixed" above. If NAAS is unable to fix the files, a red "failed" label will appear above. When NAAS has confirmed that the figure files meet our requirements, please download the file via the download option, and include these NAAS processed figure files when submitting your revised manuscript.

Reproducibility:

To enhance the reproducibility of your results, we recommend that authors deposit laboratory protocols in protocols.io, where a protocol can be assigned its own identifier (DOI) such that it can be cited independently in the future. Additionally, PLOS ONE offers an option to publish peer-reviewed clinical study protocols. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols

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Submitted filename: Review_R2.pdf

Dear Dr Parekh,

We are pleased to inform you that your manuscript entitled "FEMA-Long: Modeling unstructured covariances for discovery of time-dependent effects in large-scale longitudinal datasets" has been editorially accepted for publication in PLOS Genetics. Congratulations!

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Lin S. Chen, Ph.D.

Academic Editor

PLOS Genetics

Xiaofeng Zhu

Section Editor

PLOS Genetics

Aimée Dudley

Editor-in-Chief

PLOS Genetics

Anne Goriely

Editor-in-Chief

PLOS Genetics

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Comments from the reviewers (if applicable):

Reviewer's Responses to Questions

Comments to the Authors:

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

Reviewer #2: The authors have successfully addressed all of my concerns in the revised manuscript. I therefore recommend acceptance.

**********

Have all data underlying the figures and results presented in the manuscript been provided?

Large-scale datasets should be made available via a public repository as described in the PLOS Genetics       data availability policy, and numerical data that underlies graphs or summary statistics should be provided in spreadsheet form as supporting information.

Reviewer #2: None

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Reviewer #2: No

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