NLCD: A method to discover nonlinear causal relations among genes

PLOS Computational Biology

Dear Dr. Narayanan,

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Yuehua Cui, PhD

Academic Editor

PLOS Computational Biology

Pedro Mendes

Section Editor

PLOS Computational Biology

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1) Please ensure that the CRediT author contributions listed for every co-author are completed accurately and in full.

At this stage, the following Authors/Authors require contributions: Aravind Easwar, and Manikandan Narayanan. Please ensure that the full contributions of each author are acknowledged in the "Add/Edit/Remove Authors" section of our submission form.

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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: I have a few comments and suggestions that I think would help clarify the contribution and improve the overall presentation of the manuscript:

1. The idea of extending CIT to handle nonlinear relationships is very interesting and well motivated. It would help to more clearly explain how NLCD differs from other nonlinear or ML-based causal discovery methods, and what it adds beyond existing approaches.

2. The use of KRR, SVR, and neural networks is reasonable, and KRR appears to perform best in the benchmarks. Please explain why KRR was chosen as the default, and how sensitive results are to tuning or kernel choice.

3. For me it would be helpful to include a clearer check of p-value calibration or type I error control, particularly for nonlinear but non-causal settings.

4. Conditional feature importance is a key part of the method. A bit more intuition about when CFI works well, and when it might struggle (for example, when there is little overlap between genotype groups), would improve clarity. Also since the proposed method involves nonlinear regression and many permutations, some discussion of computation time can help readers understand when NLCD is practical to use.

5. The GTEx application is interesting, but some assessment of robustness (e.g., sensitivity to permutations, model choice) would increase confidence in these findings. In addition, a bit more discussion of biological plausibility would strengthen the real-data section.

Reviewer #2: The authors propose a method called NLCD, which extends the classical CIT framework to the nonlinear setting, and demonstrate its application to both human and yeast data. The manuscript is well written, and most methodological components are clearly explained. I have several questions and suggestions that may help further clarify and strengthen the work.

1. How does NLCD perform under a structure such as B←L→A, and at the same time A->B? In an MR framework, this corresponds to an invalid IV scenario where the instrument directly affects the outcome conditional on the exposure (horizontal pleiotropy).

2. Since NLCD is built upon the CIT framework proposed by Millstein et al. (2009), it is important to clearly explain the rationale for the four tests described in Section 2.2.4. In particular, the exact null and alternative hypotheses for each test should be explicitly stated. This would make the logical structure of the procedure more transparent and help readers understand how the joint decision rule corresponds to the overall causal hypothesis.

3. Regarding Test 1, why is a nonlinear model necessary in that step? For example, in eQTL analysis, a simple linear regression is often sufficient to test the association between a variant and expression.

4. Another concern relates to potential overfitting. If the same dataset is used for both training the nonlinear model and evaluating the test statistic, this may introduce optimism bias. Have the authors considered cross-validation or an independent test set to construct the test statistic?

5. In the yeast data application, the results suggest that NLCD does not outperform the original CIT, and even in the subset results, it is comparable to the CIT. Does this indicate that NLCD did not perform well in detecting linear relationship? It would be informative to compare NLCD and CIT at the level of the four component tests, for example by identifying which specific tests fail or differ between the two methods.

6. For human data application, how do other SOTA methods perform in this application?

7. In Figure 5b–c, the authors state that “the NLCD predictions for all three values of L are close to each other in the overlap region,” whereas in Figure 5d–e they indicate that predictions differ across values of L in the overlap region. However, the y-axis scales are not the same across panels, which makes it difficult to visually assess these differences. Clarification would be helpful. In addition, please specify what the colors of the dots represent in these plots.

8. Since the real-data results are largely comparable to existing methods, it would be helpful to briefly clarify in what settings NLCD is expected to provide clear advantages, for example, under stronger nonlinear relationships or more complex traits, and whether its intended scope extends beyond gene-level applications.

Reviewer #3: This work represents a non-trivial development of a CIT-type mediation analysis approach for non-linear settings, particularly involving gene regulatory networks. The approach is well thought-out, implemented, and the rationale is clearly explained in the manuscript. Simulations demonstrate that the approach (NLCD) out performs the CIT, Findr, and MRPC in simulated non-linear scenarios and performs competitively to the CIT in linear settings. Software is provided via GitHub. It's my opinion that this will be an important and useful tool for the scientific community for identifying causal relationships between molecular features in non-linear settings, previously a methodological gap in this field.

The manuscript is well written and organized.

I have one comment that the authors could address, and that involves heterogeneity or experimental design-related factors that might need to be considered during the analysis. For example, what if there are batches, multiple tissues, cell types, genders, etc. How can this approach accommodate adjustment covariates?

Minor comment: Change section 2.2 title from “Our NLCD Method” to something more informative, e.g., “NLCD Algorithm”

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Have the authors made all data and (if applicable) computational code underlying the findings in their manuscript fully available?

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Reviewer #1: Yes

Reviewer #2: None

Reviewer #3: Yes

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Reviewer #1: No

Reviewer #2: No

Reviewer #3: Yes:   Joshua Millstein

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Figure resubmission:

Reproducibility:

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Dear Dr. Narayanan,

We are pleased to inform you that your manuscript 'NLCD: A method to discover nonlinear causal relations among genes' has been provisionally accepted for publication in PLOS Computational Biology.

Before your manuscript can be formally accepted you will need to complete some formatting changes, which you will receive in a follow up email. A member of our team will be in touch with a set of requests.

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Thank you again for supporting Open Access publishing; we are looking forward to publishing your work in PLOS Computational Biology.

Best regards,

Yuehua Cui, PhD

Academic Editor

PLOS Computational Biology

Pedro Mendes

Section Editor

PLOS Computational Biology

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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 adequately addressed my previous comments, and I have no further questions or concerns.

Reviewer #2: The authors have addressed all my comments and I have no further comments.

Reviewer #3: The authors have adequately addressed my concerns.

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Have the authors made all data and (if applicable) computational code underlying the findings in their manuscript fully available?

The PLOS Data policy  requires authors to make all data and code 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 and code 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 or code —e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: None

Reviewer #2: None

Reviewer #3: None

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PLOS authors have the option to publish the peer review history of their article (what does this mean? ). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

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Reviewer #1: No

Reviewer #2: No

Reviewer #3: Yes:   Joshua Millstein

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