{"id":"e63e1167-1c15-4a0c-b128-45384fbad4ff","arxiv_id":"2506.06411","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"CoxNTF builds a survival-probability-weighted tensor of covariates, factorizes it with non-negative tensor factorization, and uses the resulting meta-scores in a Cox model to get interpretable clusters with prediction accuracy comparable to Coxnet.","lead":"Researchers built a survival-analysis method, CoxNTF, that turns patient covariates into a three-dimensional tensor weighted by Cox-model event probabilities, then factorizes it into interpretable patient clusters while keeping prediction accuracy close to the original Cox model. The value is interpretability: doctors can see shared covariate patterns associated with early or late events without losing much predictive power.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The reported c-index comparison may be invalid because Algorithm 2's Coxnet weights and Algorithm 1's NTF bases are fit on the full X,c,t, so test-set meta-scores are not shown to be outcome-free.","rationale":"The reader's weakest assumption already identifies the Coxnet probability model as the fragile point, and I agree that this is the main threat to the central claim. My read extends the same concern to Algorithm 1, where the NTF bases H and Q are trained on a tensor defined by observed survival times and censoring indicators for all observations; if those bases are not refit on training folds only, test patients' meta-scores are not outcome-free. The concern is concrete and testable: the paper does not state that Algorithms 1 and 2 are run separately on training folds, and no code link or commit hash is provided to resolve the ambiguity. I do not move the verdict because the issue is an addressable protocol omission and because the paper's clustering/interpretability contribution does not depend on the prediction comparison. A conditional revision requiring a clean split evaluation and a statement of the refitting protocol is the right outcome; if the re-run shows the c-index advantage disappears, the prediction claim would need to be weakened.","tokens_in":8500,"tokens_out":6853,"duration_ms":67680,"concrete_test":"Rerun the full pipeline with a strict nested protocol: for each of the 30 random splits, execute Algorithms 1 and 2 on the training partition only, compute test-set Coxnet probabilities with the training-fold Coxnet model, map test covariates using the training-fold H and Q, and evaluate the Uno c-index on the test partition. If the averaged CoxNTF c-index in Table 1 drops by more than roughly 0.01 or falls below the Coxnet c-index, the comparable-prediction claim depends on full-data weighting rather than on the method.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim, that CoxNTF's meta-scores achieve survival prediction comparable to Coxnet, requires that the meta-scores for held-out patients be computed without using their survival outcomes. As written, Algorithm 2 line 1 trains a Coxnet model on X,c,t with no statement that this model is refit on each training fold; the probabilities P(X(i,:),k) used in the weighted tensor are therefore potentially informed by the survival times and events of the very patients later placed in the test set. Algorithm 1 has the same structure: the NTF tensor is built from observed event times and censoring indicators for all observations, so the H and Q bases used to project any patient are not shown to be outcome-free. If the Table 1 c-indexes were computed after this full-data weighting and projection, they do not establish out-of-sample comparability. This is an ambiguity rather than a demonstrated error, but it is load-bearing because the paper's quantitative headline rests on it; the limitations paragraph does not address the evaluation protocol.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript proposes CoxNTF, a two-stage semi-supervised method for joint clustering and survival prediction. In the first stage, baseline covariates are placed into a three-way tensor whose time slices correspond to pre-specified survival periods; observed event times and censoring indicators determine which slice each row enters, and inverse probability of censoring weights are applied. Non-negative tensor factorization (NTF) yields covariate patterns H and temporal patterns Q. In the second stage, a Coxnet model trained on the full data supplies period-specific event probabilities used to re-weight the covariate tensor, which is then projected onto the fixed NTF bases to produce meta-scores W; a final Coxnet model is trained on W. The paper evaluates CoxNTF against Coxnet on original covariates and CoxNMF on nine datasets, reporting averaged c-indexes and numbers of retained features over 30 random partitions, and illustrates interpretable patterns on a churn dataset.","tokens_in":8651,"tokens_out":5797,"duration_ms":61015,"significance":"If the evaluation protocol is made outcome-free, CoxNTF would offer a modest but useful semi-supervised dimension-reduction tool: it preserves roughly Coxnet-level discrimination while providing interpretable, non-negative latent patterns, and it avoids CoxNMF's need for new-patient survival data at projection time. The authors are commendably explicit that CoxNTF is not meant to improve predictive accuracy, and they promise public code and data. However, the central quantitative claim of comparable out-of-sample prediction is not currently established because the algorithms as written use full-data