{"id":"cfde7fb0-fb38-4869-8449-11d7e6fd3b10","arxiv_id":"2412.05894","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"FedRBE reproduces limma's removeBatchEffect in a federated setting with negligible numerical difference, supporting missing values and non-identical feature sets across sites.","lead":"This paper introduces fedRBE, a privacy-preserving tool that applies limma's batch effect correction across hospitals without sharing raw omics data. It reports that fedRBE matches the centralized method to within about 1e-13 and handles missing values and site-specific feature sets, but the paper's own abstract promises a broader federated learning study that is absent from the text.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Missing-value equivalence is unproven: partial per-sample missingness can make a feature's reduced design rank-deficient, and fedRBE's mask-plus-normal-equations do not reproduce limma's pivoted QR in that regime.","rationale":"The central claim is not merely that fedRBE is a useful federated tool; it is that users can treat its output as a drop-in replacement for centralized limma removeBatchEffect, including when values are missing. That is what makes the tool safe to use without dataset-specific re-validation. The numerical agreement on three real datasets and simulations is real evidence, and the code is available, but the simulations intentionally contain no missing data, and the two real datasets with NAs exercise only particular missingness mechanisms. The gap is algorithmic: limma's per-feature row deletion plus pivoted QR handles a broader class of rank-deficient reduced designs than the whole-batch mask in Figure 5. Partial missingness correlated with covariates can make a batch column collinear with the covariate column after deletion; fedRBE's normal equations have no defined behavior in that case, while limma's pivoting drops a column. If the proposed synthetic test shows a divergence above floating-point noise, the 'mathematically equivalent' statement must be qualified (e.g., to full-rank per-feature reduced designs) or the federated solver must incorporate pivoting or regularization that provably matches limma. This is a correctness risk internal to the method, not a disagreement with consensus. The abstract/title mismatch about an FL batch-effect benchmarking study is a serious presentation flaw, but fixing it would not repair the equivalence proof. Because the reader already assigned CONDITIONAL on this equivalence assumption, my read does not move the verdict.","tokens_in":19664,"tokens_out":9603,"duration_ms":106264,"concrete_test":"Run a synthetic 3-client, 2-batch federated experiment with a binary covariate C and a feature f whose missingness is not at random: in batch 1, f is observed only for C=1 samples; in batch 2, f is observed only for C=0 samples; all other entries are complete. Apply fedRBE and pooled limma::removeBatchEffect() with design ~ C + batch and compare corrected values for f. The per-feature reduced X is rank-deficient even though f is present in every batch. If the maximum absolute difference exceeds ~1e-10, or fedRBE errors on the singular X^T X, the equivalence claim fails for a supported input with missing values.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Methods, 'Federated linear regression algorithm' (Figure 5) states that fedRBE 'receives results mathematically equivalent' to limma::removeBatchEffect() on the pooled dataset, and the Conclusion caps the difference at 3.6E-13. The equivalence is asserted, not proven. limma fits each feature by deleting NA rows and calling lm.fit(), which uses QR decomposition with column pivoting. fedRBE instead sums local X^T X and X^T y and solves the normal equations, removing only batch columns whose feature is entirely absent from a batch. That mask does not cover rank deficiency arising from partial missingness: after row-wise deletion for a feature, the reduced design can be collinear even though no whole-batch column vanishes (e.g., in one batch the feature is observed only for samples with covariate=1, so that batch column equals the covariate column). limma's pivoted QR then drops a dependent column; fedRBE's normal equations are singular, and the paper specifies no pseudo-inverse fallback that matches limma's pivoting. The stated requirement that covariates not linearly depend on batches applies to the full design, not to per-feature reduced designs. Since the simulations contain no missing values and only the proteomics and microarray datasets exercise NAs, the drop-in equivalence claim is not established for arbitrary missingness patterns.