{"id":"998a2a8c-7ff7-4eb4-a1ea-c7add3d98266","arxiv_id":"2505.02238","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":2,"one_line_summary":"A survey of federated causal inference that asserts, without proof, asymptotic bias and variance results showing FedProx matches pooled analysis under heterogeneous survival data.","lead":"This preprint reviews federated causal inference methods for healthcare data and claims to prove that FedProx-style regularization gives near-optimal bias and variance for Cox and competing-risk survival models under site heterogeneity. The theoretical results are presented as tables without derivations, so the central claim is not supported by the text.","discovery_kind":"review","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Theorems 1–2 (Tables 2–3) are unproven and the claimed strict FedProx advantage is contradicted by standard partial-likelihood asymptotics: under Eq. (32) each local Cox MLE is consistent for the shared beta, so FedAvg has zero asymptotic bias too.","rationale":"The reader's weakest_assumption was that Theorem 1 and Theorem 2 assume without proof that FedProx converges to a consistent shared estimator. I agree, and I find a stronger, more specific problem: the claimed bias ordering appears internally inconsistent with the Cox partial-likelihood martingale property and with the definitions in the paper (Eqs. (19) and (32)-(33)). Since local MLEs are consistent for the common coefficient under the stated heterogeneity, FedAvg should also have zero asymptotic bias, making the table's strict inequality impossible. This is not an 'outside consensus' concern but an internal consistency check. The Aalen-Johansen claim similarly lacks a well-defined global target and a mechanism for bias correction; the proximal term only penalizes parameter deviations and cannot adjust for distribution shift in the marginal CIF. Because these theorems are the advertised novel contribution and are central to the paper's stated contributions, and because they are given without proof and appear false, rejection is appropriate. The survey material may be salvageable as a separate paper, but the theoretical add-on cannot be conditionally repaired by adding a proof; it would require substantial reformulation of the claims (or restricting to settings where local estimators are inconsistent and FedProx provably corrects the inconsistency, which is not shown).","tokens_in":19134,"tokens_out":4645,"duration_ms":58701,"concrete_test":"Run a two-site Cox simulation with model (32): beta=(0.3,-0.2), site 1 baseline hazard Weibull(shape=1, scale=1), site 2 Weibull(shape=1.5, scale=0.7), X ~ N(0,1) at site 1 and X ~ N(1,1) at site 2, n_i=5000, uniform censoring. Compute local partial-likelihood MLEs, the FedAvg weighted average (19), and, if implementable, FedProx iterates; compare against the true beta. If the bias of FedAvg is statistically indistinguishable from zero (e.g., |bias| < 1.96*SE), then the nonzero FedAvg-bias row of Table 2 and inequality (40) are contradicted.","verdict_should_be":"REJECT","load_bearing_attack":"The paper's advertised contribution is the claim (Eqs. (38)–(41)) that under site-level baseline-hazard and covariate heterogeneity, FedProx achieves zero asymptotic bias and pooled variance for Cox and Aalen–Johansen estimators, strictly beating FedAvg and meta-analysis. This claim rests entirely on Theorem 1 and Theorem 2, which are presented as tables with no derivations, no regularity conditions, and no identifiability or transportability assumptions. The concern is not merely that the proof is missing; the statement conflicts with basic semiparametric theory. Under model (32), the local Cox partial-likelihood score is a martingale at the true beta: E[U_i(beta_0)]=0 follows from the martingale representation, so the local MLE is consistent for the shared coefficient regardless of site-specific baseline hazards or covariate distributions. Consequently gamma_i=0 in Eq. (33), and every convex combination of local MLEs—including FedAvg in Eq. (19)—has zero asymptotic bias. The nonzero FedAvg bias row in Table 2, and hence the ordering Bias_FedProx < Bias_FedAvg in Eq. (40), cannot be correct. For the Aalen–Johansen estimator, the issue is different but equally serious: if the true CIF F_{k,i}(t) varies across sites, no estimator can be unbiased for an external global target F_{k,0}(t) without explicit importance weighting or a transportability assumption; a proximal penalty (Eq. (20)) does not reweight the population and cannot remove this bias. Thus the central survival claim is both unsupported and, as stated, likely false. The survey taxonomy and software review may survive, but the theoretically advertised result collapses.