survival information to build the features, and Table 1 contains no uncertainty measures. The contribution is likely salvageable with a properly nested evaluation.","major_comments":[{"comment":"Algorithm 2, line 1 trains the Coxnet probability model on the full X, c, t, and Algorithm 1 builds the tensor whose NTF bases H and Q are returned using the full c and t. The Results section states only that each dataset was randomly partitioned into training, validation, and test sets and that criteria were averaged over 30 repetitions; it does not state that Algorithms 1 and 2 are refit on each training fold before validation/test meta-scores are computed. As written, therefore, the meta-scores W of a held-out patient are computed from H, Q, and Coxnet probabilities that have been informed by that patient's survival outcome, which would make the Table 1 c-indexes optimistically biased and would not establish out-of-sample comparability. Please specify a nested protocol in which Algorithm 1 and the Coxnet probability model are fit only on training folds, H, Q, and the probability model are frozen, and validation/test W are computed from covariates alone; then report the results under that protocol.","section":"CoxNTF Model Training (algorithm 2) and Results"},{"comment":"Table 1 reports averaged c-indexes over 30 partitions without standard deviations, confidence intervals, or paired comparisons. For example, on veterans lung cancer the NTF and COX c-indexes are 0.71 and 0.70; without an uncertainty measure this difference cannot be distinguished from sampling noise, and the claim that CoxNTF is 'always superior to CoxNMF' cannot be verified. Please report the distribution of c-indexes across the 30 repeats (e.g., mean with SD, or median with IQR) and provide paired tests for the NTF-versus-COX and NTF-versus-NMF comparisons.","section":"Results, Table 1"},{"comment":"The paper does not include an ablation separating the contributions of survival weighting, tensor structure, and rank selection. Algorithm 2 weights the tensor by Coxnet probabilities before projecting onto H and Q, and the NTF rank r is chosen by validation c-index; hence the reported 'average number of features retained' is partly determined by the selected rank, and the improvement over NMF could be due to the survival weighting or to the tensor structure rather than to the full CoxNTF combination. Please add ablations such as (i) NTF on an unweighted tensor, (ii) NTF on a tensor weighted by uniform probabilities, and (iii) matching the NMF rank to the NTF rank; and report the distribution of selected ranks. This would directly support the central claim that survival-informed tensor factorization, rather than the final Coxnet step alone, drives the result.","section":"Methods, NTF Rank determination and Algorithm 2"}],"minor_comments":[{"comment":"The square-root IPCW expression is rendered with a broken equation ('× p ipcwi' and 'Taking the square root of $ipcw i$'); please fix the typesetting.","section":"Algorithm 1, line 13"},{"comment":"The section contains an empty cross-reference ('section .'); please fill it in.","section":"CoxNTF Model Training (algorithm 2)"},{"comment":"The phrases 'which observed in nearly half of the patients' appear twice with the verb 'was' missing; please correct these grammatical errors.","section":"Materials"},{"comment":"The table rows labeled 'NTF', 'NMF', and 'COX' should state explicitly that these are Coxnet models applied respectively to NTF meta-scores, NMF scores, and original features; the dataset size information (n, p) would be clearer in a separate column.","section":"Results, Table 1"},{"comment":"The limitation paragraph acknowledges sensitivity to the number and percentile levels of time periods but not to the NTF rank; please add rank sensitivity analyses or state the range of ranks over which the conclusions are stable.","section":"Discussion, Limitations"}],"recommendation":"major_revision","confidential_remarks":"To the editor: the evaluation-protocol ambiguity in Algorithms 1 and 2 is the key obstacle. I do not see evidence of intent to deceive, but the manuscript as written does not demonstrate that the reported c-indexes are out-of-sample, because the feature construction appears to use the full survival data. The authors should be asked to rerun the experiments with a properly nested cross-validation in which H, Q, and the Coxnet probability model are fit only on training folds. If the comparability result survives that protocol, the contribution is a modest but useful semi-supervised dimension-reduction and clustering tool, possibly better suited to an applied statistics or bioinformatics venue than to a general machine-learning venue. The paper's own limitations section is commendably honest, and the promised code and data availability are strengths."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: CoxNTF is a real methodological novelty. Constructing a third-order tensor whose slices are covariates weighted by Coxnet event-period probabilities, then projecting new data onto fixed NTF factors before fitting Coxnet, is not in the cited literature. The paper is also refreshingly honest about scope: it claims comparable prediction, not better, and positions itself as an interpretability and clustering tool. Credit where due: the NTF pattern illustration on ds2 is clear, and the discussion of collinearity handling is sensible.