DNNSurv: Deep Neural Networks for Survival Analysis Using Pseudo Values

Dai Feng; Lili Zhao

REVIEW 4 major objections 6 minor 1 cited by

DNNSurv: Deep Neural Networks for Survival Analysis Using Pseudo Values

T0 review · 4 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read DNNSurv turns censored survival analysis into an ordinary regression problem using jackknife pseudo probabilities.

desk verdict 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. read the letter →

arxiv 1908.02337 v2 pith:CESAI2OK submitted 2019-08-06 stat.ML cs.LG

Lili Zhao , Dai Feng This is my paper · ORCID

classification stat.MLcs.LG MSC 62N0168T07

keywords survivalanalysisdeepneuralnetworkpseudo-observationsjackkniferightcensoringinverseprobabilityofweightingriskpredictiondiscrete-time

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

What carries the argument

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.

What would settle it

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.

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Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

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.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the 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.

What'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.

Soft 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.

Second, 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.

Third, 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.

Bottom 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.

Referee Report

4 major / 6 minor

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.

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 (4)

[Sections 2.2, 3.3, and 4] 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 2.2, paragraph 4] 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 4, Table 3] 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.
[Sections 2.1-2.3 and 5] 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.

minor comments (6)

[Section 2.2, Table 1] 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 3.4, last paragraph] There is a typo: 'DDNSurv' and 'DDNSurv_ipcw' should be 'DNNSurv' and 'DNNSurv_ipcw' in the list of applied neural network models.
[Section 2.6] The name 'nnet-survvial' is misspelled; it should be 'nnet-survival'.
[Section 4, SRTR paragraph] 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 3.1] 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 2.2] 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.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity in DNNSurv derivation; pseudo-values are external targets, and no prediction reduces to a fitted parameter.

full rationale

DNNSurv's derivation chain is self-contained. Equation (2) defines jackknife pseudo conditional survival probabilities from Kaplan-Meier estimates of the observed censored/uncensored survival times, and Equation (3) replaces the KM estimator with an IPCW estimator when censoring depends on covariates. These pseudo-values are external regression targets: the network is trained to predict them from covariates and time indicators using squared error, and Section 2.4 defines the marginal survival curve as the product of predicted conditional probabilities. No step defines the pseudo-values in terms of the network output, and no parameter fitted to the evaluation metric is presented as a prediction. The IPCW Cox censoring model is a nuisance adjustment only, not a source of the survival prediction. There are no load-bearing self-citations; the pseudo-observation theory is cited to external references [10-13,15]. The skeptic's concern that pseudo-values may have been computed on the full dataset before the 75/25 split is a potential data-leakage issue, not a circularity: even under that implementation, the predicted probabilities are not equal by construction to the training targets; the issue is evaluation independence. Thus the circularity score is 0.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The paper introduces no invented physical or statistical entities. It relies on established pseudo-observation machinery (KM estimator, jackknife) and standard DNN training. The additional assumptions are the transfer of pseudo-value consistency to nonparametric regression and the unproven conditional independence of the constructed pseudo conditional probabilities.

free parameters (4)

Number of time intervals J = 6 in simulations; 15 for CHS, 2 for MESA, 5 for SRTR
Chosen by the analyst, not derived; sensitivity analysis shows robustness to 2 vs 6 intervals, but the choice affects the pseudo-value targets.
Time grid (interval boundaries) = 10th to 60th percentiles in AFT simulations; annual in CHS; 3 and 5 years in MESA; 1 day to 1 year in SRTR
Determines the conditional survival probabilities modeled; choice is subjective or based on clinical relevance.
Network hyperparameters = Selected by random grid search with 5-fold CV on training data
Includes number of layers, nodes, dropout/ridge, activation, and learning rate; results depend on the chosen configuration.
IPCW censoring model (Cox) = In CHS, four variables significantly associated with censoring
IPCW pseudo-values depend on correct specification of this model; it is fitted once and reused.

assumptions (4)

standard math Kaplan-Meier estimator is approximately unbiased under independent censoring
Invoked in Section 2.1 to justify the pseudo-observation approach; standard survival-analysis result.
domain assumption Pseudo-observation regression estimators are approximately consistent for parametric regression models
The paper relies on theory from Andersen et al. (cited [10,12]) and extends it to deep networks without proof.
ad hoc to paper The pseudo conditional probabilities are conditionally independent across time intervals within a subject
Stated in Section 2.2 without proof; underlying KM-based pseudo-values share overlapping data, so the assumption is questionable.
domain assumption Survival and censoring times are independent (or, for IPCW, censoring model is correctly specified)
Stated at the start of Section 2; required for KM/IPCW validity.

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Cite this review

Pith. "Pith review of DNNSurv: Deep Neural Networks for Survival Analysis Using Pseudo Values." pith.science (2026). https://pith.science/paper/CESAI2OK

@misc{pith2026190802337,
  author       = {Pith},
  title        = {Pith review of: DNNSurv: Deep Neural Networks for Survival Analysis Using Pseudo Values},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CESAI2OK}},
  note         = {Machine review of arXiv:1908.02337}
}

read the original abstract

There has been increasing interest in modelling survival data using deep learning methods in medical research. Current approaches have focused on designing special cost functions to handle censored survival data. We propose a very different method with two steps. In the first step, we transform each subject's survival time into a series of jackknife pseudo conditional survival probabilities and then use these pseudo probabilities as a quantitative response variable in the deep neural network model. By using the pseudo values, we reduce a complex survival analysis to a standard regression problem, which greatly simplifies the neural network construction. Our two-step approach is simple, yet very flexible in making risk predictions for survival data, which is very appealing from the practice point of view. The source code is freely available at http://github.com/lilizhaoUM/DNNSurv.

Figures

Figures reproduced from arXiv: 1908.02337 by the authors.

**Figure 2.** Boxplots of c-index (left) and Brier score (right) from DNNSurv, DeepSurv, Cox-nnet, and nnet-survival over [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗

**Figure 3.** Boxplots of c-index (left) and Brier score (right) for the 100 simulated datasets generated from the simple [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Survival Analysis as Imprecise Classification with Trainable Kernels
cs.LG 2025-06 conditional novelty 5.0 of 10

The authors present iSurvM, iSurvQ, and iSurvJ, nonparametric survival models that treat censored event times as imprecise interval labels and learn attention weights with kernel regression.

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

Martinsson

E. Martinsson. WTTE-RNN: Weibull time to event recurrent neural network. Master’s thesis, University of Gothenburg, Sweden, 2016

work page 2016

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J. L. Katzman, U. Shaham, A. Cloninger, J. Bates, T. Jiang, and Y . Kluger. Deepsurv: personalized treatment recommender system using a cox proportional hazards deep neural network. BMC medical research methodology, 18:24, 2018

work page 2018

[3] [3]

Ching, X

T. Ching, X. Zhu, and L. X. Garmire. Cox-nnet: An artiﬁcial neural network method for prognosis prediction of high-throughput omics data. PLoS Comput. Biol., 14:e100607, 2018

work page 2018

[4] [4]

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Jiawen Yao Xinliang Zhu and Junzhou Huang. Deep convolutional neural network for survival analysis with pathological images. IEEE International Conference on Bioinformatics and Biomedicine (BIBM), 2016

work page 2016

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Gensheimer and Balasubramanian Narasimhan

Michael F. Gensheimer and Balasubramanian Narasimhan. A scalable discrete-time survival model for neural networks. PeerJ, 7:e6257, 2019

work page 2019

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Stephane Fotso. Deep neural networks for survival analysis based on a multi-task framework. arXiv, 2018

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