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This manuscript is a review of federated causal inference methods for binary/continuous and time-to-event outcomes, together with a claimed theoretical analysis of asymptotic bias and variance under data heterogeneity. The authors organize methods into weight-based and optimization-based categories, describe FedProx, personalized federated learning, peer-to-peer communication, and model decomposition frameworks, review software tools and applications, and conclude in Eqs. (40)-(41) that FedProx-style regularization achieves zero asymptotic bias and pooled-level asymptotic variance for Cox proportional hazards and Aalen-Johansen estimators under heterogeneous site-level baseline hazards and covariate distributions.","tokens_in":19455,"tokens_out":4616,"duration_ms":55961,"significance":"If the central theoretical claim (Theorems 1-2, Eqs. (40)-(41)) were correct, it would be a substantial contribution: it would show that communication-efficient proximal federated estimation matches centralized pooled analysis in survival settings. The paper also usefully summarizes the Khellaf et al. theory for ATE estimation and surveys an emerging software ecosystem. However, the central time-to-event theorem is presented as a table without proof, and the claimed ordering is contradicted by standard partial-likelihood asymptotics under the authors' own model. The review material is broad but largely descriptive, and the theoretical contribution, which is the advertised novelty, is not established.","major_comments":[{"comment":"The central results are asserted without proof. The abstract claims the paper derives asymptotic bias and variance, but the time-to-event section provides only Definitions 1-4 followed directly by two tables with garbled entries. No regularity conditions, identifiability assumptions, or derivations are supplied, so the claimed zero-bias and variance equalities are not established. A theorem presented as a table with corrupted symbols is not a theorem as it stands.","section":"Theoretical Foundations of Federated Estimators for Time-to-Event Outcomes, Theorems 1-2 (Tables 2-3, Eqs. (38)-(39))"},{"comment":"Under the model in Eq. (32), with site-specific baseline hazard h_0i(t) and a shared coefficient beta_0, the local maximum partial likelihood estimator beta_i is consistent for beta_0 under standard independent censoring conditions, because the local partial likelihood score has expectation zero at beta_0 by the martingale property. Consequently, gamma_i in Eq. (33) is zero and the FedAvg estimator in Eq. (19), a convex combination of consistent local estimators, also has zero asymptotic bias. The nonzero FedAvg bias row in Table 2 and the strict ordering Bias_FedProx < Bias_FedAvg in Eq. (40) are therefore incompatible with the model as stated; the authors would need to add an explicit source of local inconsistency and prove that FedProx remains consistent under that alternative.","section":"Eq. (32) and Table 2 (Cox model)"},{"comment":"Definition 2 and the heterogeneous-setting paragraph define site-specific true CIFs F_{k,i}(t). If these differ across sites, no estimator computed from local data can be unbiased for an arbitrary external global target F_{k,0}(t) without either defining that target as a known mixture of the site-specific CIFs or imposing an explicit transportability/importance-sampling assumption. The proximal penalty in Eq. (20) does not reweight the populations, so it cannot remove the difference between the local estimands and an unspecified global target. The zero-bias claim in Eq. (41) requires an explicit definition of the global estimand and a positivity condition, neither of which is supplied.","section":"Theorem 2/Table 3 (Aalen-Johansen estimator)"},{"comment":"The asymptotic variance entries in Tables 2 and 3 are garbled to the point of being unreadable, for example '1-#&!!.!