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript presents fedRBE, a federated implementation of limma's removeBatchEffect() built on the FeatureCloud platform, augmented with additive-secret-sharing SMPC and designed to accept missing values and non-identical feature sets across clients. The authors evaluate fedRBE on a set of simulations and on three real omics datasets (E. coli mass-spectrometry proteomics, ovarian-cancer microarray transcriptomics, and colorectal-cancer shotgun metagenomics), reporting maximum absolute differences on the order of 1e-13 relative to centralized limma. The abstract additionally claims a systematic assessment of how uncorrected batch effects impair federated k-means clustering and federated random forest classification on four datasets including metabolomics, but that assessment does not appear in the main text.","tokens_in":19860,"tokens_out":7421,"duration_ms":80799,"significance":"As a tool paper, fedRBE is a useful contribution: a drop-in federated replacement for a widely used batch-effect correction routine would enable privacy-preserving multi-center omics workflows, and the empirical validation against the external limma standard is a genuine strength. The numerical equivalence on the tested data is well supported, and the provision of code, app, and public datasets is commendable. The broader claim in the title and abstract about systematically quantifying the impact of batch effects on federated k-means and random forest is not supported by the presented experiments, so the significance of the paper as a study of batch effects in FL is currently much weaker than the framing suggests.","major_comments":[{"comment":"The abstract and title promise a systematic assessment of uncorrected batch effects on federated k-means clustering and federated random forest classification using four multi-center omics datasets, including metabolomic data. The main text contains no such assessment: Table 2 lists three datasets, none of them metabolomic, and the Results section only evaluates the numerical equivalence of fedRBE to centralized limma. This mismatch is load-bearing for the paper's stated contribution; the authors must either include the promised FL experiments or revise the title, abstract, and framing to describe a tool paper on fedRBE.","section":"Abstract and Title"},{"comment":"The claim that fedRBE 'receives results mathematically equivalent' to limma::removeBatchEffect() is asserted but not proven for the missing-value patterns that the tool advertises. limma fits each feature after row-wise deletion of NA samples and uses lm.fit(), i.e., QR decomposition with column pivoting, which can drop dependent columns when the per-feature reduced design is rank deficient. fedRBE instead sums local X^T X and X^T y and solves the normal equations, with masking only for whole batches in which a feature is entirely absent. Partial missingness can make a reduced design rank deficient without removing a whole batch column, for example when a feature is observed in exactly the samples of one batch that have a particular covariate value; in that case the normal equations are singular and the paper specifies no pseudo-inverse or pivoting rule matching limma. Since the simulations contain no missing values and only the proteomics and microarray datasets exercise NAs, the drop-in equivalence claim for arbitrary missingness patterns is not established.","section":"Methods, Federated linear regression algorithm (Figure 5)"},{"comment":"The stated requirement that covariates not linearly depend on other covariates or on batches applies to the full design matrix, but limma's per-feature fit uses the row-wise reduced design after NA deletion. Even a full-rank complete-data design can become rank deficient after such deletion for a specific feature, so the authors' masking criterion based only on whole-batch feature presence does not cover all supported inputs. The equivalence claim therefore needs either a rigorous proof or a restricted missingness model stated explicitly in the Methods.","section":"Methods, The fedRBE workflow"}],"minor_comments":[{"comment":"There is a stray Cyrillic character in 'a total of 98 samplesб'; the manuscript needs a proofreading pass.","section":"Methods, Proteomics dataset"},{"comment":"The text cites 'Hardebrodt et al.' for the federated QR decomposition, but the reference list and the published author name use 'Hartebrodt'; please unify the spelling.","section":"References"},{"comment":"The description of the secret-sharing protocol says that each client creates c-1 random pieces and then holds 'c pieces in total' after distributing all but one piece; this wording is confusing and should be clarified.","section":"Methods, Enhancing privacy with additive secret sharing"},{"comment":"The table uses '+/—' for d-ComBat's privacy-aware analysis but the legend does not define the symbol; please add a legend or use the same symbols as the other rows.","section":"Table 1"},{"comment":"The phrase 'mathematically equivalent' is used where the evidence is numerical equality on tested datasets; unless a proof is supplied, recommend rewording to 'numerically equivalent on the tested datasets'.","section":"Conclusion"}],"recommendation":"major_revision","confidential_remarks":"The gap between the abstract and the actual content is unusually large and should be resolved before publication: either the systematic FL assessment is added, which is a substantial amount of new work, or the paper is reframed as a fedRBE tool paper. The core fedRBE result appears salvageable and empirically solid, but the current framing overstates the contribution."