{"id":"a38c166a-f1c8-4074-8fd7-7477a52b1cd2","arxiv_id":"1908.02337","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"A deep neural network trained by regression on jackknife pseudo conditional survival probabilities matches or beats existing deep survival models, especially when proportional hazards is violated.","lead":"DNNSurv is a two-step survival model that replaces censored survival times with jackknife pseudo conditional survival probabilities, then trains a standard deep neural network to predict them. It offers a simpler way to apply deep learning to medical survival data without custom loss functions or proportional-hazards assumptions.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Pseudo-values may be computed on the full dataset before train/test splitting, leaking test survival times into training responses and potentially inflating the reported superiority.","rationale":"The reader's weakest assumption is the unproven conditional-independence claim used to justify the simple squared-error loss. While that is a real gap in the theoretical transfer, it is unlikely to be fatal in practice: for a flexible neural network, squared-error regression can still recover conditional means even with correlated pseudo-value errors, and the paper makes no inferential claims requiring independence. The more load-bearing concern is the train/test integrity of the empirical evaluation. The method section describes computing pseudo-values on the full sample before any mention of train/test splitting, and the later split descriptions do not say the pseudo-values are recomputed within each split. If they are not, the training responses incorporate test subjects' survival times through the leave-one-out KM estimators, directly contaminating the reported c-index comparisons. This would invalidate the paper's headline empirical claim that DNNSurv is superior when PH is violated. Because the manuscript is ambiguous rather than explicit, the concern merits a check of the code rather than an immediate rejection; if confirmed, the evaluation must be redone. The reader's conditional verdict already allows for such a check, so the recommended verdict remains CONDITIONAL, hence unchanged.","tokens_in":10402,"tokens_out":8214,"duration_ms":102203,"concrete_test":"Inspect the getPseudoConditional and data-splitting code in the GitHub repository, and re-run the SRTR comparison recomputing pseudo conditional survival probabilities from the training split only (refitting interval boundaries and the Kaplan-Meier estimator on training data). Compare DNNSurv vs CPH c-index (mean over 10 splits) under this split-specific computation against the values in Table 3. If the gap shrinks or reverses, the reported superiority is an artifact; if the gap persists, the concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 2.1–2.2 defines pseudo conditional survival probabilities via jackknife Kaplan-Meier estimators over 'all n subjects' (Eqs. 1–2). The simulation and real-data sections then split the same subjects into 75% training and 25% test sets, but nowhere state that pseudo-values are recomputed from the training set alone before fitting DNNSurv. If the implementation follows the text literally, each training-row response is a function of the full sample, including test subjects' survival times. Because the pseudo-value is a smoothed jackknife estimator, test outcomes would enter training responses indirectly through the KM estimates; the model could then appear better calibrated on test data than a genuinely independent fit. This directly affects the central claim of 'superior performance... when the PH assumption is violated' (SRTR, Table 3). The problem is checkable from the public repository, but the manuscript's omission prevents the reader from verifying whether the evaluation is leak-free.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes DNNSurv, a two-step deep learning method for survival analysis. In the first step, each subject's observed survival time (censored or not) is transformed into a series of jackknife pseudo conditional survival probabilities at a set of discrete time intervals, computed from Kaplan-Meier or IPCW Kaplan-Meier estimates. In the second step, these pseudo probabilities are used as quantitative responses in a standard feedforward neural network with squared-error loss, with time-interval indicators and covariates as inputs; marginal survival probabilities are obtained by multiplying predicted conditional probabilities. The method is compared with Cox-nnet, DeepSurv, nnet-survival, and a standard Cox model in simulations under an AFT model with 20-60% censoring, in a simulation with covariate-dependent censoring, and on three real datasets (CHS, MESA, SRTR). The central claim is that the pseudo-value construction reduces survival analysis to standard regression, avoiding special censoring-aware loss functions, and that