Tabular Foundation Models Can Do Survival Analysis

Da In Kim; Kelly W. Zhang; Wei Siang Lai

REVIEW 3 major objections 4 minor 15 references

Tabular Foundation Models Can Do Survival Analysis

T0 review · 3 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Reformulating survival analysis as binary classification lets tabular foundation models recover true survival probabilities and beat specialized baselines on average.

desk verdict A sound and useful classification wrapper for tabular FMs in survival analysis, but the headline numbers rest on marginal IPCW metrics that are not justified under the paper's own censoring assumption. read the letter →

arxiv 2601.22259 v2 pith:N5NYDYKY submitted 2026-01-29 cs.LG

Da In Kim , Wei Siang Lai , Kelly W. Zhang This is my paper · ORCID

classification cs.LG

keywords survivalanalysistabularfoundationmodelsbinaryclassificationright-censoringin-contextlearningconsistencydiscrete-timedynamic

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

This paper sets out to show that survival analysis — estimating time to an event from right-censored data — can be reduced to a sequence of ordinary binary classification problems, and that this reduction lets off-the-shelf tabular foundation models match or beat specialized survival models without survival-specific training. The proposed construction discretizes event times, labels each subject at each time point by whether the event has already occurred, and treats censored rows as missing labels. The theoretical centerpiece is a consistency theorem: under conditionally independent censoring, minimizing the binary cross-entropy loss over observed labels recovers the true survival probabilities as the sample grows. Empirically, the authors report that tabular foundation models using this formulation outperform classical and deep survival baselines on average across 43 static and 5 dynamic real-world datasets. A reader should care because the result turns a specialist modeling task into a standard classification task, making pretrained tabular models available for time-to-event prediction in small-sample clinical and social-science settings.

What carries the argument

The load-bearing object is the expanded classification dataset: each subject's continuous event time is replaced by $K-1$ binary labels $Y_{i,k} = \mathbf{1}(T_i \le t_k)$ at interval boundaries $t_k$, with rows at which the censoring time has already passed removed from the loss. The paper trains a standard binary classifier $\hat{p}$ on this dataset by binary cross-entropy and reads off survival as $\hat{S}(t_k \mid x) = 1 - \hat{p}(x, t_k)$, clipped to enforce monotonicity. The mechanism making this valid is Theorem 3.1, which shows that under conditionally independent censoring the censored BCE loss factorizes so that its unique minimizer is the true cumulative failure probability $1 - S(t_k \mid x)$. The same construction, with covariate histories and survival-so-far as inputs, extends to dynamic predictions over a horizon $\Delta$.

What would settle it

Run a simulation with known ground-truth survival times and informative censoring driven by an unobserved confounder; if the loss-minimizing classifier still converges to the true survival probabilities despite violating Assumption 2.1, the theorem's stated condition is not necessary — if it drifts, the assumption is doing the work.

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Extended reading notes

Core claim

The paper's central claim is that a discrete-time survival model should estimate the cumulative failure probability $1 - S(t_k \mid x)$ directly rather than the discrete hazard $\lambda(t_k \mid x)$. It constructs, for each subject, binary labels $Y_{i,k} = \mathbf{1}(T_i \le t_k)$ at each discretized time $t_k$, and keeps only labels with $t_k < C_i$, so censoring enters as missing data. Theorem 3.1 proves that the population binary cross-entropy loss over these observed labels is minimized exactly when $p(x, t_k) = P(T_i \le t_k \mid X_{i,0} = x)$, provided event and censoring times are conditionally independent given covariates; hence a perfect classifier produces the correct survival curve. The empirical section reports that MITRA and TabPFN, used as in-context classifiers with this formulation, beat classical and deep survival baselines on average across multiple survival metrics on the 43 static and 5 dynamic datasets, and that modeling cumulative failure probabilities is less sensitive to the number of discretization bins than accumulating hazard estimates.

Load-bearing premise

The entire consistency argument rests on Assumption 2.1: given the measured covariates, the event time and the censoring time are independent; if unobserved risk factors influence both when the event happens and when observation ends, the loss minimizer is no longer the true survival probability and the reported IPCW metrics become biased.

Editorial extensions

If this is right

Any binary classifier, including off-the-shelf tabular foundation models used in-context, becomes a survival model without survival-specific training or hyperparameter tuning.
Modeling cumulative failure probabilities instead of discrete hazards avoids multiplicative accumulation of per-bin errors, so performance stays more stable as the number of time intervals $K$ changes.
Minimizing the binary cross-entropy loss recovers the true survival probabilities as the training set grows, under conditionally independent censoring.
The same formulation covers the dynamic setting, yielding conditional survival predictions $S(t+\Delta \mid T > t, H_{i,t})$ from longitudinal histories.
In the reported averages, the classification-based tabular foundation models lead on C-index, integrated AUC, and integrated Brier score, beating classical and deep survival baselines in both static and dynamic settings.

