Review Reports

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This manuscript focuses on the application of additive Bayesian networks (ABNs) to grouped data, such as multicenter clinical datasets, and presents an extensive simulation study comparing three strategies for handling group structure: partial pooling (PP, using mixed-effects models), complete pooling (CP, ignoring grouping), and no pooling (NP, modeling each group independently). The work is methodologically innovative and substantively rich. Acceptance would be appropriate upon addressing the following points:

1. Reference [8] corresponds to the authors’ prior work but does not clearly articulate its incremental contribution relative to the present study.
2. In Section 2.1.1 “Modeling Grouped Data,” only random intercepts (and not random slopes) are included. Is this sufficient to capture between-group heterogeneity in the relationships among variables?
3. In Section 2.2.2 “Data Simulation,” the simulation design excludes Poisson-distributed variables. What is the rationale for this exclusion?
4. In Section 2.1.3 “Model Complexity,” the model complexity calculation (Equation 3) appears to omit the covariance structure of the random effects. Could this omission affect the Bayesian Information Criterion (BIC) score?
5. In Section 2.2.3 “Parameters of the Algorithm,” an exact search algorithm is used for structure learning, yet the maximum number of parents (max.parents) is restricted to 3-4. Might this constraint limit the exploration of plausible network structures?
6. In Section 4 “Discussion,” the simulation data are generated entirely under the assumed model framework. Has the robustness of the approach been evaluated under violations of key assumptions, for example, non-normal random effects?
7. Several equations in the manuscript lack numbering, which hinders cross-referencing and clarity.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

• The model assumes only random intercepts across groups. While this simplifies computation, it overlooks important group-level variation in relationships (slopes) between variables — potentially underfitting complex hierarchical structures.

• The method struggles when the number of groups is small, especially k = 2. This is a known weakness in hierarchical models where random effects become poorly estimable, leading to unstable predictions and structural recovery. 

• Poisson-distributed variables, common in epidemiological and count data, were excluded due to modeling difficulties. This reduces the generalizability of the framework to important domains like genomics or event modeling.

• The paper relies on exact search for DAG structure learning, which does not scale well beyond small-to-moderate networks (p > 12). This limits applicability to real-world high-dimensional data.

• The mixed-effect ABN model (PP) consistently incurs the highest computational cost, which can be impractical for large-scale or time-sensitive applications.
• The study is purely simulation-based. There's no empirical demonstration of the method's performance on actual clinical or multi-center datasets, limiting insight into its real-world robustness.
• Evaluation focuses on SHD and KL divergence but lacks edge-level precision/recall, which are often more informative in real-world applications (e.g., false positive edge control).
• While BNs often support causal inference, the paper does not explore causal implications of the learned networks or whether partial pooling impacts causal interpretation.
• The simulations assume the data-generating process matches the model assumptions exactly (e.g., linearity, normality), but robustness to misspecification (e.g., non-Gaussian random effects, nonlinearities) was not tested.

Comments on the Quality of English Language

Approved

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

1. The title is too abstract; please highlight keywords like "mixed-effects" or "grouped data."
2. The abstract is too long; shorten the background and emphasize the core conclusion that "partial pooling is superior."
3. The introduction repeats criticisms of complete/no pooling; please condense and add biomedical examples of ABN.
4. Equation (3) for model complexity appears abruptly; explain its relation to the BIC penalty term.
5. Only random intercepts are used; add discussion on why random slopes are not adopted.
6. Poisson variables are excluded; provide preliminary results or stability analyses in the appendix.
7. The threshold of ≥25 samples per group lacks literature support; cite references or offer sensitivity analyses.
8. Figures 1–4 have poor color/legend distinction; add significance markers and improve readability.
9. Prediction error mixes multiple metrics; show details by variable type in the appendix.
10. The discussion of limitations is too long; create a separate "future research" section and give a practical decision table.

Author Response

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Author Response File: Author Response.pdf