DNNSurv performs competitively or better than existing deep survival models, especially when proportional hazards is violated.","tokens_in":10588,"tokens_out":3351,"duration_ms":33758,"significance":"If the central claim holds, the paper offers a practically attractive simplification: deep survival modeling with a conventional loss function, direct output of survival probabilities, no PH assumption, and a theoretically motivated treatment of censoring via pseudo-observations. The manuscript includes an IPCW extension for covariate-dependent censoring, simulation studies with a flexible data-generating process, and publicly available source code, which are concrete strengths. However, the theoretical transfer from pseudo-value GEE theory to flexible deep regression is not established, and the evaluation protocol has a potential leakage problem that directly affects the reported superiority. The real-data comparisons lack uncertainty quantification and omit Brier scores. These issues are fixable but currently leave the central claim only partially supported.","major_comments":[{"comment":"The manuscript does not specify whether pseudo conditional probabilities are recomputed within each training split before fitting DNNSurv. Equations (1)-(2) define pseudo-values using KM estimates over 'all n subjects' or 'all patients still at-risk'; the simulation (Section 3.3) and real-data sections (Section 4) then split subjects into 75% training and 25% test sets. If pseudo-values are computed once on the full sample, test subjects' survival and censoring times enter the KM estimates used to construct training responses, so test outcomes leak into the training targets through the jackknife estimator. This would inflate the reported test performance, particularly the SRTR c-index advantage in Table 3. The authors must clarify the exact protocol, and if pseudo-values are not recomputed from the training set alone, the evaluation should be redone with a leak-free protocol.","section":"Sections 2.2, 3.3, and 4"},{"comment":"The assertion that 'our pseudo probabilities are conditionally independent and we do not need to consider the within-subject correlation' is not proven and is doubtful: pseudo conditional probabilities for successive intervals of the same subject are computed from overlapping risk sets and from KM estimators that share subjects, so the jackknife pseudo-values are generally correlated across intervals. This claim is load-bearing because it justifies using a plain squared-error loss instead of a GEE-type or otherwise correlation-aware loss. The authors should either provide a rigorous asymptotic argument, replace the claim with a more defensible justification, or report an empirical check (e.g., comparing squared-error loss with a loss that accounts for within-subject correlation).","section":"Section 2.2, paragraph 4"},{"comment":"The real-data results report only averaged c-index values over 10 random splits, without standard errors, confidence intervals, or paired tests, while the text states that DNNSurv and nnet-survival had 'significantly better' performance than the PH-based models in SRTR. No significance test is described or referenced. Additionally, the statement that 'All models had the same Brier scores, so those results are not presented here' is implausible as written: Brier scores are continuous, model-specific quantities, and exact equality across all five models would require explanation. The authors should report Brier scores (as in the simulation sections) with measures of variability, or justify their omission, and support any significance claims with appropriate tests.","section":"Section 4, Table 3"},{"comment":"The theoretical support cited for pseudo-observations (Andersen et al. 2003; Klein and Andersen 2005) concerns regression coefficients in GEE models fitted to pseudo-values, typically with a correctly specified link and estimating equations. The paper instead uses pseudo-values as targets in a flexible deep neural network trained with squared-error loss, and does not establish that consistency or calibration of the pseudo-value approach carries over to the DNN estimator, especially given that pseudo-values can fall outside [0,1] (acknowledged in Section 2.2) while the final sigmoid layer constrains predictions to [0,1]. This gap weakens the claim that the method is 'theoretically justified' relative to ad-hoc censoring handling; the authors should explicitly delineate which properties are proven, which are assumed, and which are supported only by the simulations.","section":"Sections 2.1-2.3 and 5"}],"minor_comments":[{"comment":"The example in Table 1 shows a pseudo probability of -0.014, outside [0,1], while the network's final sigmoid layer restricts predictions to [0,1]; the manuscript would benefit from a brief discussion of this target-prediction mismatch and its implications for training.","section":"Section 