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The useful part of this paper is fedRBE, a federated implementation of limma's removeBatchEffect that handles missing values and non-identical feature sets across clients. That is genuinely new: prior distributed ComBat variants don't handle NAs, and the mask-based re-referencing for features missing in the reference batch is a real extension. The evaluation is also honest as far as it goes: three real omics datasets and simulations, all compared against centralized limma, with maximum absolute differences around 1e-13. Code and data are public. That is real evidence.\n\nBut two things bother me. First, the arXiv abstract promises a systematic study of how batch effects impair federated k-means and random forest on four datasets. That study is not in the paper. The full text is entirely about fedRBE. The abstract needs to be rewritten to match content, or the experiments need to be added. Second, the claim of \"mathematically equivalent\" is not supported. limma uses pivoted QR, which drops dependent columns when the per-feature design is rank-deficient after row-wise deletion of NAs. fedRBE solves normal equations after removing whole-batch columns only. Partial missingness can make a reduced design collinear without removing any whole batch, and the normal equations are singular then; the paper gives no fallback that matches limma's pivoting. The requirement that covariates not depend on batches is stated for the full design, not for the per-feature reduced designs. The simulations intentionally contain no missing values, so the missing-value behavior is only empirically tested on the proteomics and microarray datasets, which may not exercise these edge cases. So the drop-in equivalence is plausible but not proven.\n\nThe paper deserves serious peer review. It's a useful tool and the core idea is sound. I'd recommend a conditional accept with two requests: align the abstract with the actual contribution, and either soften the equivalence claim to \"empirically equivalent in tested scenarios\" or add a proper analysis (or at least more adversarial missingness patterns) showing when the masking matches limma.\n\nThis is a paper for people building federated omics pipelines; I'd read it and cite the tool if I worked in that area. It's not a methods breakthrough, but it fills a practical gap.","headline":"A useful federated batch-correction tool with solid empirical equivalence checks, but the abstract overpromises and the missing-value equivalence is asserted rather than proven.","tokens_in":20485,"tokens_out":2535,"would_cite":true,"duration_ms":24352,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"FedRBE, a privacy-preserving federated implementation of limma's removeBatchEffect(), matches centralized results to within 3.6E-13 on real and simulated omics data.","keywords":["federated learning","batch effect correction","limma","secure multi-party computation","missing values","multi-center omics","privacy-preserving","omics integration"],"falsifier":"Construct a distributed dataset with a feature missing from the reference batch and present in a non-contiguous subset of other batches, run fedRBE and centralized limma, and check whether any corrected value differs by more than about $10^{-10}$; a larger difference would refute the claimed mathematical equivalence.","tokens_in":19385,"feed_emoji":"🧬","tokens_out":5784,"duration_ms":51906,"temperature":0.7,"pith_summary":"FedRBE is a federated implementation of limma's removeBatchEffect() that performs batch-effect correction across distributed omics datasets without pooling raw data. The paper seeks to prove that fedRBE produces corrected values mathematically equivalent to applying limma to the pooled dataset, even when clients have missing values and different feature sets. On three real multi-center datasets (proteomics, microarray transcriptomics, metagenomics) and 90 simulated datasets, the maximum absolute difference from centralized limma was 3.6E-13, i.e., floating-point-level agreement. This matters because it makes standard batch-effect correction compatible with privacy requirements in multi-center studies, including data types where missing values previously blocked federated correction.","feed_headline":"Federated batch correction matches pooled limma to 3.6E-13","feed_subtitle":"fedRBE corrects omics data across centers without sharing raw data, handling missing values and differing feature sets.","key_machinery":"The load-bearing machinery is a federated linear regression built on aggregating local cross-product matrices $X_i^T X_i$ and $X_i^T y_j$ instead of raw data, following the secure-regression approach of Karr et al. Because the existing federated QR decomposition lacks column pivoting, fedRBE adds a per-feature global mask that removes whole batch columns from the design matrix when a feature is absent from a batch, and redefines the reference batch when the original reference lacks the feature. This mask is what lets the method handle missing values and non-identical