(+)' in Table 3. Even setting legibility aside, the manuscript never states which matrices or variance functional the entries denote, nor does it define the pooled estimator in the heterogeneous survival setting. As a result, the claimed variance ordering Varpooled = VarFedProx < VarFedAvg etc. cannot be verified or falsified from the text, and the central comparison is not mathematically meaningful.","section":"Eqs. (38)-(39) and (40)-(41)"}],"minor_comments":[{"comment":"The equation number (1) is used twice: once for the ATE definition and once for the local estimator in the Khellaf et al. summary; all equations should be renumbered consistently.","section":"Section 'Considering Local Estimator' and earlier ATE section"},{"comment":"Algorithm 1 uses z for the proximal coefficient while Eq. (20) uses mu; unify the notation for the FedProx regularization strength.","section":"Algorithm 1 and Eq. (20)"},{"comment":"The kernel bandwidth h in Eq. (7) is never defined in terms of a data-dependent choice, and the FedProx coefficient is not given any selection guidance; the paper should at least discuss sensitivity to these tuning parameters.","section":"Eq. (7)"},{"comment":"Many references are given only as 'Google Search' entries or bare URLs without full bibliographic information, including refs. 4, 54, 56, 61, 63, 67, 73, 75-77, 79-81, 83, 95, 99, 101, 105, and 110; these are not citable in a journal publication.","section":"Reference list"},{"comment":"Figure 2 appears twice with different content, once as the graphical model for heterogeneous distributions and once as a characteristics comparison of meta-analysis, FedAvg, and FedProx; renumber the figures.","section":"Figure numbering"},{"comment":"The sentence 'Among them, FLAME and dsSurvival provide the most direct support for causal inference tasks' is unsupported because FLAME does not appear in Table 4.","section":"Software Tools section"},{"comment":"The manuscript contains several typos and garbled glyphs, including 'dost not hold', 'contributions are three folds', and the use of '!' for treatment and '(' for outcome in the binary/continuous outcome section; these should be corrected carefully.","section":"Proofreading"}],"recommendation":"reject","confidential_remarks":"The central time-to-event theoretical claims, which are the paper's advertised novelty, are unproven and appear to be inconsistent with standard Cox partial-likelihood asymptotics under the authors' own model. The review portions are descriptive and contain numerous citation and presentation problems. I recommend rejection; a resubmission would need a rigorous, correctly stated theory with explicit assumptions and proofs, or removal of the unsupported survival claims."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The review half of this paper is worth your time: the weight-based versus optimization-based taxonomy is a clean way to organize the federated causal inference literature, and the summary of Khellaf et al.'s binary/continuous ATE results is accurate and properly attributed. The software survey and application overview are also reasonable. If the paper were just that, I'd call it a serviceable, if not exciting, review.\n\nThe problem is the advertised theoretical contribution. The abstract says the authors derive asymptotic bias and variance for federated Cox and Aalen–Johansen estimators under heterogeneity, and Tables 2 and 3 claim FedProx achieves zero bias and pooled variance while FedAvg and meta-analysis are strictly worse. There is no derivation. More seriously, the claim conflicts with standard semiparametric theory. Under the Cox model in Eq. (32), with a shared coefficient vector and site-specific baseline hazards, the local partial-likelihood score is a martingale at the true beta. So each local MLE is consistent for beta, and any convex combination—including FedAvg—has zero asymptotic bias. The nonzero FedAvg bias row in Table 2 cannot be right. For Aalen–Johansen, if the true cumulative incidence functions genuinely vary across sites, no estimator can be unbiased for some external global target without importance weighting or explicit transportability assumptions; a proximal penalty does not reweight the population. So the central survival claim is not merely unproved, it is likely false as stated.\n\nThe paper also has mechanical problems: the theorem tables contain corrupted symbols, several references are literally 'Google Search' strings, and the abstract's 'deriving' overstates what is actually presented. These are minor compared to the theoretical collapse, but they reinforce the impression that the survival section was not carefully checked.