\n\nThe soft spot is the evaluation protocol. Algorithm 1 and Algorithm 2 are written on the full X, c, t. Algorithm 2 trains Coxnet on all patients, then uses those probabilities to weight the tensor; Algorithm 1 builds the tensor from observed event times and censoring indicators for everyone. If test patients are included in either step, the W meta-scores for held-out patients are outcome-informed, and the comparable c-indexes in Table 1 would not establish out-of-sample performance. The paper never states that H and Q are estimated on training folds only, or that Coxnet probabilities are refit per fold. This is an ambiguity rather than a demonstrated error — the actual implementation may be clean — but it is load-bearing because the headline result rests on it.\n\nSecondary issues: Table 1 reports means over 30 splits with no standard errors or CIs; there is no ablation separating the survival weighting from plain tensor factorization; and sensitivity to NTF rank and time-window percentiles is left unexplored (the limitations paragraph admits this). Code is said to be available but the paper gives no direct URL or commit hash, so I could not verify the protocol.\n\nThe math of the factorization itself is standard NTF; the novelty is in the weighting and projection scheme, and that is coherent. The citation pattern looks fair, with the key comparisons (CoxNMF, Li et al.) discussed accurately. The paper does not oversell; the limitations paragraph is honest.\n\nWho should read it: anyone working on latent representations for survival data or on making Cox-type models more interpretable. It deserves a serious referee, but the authors need to clarify the cross-validation nesting and ideally release code before I would trust the numbers. If the clean protocol exists, this is a useful contribution.","headline":"A genuinely new survival-weighted tensor factorization with an underspecified evaluation protocol that may leak test-set survival information into the meta-scores.","tokens_in":9265,"tokens_out":2554,"would_cite":false,"duration_ms":25541,"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":"CoxNTF compresses baseline covariates into interpretable survival-linked factors without losing Coxnet's predictive accuracy.","keywords":["survival analysis","non-negative tensor factorization","Coxnet","latent representation","clustering","censoring","concordance index","feature redundancy"],"falsifier":"Re-run the evaluation with a strict protocol that fits the weighting Coxnet on training folds only and generates the tensor weights for test patients from that fitted model; if the c-index gap between CoxNTF and Coxnet widens substantially relative to the reported values, the comparable-accuracy claim fails.","tokens_in":8265,"feed_emoji":"⏳","tokens_out":7374,"duration_ms":64599,"temperature":0.7,"pith_summary":"Survival models usually need original covariates, and unsupervised latent representations like NMF lose survival information. CoxNTF instead builds a three-dimensional tensor whose third axis is time periods, weights each covariate entry by the Coxnet-estimated probability that the event occurs in that period, and factorizes the tensor non-negatively into patient meta-scores, covariate patterns, and temporal patterns. The paper claims that feeding these meta-scores to Coxnet gives survival predictions as accurate as using the original covariates on all nine studied datasets, while producing a smaller number of interpretable survival-associated clusters. The method is offered as a semi-supervised representation and clustering tool rather than as a way to improve prediction accuracy. If the claim holds, practitioners could compress large collinear covariate sets into a handful of interpretable factors without paying a predictive price.","feed_headline":"CoxNTF matches Coxnet accuracy with interpretable factors","feed_subtitle":"Semi-supervised tensor factorization clusters patients into survival-linked patterns without sacrificing predictive power.","key_machinery":"The central machinery is the weighted covariate tensor X(i,:,k) = P(X(i,:), k)^(1/2) X(i,:), where the third dimension indexes time periods (s(k-1), s(k)] and P is the Coxnet-estimated probability that the event occurs in period k. Non-negative tensor factorization then approximates this tensor by a sum of r outer products w_k ◦ h_k ◦ q_k, yielding patient meta-scores W, covariate patterns H, and temporal survival patterns Q; the meta-scores W are the final covariates for a Coxnet model. The first stage builds an unweighted tensor with indicator weights and inverse-probability-of-censoring weights to learn H and Q, and the second stage fixes H and Q to project the Coxnet-weighted tensor onto W. The survival probabilities are what make the factorization survival-aware, in contrast to plain NMF. The factorization algorithm used is Fast-HALS (fast hierarchical alternating least squares).","core_discovery":"On its own terms, the paper's central discovery is that a non-negative factorization of a survival-weighted covariate tensor produces latent meta-scores that preserve Coxnet's discriminative performance: across the nine datasets, the CoxNTF IPCW c-index is consistently close to that of Coxnet on original covariates (e.g., 0.77 vs 0.78 on flchain) and generally above CoxNMF (e.g., 0.77 vs 0.68 on flchain). The key result is that the NTF latent space carries essentially the same survival information as the original covariates, so the meta-scores can substitute for them. The paper also reports that Coxnet retains far fewer features when given NTF meta-scores