feature sets while mimicking limma's row-wise deletion and QR-based least-squares fit. Additive secret sharing (splitting each shared matrix into random pieces that sum to the original) is layered on top to hide individual contributions during aggregation.","core_discovery":"The central claim is that fedRBE is a drop-in federated substitute for limma::removeBatchEffect(): it receives results mathematically equivalent to the centralized result by computing, per feature, the same linear-regression adjustment from aggregated local matrices. Each client computes local $X^T X$ and $X^T Y$ for its samples; the coordinator sums them across clients, applies a per-feature mask that drops batches where the feature is absent (re-selecting the reference batch when needed), and solves for the regression coefficients that are then used to subtract the batch effect locally. Because only the aggregated cross-product matrices are exchanged, and because additive secret sharing masks those matrices in transit, patient-level data stay local. The paper's empirical comparison shows maximum absolute differences of $2.2\\times10^{-13}$ on real datasets without SMPC and up to $3.6\\times10^{-13}$ across simulations.","pith_inferences":["If the equivalence holds for arbitrary missingness patterns, a similar aggregation strategy could be applied to other linear-model-based harmonization methods, reusing the same cross-product aggregation.","The per-feature mask's replacement of missing batch columns suggests that batches with very few observed features will have their effects estimated from a shrinking subset of samples; future work could quantify the minimal feature presence required for stable correction.","Because the app is deployed on a federated platform, in practice the bottleneck may shift from the math to governance: deciding which features and covariates are hashed and shared, and whether the union-of-features policy leaks information about which centers measure which analytes."],"forward_implications":["Multi-center omics studies can correct batch effects without a central data repository, so downstream analyses like clustering or co-expression can run federated end-to-end.","Proteomics and metabolomics data, which commonly contain missing values, become eligible for federated batch-effect correction without prior imputation.","Because fedRBE is mathematically equivalent to limma, results from federated analyses can be compared directly with historical centralized limma-corrected results.","The SMPC component protects intermediate computations from reconstruction attacks, addressing a known vulnerability of earlier distributed ComBat implementations."],"supporting_citations":[{"why":"Defines removeBatchEffect(), the centralized algorithm whose federated equivalent fedRBE reproduces.","marker":"[32]"},{"why":"Supplies the secure distributed regression approach (aggregating local $X^TX$ and $X^TY$) that fedRBE adapts.","marker":"[58]"},{"why":"Provides the federated QR decomposition that lacks column pivoting, motivating fedRBE's masking alternative.","marker":"[57]"},{"why":"Describes additive secret sharing used to protect intermediate matrices.","marker":"[48]"},{"why":"Provides the simulation framework and the proteomics dataset used to evaluate equivalence.","marker":"[24]"}],"fun_headline_variants":["Batch effects can wreck federated omics studies","fedRBE matches centralized limma to 3.6E-13 precision","Federated batch correction: privacy preserved, results identical","Multi-center omics: batch effects impair FL, fedRBE fixes","Drop-in federated limma: matches pooled results exactly"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The claim that the per-feature masking exactly reproduces limma's row-wise deletion and QR-based fit for every possible missingness pattern is asserted mathematically but only tested on three real datasets and simulations; unusual patterns could yield different corrected values.","fun_headline_variants_meta":{"raw":{"variants":["Batch effects can wreck federated omics studies","fedRBE matches centralized limma to 3.6E-13 precision","Federated batch correction: privacy preserved, results identical","Multi-center omics: batch effects impair FL, fedRBE fixes","Drop-in federated limma: matches pooled results exactly"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000232,"raw_usage":{"total_tokens":1469,"prompt_tokens":902,"completion_tokens":567,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":518,"completion_tokens_details":{"reasoning_tokens":480}},"tokens_in":518,"tokens_out":567,"duration_ms":5791,"temperature":1.0,"reasoning_tokens":480,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T20:13:46.031425+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Construct a distributed dataset with a feature missing from the reference batch and present in a non-contiguous subset of other batches, run fedRBE and centralized limma, and check whether any corrected value differs by more than about $10^{-10}$; a larger difference would refute the claimed mathematical equivalence.","supporting_citations":[],"review_version":1}