2.2, Table 1"},{"comment":"There is a typo: 'DDNSurv' and 'DDNSurv_ipcw' should be 'DNNSurv' and 'DNNSurv_ipcw' in the list of applied neural network models.","section":"Section 3.4, last paragraph"},{"comment":"The name 'nnet-survvial' is misspelled; it should be 'nnet-survival'.","section":"Section 2.6"},{"comment":"The text lists 'four time points: 1 day, 1 month, 6 months, 8 months and 1 year,' which is five time points; please correct the count or the list.","section":"Section 4, SRTR paragraph"},{"comment":"The c-index description cites Harrell et al. (1996); for right-censored data with time-dependent predictions, a reference to Uno's c-index or an explicit statement of how censored observations are handled in the c-index computation would improve reproducibility.","section":"Section 3.1"},{"comment":"The term 'conditionally independent' is used without a formal definition or citation; since this is central to the loss-function justification, a precise definition or reference to a regularity condition is needed.","section":"Section 2.2"}],"recommendation":"major_revision","confidential_remarks":"The core idea is simple and potentially useful, and the code availability is a plus. However, the potential data leakage in the evaluation protocol is the most serious issue: if pseudo-values are computed on the full dataset before splitting, the reported test-set superiority in Table 3 could be an artifact. The authors need to clarify and correct this. The conditional-independence claim also needs a rigorous treatment or an explicit downgrade. I would recommend the editor seek a revised version that addresses these points before a decision on acceptance."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's the short version: this is a genuinely useful method paper. The idea is to take jackknife pseudo conditional survival probabilities and feed them to a standard DNN as numeric responses, trained with plain squared error. That combination is new as far as I know, and it works in their simulations. The paper is worth a serious look, but there's a possible leakage problem in how the pseudo-values are computed relative to the train/test split, and they make one statistical claim that doesn't hold up.\n\nWhat's actually new: prior pseudo-value work used GEE or GLM, and prior deep survival models used custom loss functions. DNNSurv reduces survival analysis to ordinary regression, which is a real practical simplification. The simulation study under an AFT model with nonlinear effects is decent, and the IPCW extension for covariate-dependent censoring is a sensible addition. The code is on GitHub, which makes the method reproducible.\n\nSoft spots, in order of importance. First, the leakage concern. Equations (1)-(2) define pseudo conditional probabilities using all n subjects. The simulations and real data then split 75/25, but the text never says the pseudo-values are recomputed from the training set alone. If they're computed once on the full data, test survival times enter the training responses through the jackknife KM estimates. That would directly inflate the reported superiority in the SRTR analysis, where they claim DNNSurv beats PH models under non-PH. I'm not saying this is what the code does—the code is public and checkable—but the manuscript needs to state it explicitly. This is the first thing a referee should verify.\n\nSecond, Section 2.2 says the pseudo conditional probabilities are conditionally independent, so the within-subject correlation can be ignored. That's not proven and seems unlikely, since they're all functions of overlapping KM estimates. The practical impact may be small—the method still predicts well in simulations—but calling them independent is an overstatement.\n\nThird, the real-data comparisons show only averaged c-index values, with no standard errors or tests. The claim that DNNSurv is 'significantly better' in SRTR is not supported by any uncertainty measure. Brier scores are mentioned but not shown. This is fixable but should be in the paper.\n\nBottom line: this is a solid, useful paper with a real methodological contribution and a public implementation. The central idea is sound; the gaps are in the evaluation and the statistical justification, not in the concept. It deserves peer review. A careful referee should run the code to check the pseudo-value splitting, and the authors should add error bars and tone down the conditional independence claim. I'd bring it to a reading group and would cite it if I worked in survival prediction.","headline":"A useful and simple deep survival method built on pseudo-observations, worth serious review—but the train/test handling of pseudo-values needs checking before the reported gains are trusted.","tokens_in":11044,"tokens_out":2792,"would_cite":true,"duration_ms":29288,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["62N01","68T07"],"pacs":[],"model":"deepseek-v4-flash","headline":"DNNSurv