than when given NMF factors (up to 45% fewer), and that the learned covariate patterns are interpretable and consistent with the hazard-ratio forest plot. The paper is explicit that CoxNTF is not meant to improve survival prediction accuracy; its purpose is joint interpretable clustering and prediction at no loss of accuracy.","pith_inferences":["The comparison with plain NMF suggests that it is the survival weighting, not the tensor structure alone, that preserves accuracy; without the Coxnet event probabilities, the factorization would reduce to an unsupervised decomposition that the paper shows performs worse.","The paper does not spell out that the Coxnet weighting model must be refit on training folds only to generate weights for test patients; a reader should check that the reported c-indexes came from such a clean protocol, because any leakage of test survival information into the weights would inflate the apparent match with Coxnet.","The sensitivity of the results to the chosen time-window percentiles and NTF rank is acknowledged in the paper but not quantified, so a natural test is whether the comparable-accuracy finding is stable across alternative choices of these hyperparameters.","Because the meta-scores are generic non-negative features, they could in principle be fed to any survival model, not just Coxnet, although the paper only demonstrates Coxnet."],"forward_implications":["Coxnet trained on NTF meta-scores achieves a c-index comparable to Coxnet on original covariates across all nine datasets, so the latent representation can replace the original covariates without losing discriminative power.","The NTF meta-scores yield interpretable patient clusters and covariate patterns linked to early versus late events, as illustrated on the telecom churn dataset where month-to-month contracts are associated with early departure.","Coxnet retains substantially fewer features when given NTF meta-scores than NMF factors (up to 45% fewer), so the method compresses the covariate set.","CoxNTF handles redundant and collinear features without arbitrarily eliminating dummy-coded categories, avoiding the arbitrary zeroing seen in elastic-net forest plots.","The approach extends to time-varying covariates by modifying the weighting and tensor construction, though that extension is not tested in the paper."],"supporting_citations":[{"why":"Supplies the non-negative matrix factorization latent-representation approach that CoxNTF extends to tensor data.","marker":"Lee and Seung 1999"},{"why":"Supplies the non-negative tensor factorization decomposition and the Fast-HALS algorithm used to factorize the weighted covariate tensor.","marker":"Cichocki and Phan 2009"},{"why":"Coxnet is the survival model used both to estimate event probabilities for tensor weighting and to train the final predictor on the meta-scores.","marker":"Simon et al. 2011"},{"why":"Proposes CoxNMF, the survival-aware NMF baseline that CoxNTF is compared against and whose limitation (requiring survival data to map new patients) motivates the design.","marker":"Huang et al. 2020"},{"why":"Defines the concordance index (c-index) used to measure survival prediction performance.","marker":"Harrell, Lee, and Mark 1996"},{"why":"Provides the inverse-probability-of-censoring-weighted c-index used to evaluate predictions under right censoring.","marker":"Uno et al. 2011"}],"fun_headline_variants":["CoxNTF: same survival accuracy, interpretable clusters","Tensor factorization matches Coxnet, adds clustering","Survival prediction with interpretable clusters via CoxNTF","CoxNTF: interpretable factors, no accuracy loss","Joint clustering and prediction without sacrificing accuracy"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the Coxnet event probabilities used to weight the tensor are computed without using the survival outcomes of the patients whose predictions are later evaluated; if those probabilities see the test data, the reported match with Coxnet is optimistically biased.","fun_headline_variants_meta":{"raw":{"variants":["CoxNTF: same survival accuracy, interpretable clusters","Tensor factorization matches Coxnet, adds clustering","Survival prediction with interpretable clusters via CoxNTF","CoxNTF: interpretable factors, no accuracy loss","Joint clustering and prediction without sacrificing accuracy"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000595,"raw_usage":{"total_tokens":2755,"prompt_tokens":886,"completion_tokens":1869,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":502,"completion_tokens_details":{"reasoning_tokens":1793}},"tokens_in":502,"tokens_out":1869,"duration_ms":12406,"temperature":1.0,"reasoning_tokens":1793,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T05:58:25.743534+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Re-run the evaluation with a strict protocol that fits the weighting Coxnet on training folds only and generates the tensor weights for test patients from that fitted model; if the c-index gap between CoxNTF and Coxnet widens substantially relative to the reported values, the comparable-accuracy claim fails.","supporting_citations":[{"cited_title":"Low-Rank Reorganization via Proportional Hazards Non-negative Matrix Factorization Unveils Survival Associated Gene Clusters","cited_arxiv_id":"2008.03776","evidence_quote":"Proposes CoxNMF, the survival-aware NMF baseline that CoxNTF is compared against and whose limitation (requiring survival data to map new patients) motivates the design."}],"review_version":1}