\n\nWhere does this leave the paper? The survey content may be useful to someone entering the field, but the main advertised result—that FedProx matches pooled survival analysis under heterogeneity—does not hold up. If the authors revise, they should either drop the survival theory entirely or provide proper proofs with the right assumptions; the current version would not survive serious scrutiny. I would not cite the theoretical claims, though I might cite the taxonomy if I needed a citable overview. A serious referee could help the authors see what needs to change, so I would not desk-reject it outright, but my own verdict is clearly negative on the current version.","headline":"The survey taxonomy is useful, but the claimed survival-theory results are unsupported and almost certainly wrong—FedAvg is not biased under a shared Cox coefficient.","tokens_in":20011,"tokens_out":3222,"would_cite":false,"duration_ms":42788,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["62F12","62N01","62N02"],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper argues that a FedProx-style proximal update achieves zero asymptotic bias and pooled-level variance for Cox and Aalen-Johansen treatment-effect estimators under site-level heterogeneity.","keywords":["federated learning","causal inference","treatment effect estimation","survival analysis","Cox proportional hazards model","Aalen-Johansen estimator","data heterogeneity","healthcare"],"falsifier":"Simulate two sites with different baseline hazard functions and covariate distributions but a common true hazard ratio; run the paper's Algorithm 1 with a Cox local loss and compare the FedProx coefficient to the pooled maximum partial likelihood estimate as the sample size $n$ grows. If FedProx bias does not shrink to zero while pooled bias does, or if its variance remains above the pooled variance, the claimed equality in Eqs. (40)-(41) fails. A complementary check would compare FedProx Aalen-Johansen cumulative incidence curves with the pooled Aalen-Johansen curve under site-specific competing risks.","tokens_in":18911,"feed_emoji":"🏥","tokens_out":9666,"duration_ms":120300,"temperature":0.7,"pith_summary":"This paper is a survey-and-theory contribution to federated causal inference in healthcare. It classifies existing methods into weight-based and optimization-based approaches, then supplies new asymptotic bias and variance comparisons for time-to-event outcomes under site heterogeneity. Its headline result is that a FedProx-style regularized federated estimator matches pooled analysis, with zero asymptotic bias and pooled-level variance, for both Cox and Aalen-Johansen estimators, while naive averaging and meta-analysis are both biased and less efficient. If that result holds, multi-site treatment-effect studies could obtain centralized accuracy without sharing patient-level data.","feed_headline":"Proximal federated learning matches pooled survival analysis","feed_subtitle":"Site-specific hazards and covariate shifts need not cost accuracy: a proximal update reaches pooled-level precision without sharing…","key_machinery":"The central mechanism is the FedProx proximal objective: each site minimizes its local Cox or Aalen-Johansen loss $\\mathcal{L}_i(\\theta)$ plus a quadratic penalty $\\frac{\\mu}{2}\\|\\theta-\\theta_{\\mathrm{global}}\\|^2$ that keeps local updates close to the current global parameter. The proximal term is what the paper credits for pulling site-specific estimators toward a shared coefficient vector and for making the aggregated estimator consistent for the global target, despite differences in baseline hazards and covariate distributions across sites.","core_discovery":"The paper's central claim is that when each site has its own baseline hazard and covariate distribution but shares a common treatment-coefficient vector, a FedProx-style proximal regularized federated estimator is asymptotically unbiased and achieves the same variance as an analysis of all pooled data, for both Cox proportional hazards and Aalen-Johansen competing-risk estimators. The paper states this as Eqs. (40)-(41): $\\mathrm{Bias}_{\\mathrm{pooled}}=\\mathrm{Bias}_{\\mathrm{FedProx}}=0<\\mathrm{Bias}_{\\mathrm{FedAvg}},\\mathrm{Bias}_{\\mathrm{Meta\\text{-}fixed}},\\mathrm{Bias}_{\\mathrm{Meta\\text{-}random}}$ and $\\mathrm{Var}_{\\mathrm{pooled}}=\\mathrm{Var}_{\\mathrm{FedProx}}<\\mathrm{Var}_{\\mathrm{FedAvg}},\\mathrm{Var}_{\\mathrm{Meta\\text{-}fixed}},\\mathrm{Var}_{\\mathrm{Meta\\text{-}random}}$. This matters because it promises communication-efficient, privacy-preserving multi-site survival analysis with centralized-quality estimates.","pith_inferences":["Editorial inference: if the asymptotic claim holds, the FedProx estimator could serve as a finite-sample benchmark in multi-site trial emulations, but the paper does not provide a convergence-rate or confidence-interval construction.","Editorial inference: the same proximal argument might extend to time-varying exposures or recurrent-event models, because the local-loss-plus-quadratic-penalty structure does not depend on a specific hazard form.","Editorial inference: a direct testable extension would be to derive the fixed point of the proximal update for Aalen-Johansen cumulative incidence functions and check whether it equals the pooled estimator; the paper leaves the mechanism as an assertion."],"forward_implications":["If the claim holds, a communication-efficient FedProx-style algorithm can replace centralized data pooling for Cox and Aalen-Johansen treatment-effect estimation without asymptotic loss.","Under site-level heterogeneity, naive FedAvg and inverse-variance meta-analysis are dominated in both bias and variance, so they should not be the default aggregation in survival settings.","The result implies that the proximal regularization coefficient acts as a tuning parameter controlling the bias-variance trade-off; the paper's comparisons assume this coefficient is chosen suitably.","A single federated estimation framework covers binary, continuous, and time-to-event outcomes, since the local losses can be linear, logistic, Cox, or Aalen-Johansen.","Privacy-preserving federated networks of hospitals could achieve pooled-level statistical efficiency while keeping patient-level data in place."],"supporting_citations":[{"why":"Introduces the FedProx proximal objective that the paper adopts as its main optimization-based estimator.","marker":"9"},{"why":"Supplies the Cox proportional hazards partial likelihood formulation used for the local survival estimators.","marker":"21,22"},{"why":"Defines the Aalen-Johansen estimator for cumulative incidence under competing risks, the paper's second survival setting.","marker":"23"},{"why":"Provides the inverse-variance weighting scheme for cumulative incidence aggregation that serves as a comparator.","marker":"26"},{"why":"Gives the asymptotic bias and variance theory for federated ATE estimation that the paper's theoretical framework builds on and extends to survival outcomes.","marker":"28"}],"fun_headline_variants":["FedProx survival matches pooled-data accuracy","Proximal federated survival hits pooled precision","Federated Cox with FedProx beats meta-analysis","Survival federated learning: proximal wins over pooling","FedProx survival bias-variance matches centralized data"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that minimizers of the FedProx proximal objective converge to the true shared coefficient vector and global cumulative incidence functions even when each site has its own baseline hazard and covariate distribution; the paper asserts this in Theorems 1 and 2 without proof, and if local estimators are inconsistent under such heterogeneity, adding a norm penalty cannot repair them.","fun_headline_variants_meta":{"raw":{"variants":["FedProx survival matches pooled-data accuracy","Proximal federated survival hits pooled precision","Federated Cox with FedProx beats meta-analysis","Survival federated learning: proximal wins over pooling","FedProx survival bias-variance matches centralized data"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000138,"raw_usage":{"total_tokens":1145,"prompt_tokens":926,"completion_tokens":219,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":542,"completion_tokens_details":{"reasoning_tokens":145}},"tokens_in":542,"tokens_out":219,"duration_ms":3426,"temperature":1.0,"reasoning_tokens":145,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T00:57:25.151751+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Simulate two sites with different baseline hazard functions and covariate distributions but a common true hazard ratio; run the paper's Algorithm 1 with a Cox local loss and compare the FedProx coefficient to the pooled maximum partial likelihood estimate as the sample size $n$ grows. If FedProx bias does not shrink to zero while pooled bias does, or if its variance remains above the pooled variance, the claimed equality in Eqs. (40)-(41) fails. A complementary check would compare FedProx Aalen-Johansen cumulative incidence curves with the pooled Aalen-Johansen curve under site-specific competing risks.","supporting_citations":[],"review_version":1}