turns censored survival analysis into an ordinary regression problem using jackknife pseudo probabilities.","keywords":["survival analysis","deep neural network","pseudo-observations","jackknife","right censoring","inverse probability of censoring weighting","risk prediction","discrete-time survival"],"falsifier":"Compute, under independent censoring, the empirical correlation between a subject's pseudo conditional probabilities in adjacent intervals across many simulated datasets; if the correlations are substantially nonzero, the conditional-independence claim that justifies the simple loss fails. Alternatively, compare DNNSurv's predicted conditional probabilities against a correctly specified discrete-time survival model on data with strong within-subject dependence, and check whether calibration or coverage degrades.","tokens_in":10207,"feed_emoji":"📈","tokens_out":4617,"duration_ms":43570,"temperature":0.7,"pith_summary":"The paper proposes a two-step recipe that turns censored survival analysis into an ordinary regression problem. Each subject's survival time is converted into a series of jackknife pseudo conditional survival probabilities, one per follow-up interval, and these pseudo probabilities become the numeric response in a deep neural network trained with plain squared-error loss. The claim is that this removes the need for special censoring-aware cost functions and for the proportional-hazards assumption, while still producing direct survival-probability predictions. A sympathetic reading takes the core assertion to be that pseudo conditional probabilities are valid regression targets for a flexible network, with simulations and three real datasets offered as evidence that accuracy matches or beats existing deep survival models, especially when proportional hazards fails.","feed_headline":"Pseudo probabilities turn survival analysis into plain regression","feed_subtitle":"DNNSurv skips special loss functions and stays accurate when proportional hazards fails.","key_machinery":"The central object is the jackknife pseudo conditional survival probability, $\\hat{S}_{ij}(t_{j+1} \\mid R_j) = R_j \\hat{S}(t_{j+1} \\mid R_j) - (R_j - 1)\\hat{S}_{-i}(t_{j+1} \\mid R_j)$, where $\\hat{S}$ is the Kaplan-Meier estimator on the at-risk set $R_j$ and $\\hat{S}_{-i}$ is the same estimator with subject $i$ removed. This quantity is used as a quantitative response for each interval, so a conventional fully connected network with sigmoid output and squared-error loss can be trained without a bespoke likelihood. The discrete-time framework lets the network predict conditional survival probabilities directly, and multiplying them yields marginal survival probabilities; an IPCW version of the pseudo values is introduced for covariate-dependent censoring.","core_discovery":"By using pseudo conditional survival probabilities computed from leave-one-out Kaplan-Meier estimates within discrete time intervals, the paper reduces a complex survival analysis to a standard regression problem. Each subject contributes one pseudo conditional probability per interval in which they remain at risk; the network maps covariates plus interval indicators to the conditional survival probability, and marginal survival probabilities are recovered by multiplying conditional probabilities across intervals. DNNSurv therefore avoids the PH assumption and outputs survival probabilities directly, and the paper reports that it outperforms PH-based neural network models when the PH assumption is violated while staying competitive when it holds. For covariate-dependent censoring, replacing the KM estimator with an inverse-probability-of-censoring weighted estimator is proposed to remove bias.","pith_inferences":["Editorial inference: if the pseudo conditional probabilities are not actually independent across intervals, the squared-error loss is a heuristic rather than a fully justified likelihood, though the empirical results may still stand.","Editorial inference: the same pseudo-value transformation could be plugged into any flexible regression learner, not only deep networks, potentially extending the approach to gradient-boosted trees or Gaussian processes.","Editorial inference: because pseudo values can fall outside [0,1], squeezing them through a sigmoid output may warp the target; a direct comparison with identity output or bounded loss could clarify whether this matters.","Editorial inference: a natural testable extension is to apply DNNSurv to competing-risk settings, where pseudo values of cumulative incidence functions already have established theory."],"forward_implications":["Any standard deep regression network can be applied to survival data without designing a custom loss for censoring.","The method produces conditional and marginal survival probabilities directly, instead of hazard ratios or prognostic indices.","Predictions remain competitive with or better than PH-based deep models when the proportional-hazards assumption is violated.","The number and placement of follow-up intervals is a tunable modeling choice, with results reported to be fairly robust to coarser interval grids.","When censoring depends on covariates, IPCW pseudo values reduce bias relative to ordinary pseudo values."],"supporting_citations":[{"why":"Supplies the pseudo-observation regression framework that the method adapts to conditional probabilities.","marker":"[10]"},{"why":"Establishes computing a vector of pseudo survival probabilities at multiple time points and modeling them with GEE.","marker":"[12]"},{"why":"Reviews pseudo-observation properties, including the fact that pseudo values can fall outside [0,1].","marker":"[13]"},{"why":"Provides the IPCW pseudo-observation approach for covariate-dependent censoring that underlies DNNSurv_ipcw.","marker":"[18]"},{"why":"Defines the nnet-survival discrete-time comparator whose ad-hoc censoring handling DNNSurv aims to improve.","marker":"[5]"},{"why":"Supplies the DeepSurv PH-based deep neural network model used as a baseline.","marker":"[2]"},{"why":"Supplies the Cox-nnet PH-based deep neural network model used as a baseline.","marker":"[3]"},{"why":"Defines the time-dependent concordance index used to evaluate prediction performance.","marker":"[21]"},{"why":"Defines the Brier score used to evaluate the accuracy of predicted survival probabilities.","marker":"[22]"}],"fun_headline_variants":["Pseudo values turn survival analysis into plain regression","Survival via pseudo probabilities, no PH assumption needed","DNNSurv: survival as regression using pseudo values","Avoid special loss functions with pseudo probabilities"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the pseudo conditional survival probabilities for different intervals behave as conditionally independent responses, so that training a network with plain squared-error loss is statistically justified; the paper asserts this but does not prove it, and the overlapping Kaplan-Meier estimates make the independence questionable.","fun_headline_variants_meta":{"raw":{"variants":["Pseudo values turn survival analysis into plain regression","Survival via pseudo probabilities, no PH assumption needed","DNNSurv: survival as regression using pseudo values","Avoid special loss functions with pseudo probabilities"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000234,"raw_usage":{"total_tokens":1429,"prompt_tokens":811,"completion_tokens":618,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":427,"completion_tokens_details":{"reasoning_tokens":558}},"tokens_in":427,"tokens_out":618,"duration_ms":6806,"temperature":1.0,"reasoning_tokens":558,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T14:46:56.912588+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute, under independent censoring, the empirical correlation between a subject's pseudo conditional probabilities in adjacent intervals across many simulated datasets; if the correlations are substantially nonzero, the conditional-independence claim that justifies the simple loss fails. Alternatively, compare DNNSurv's predicted conditional probabilities against a correctly specified discrete-time survival model on data with strong within-subject dependence, and check whether calibration or coverage degrades.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the pseudo-observation regression framework that the method adapts to conditional probabilities."},{"cited_title":"K Andersen and J","cited_arxiv_id":null,"evidence_quote":"Establishes computing a vector of pseudo survival probabilities at multiple time points and modeling them with GEE."},{"cited_title":"K Andersen and M","cited_arxiv_id":null,"evidence_quote":"Reviews pseudo-observation properties, including the fact that pseudo values can fall outside [0,1]."},{"cited_title":"Gerds, and Per Kragh Andersen","cited_arxiv_id":null,"evidence_quote":"Provides the IPCW pseudo-observation approach for covariate-dependent censoring that underlies DNNSurv_ipcw."},{"cited_title":"Gensheimer and Balasubramanian Narasimhan","cited_arxiv_id":null,"evidence_quote":"Defines the nnet-survival discrete-time comparator whose ad-hoc censoring handling DNNSurv aims to improve."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the DeepSurv PH-based deep neural network model used as a baseline."},{"cited_title":"Ching, X","cited_arxiv_id":null,"evidence_quote":"Supplies the Cox-nnet PH-based deep neural network model used as a baseline."},{"cited_title":"Harrell, Kerry L","cited_arxiv_id":null,"evidence_quote":"Defines the time-dependent concordance index used to evaluate prediction performance."},{"cited_title":"K Andersen and M","cited_arxiv_id":null,"evidence_quote":"Defines the Brier score used to evaluate the accuracy of predicted survival probabilities."}],"review_version":1}