Reading between the lines

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

A testable stress test would simulate informative censoring — censoring driven by unobserved risk factors — and check whether the loss-minimizing classifier drifts away from the true survival curve; Theorem 3.1 implies it should, since its assumption would be violated.
The same missing-label construction could plausibly transfer to other partially observed outcomes, such as competing risks or interval censoring, whenever the observation mechanism is conditionally independent of the event process.
Because the consistency result holds for any classifier, the pretrained-model advantage is likely to be largest in the small-sample regime; one could test this by plotting the performance gap against dataset size across the paper's testbed.
The robustness to the number of bins suggests that directly estimating cumulative failure probabilities could also make other discrete-time survival pipelines less sensitive to the choice of discretization grid.

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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

The core idea is sound and genuinely useful. Casting survival analysis as binary classification on discretized cumulative failure labels, then handing the expanded data to MITRA or TabPFN, is a practical move that works. The consistency theorem is correct as far as it goes, though it is the standard BCE-minimizer-equals-conditional-probability argument under ignorable missing labels. What is actually new is the SurvSet benchmark: 43 static datasets, several discretizations, and a clean comparison showing classification-based TFMs and XGBoost beating CoxPH, RSF, DeepHit, and DeepSurv on average. That is a real empirical contribution, and the paper is honest about the existing discrete-time classification literature.

The main soft spot is not a quibble. The evaluation in Appendix B uses IPCW weights with the marginal censoring function G(t)=P(C>t), estimated by Kaplan-Meier. Under Assumption 2.1, censoring may depend on observed covariates X, and then inverse weighting by 1/G(t) does not recover the intended estimand. For example, the first term in Eq. (24) becomes E[1(T<=t)P(C>T|X)(0-Shat)^2/G(T)], which equals the unweighted Brier term only if P(C>T|X)=G(T). The same issue enters the C-index and AUC estimators. So the headline comparisons in Tables 1-2 and the r=0.89 correlation can be biased under covariate-dependent censoring. The training theorem is unaffected, but the empirical claims are not established under the paper's stated assumption. The fix is straightforward in principle: use conditional censoring weights G(t|X), or state the stronger assumption that censoring is independent of covariates.

Other soft spots are smaller. The dynamic analysis is only five datasets with large standard errors, and "MITRA dominates" overstates a C-index where the Joint Model has better average rank and ELO. The claimed robustness of cumulative-vs-hazard modeling is supported by no reported head-to-head experiment. There are also unresolved inconsistencies: the abstract says 48 datasets in one place and 53 in another, the static K grid is {4,5,10,15,20} in Table 1 but {4,5,8,10,15,20} in Appendix B.3, and no code is released. The citation pattern looks fine.

This paper deserves a serious referee, not a desk reject. The method and benchmark are useful, and the metric issue is substantive but fixable. I would send it out and ask for major revision.

Referee Report

3 major / 4 minor

Summary. The paper proposes a classification-based framework for static and dynamic survival analysis. Event times are discretized into intervals, binary labels Y_{i,k}=1(T_i <= t_k) are defined, and a standard binary cross-entropy loss is minimized over examples whose labels are uncensored. The authors prove that under conditional independent censoring (Assumption 2.1 and its dynamic analogue), the population loss minimizer equals the true conditional failure probability, so the survival curve is recovered asymptotically. They instantiate the framework with off-the-shelf tabular foundation models (MITRA, TabPFN) and XGBoost, and evaluate on 43 static and 5 dynamic SurvSet datasets against CoxPH, RSF, DeepSurv, DeepHit, landmark models, Dynamic DeepHit, and joint models. The central empirical claim is that the classification-based TFMs outperform classical and deep baselines on average across C-index, integrated AUC, and integrated Brier score.

Significance. The theoretical contribution is clean and practically meaningful: it provides a simple, self-contained reduction of censored survival estimation to binary classification, with a correct consistency proof under standard assumptions. This opens the door for tabular foundation models to be applied to survival data without bespoke likelihoods or training, and the computational advantage claimed (about 30 minutes for the static TFM evaluation) is attractive. The static benchmark is broad (43 real datasets), and the paper's honest reporting of standard errors is a plus. However, the empirical claims are not yet established because the IPCW evaluation metrics are inconsistent under the paper's own censoring assumption when censoring is covariate-dependent, and some summary statements overstate the benchmark results. The method itself remains plausible and worth further consideration after the evaluation is corrected or suitably qualified.

major comments (3)

[Appendix B.1.1, Eqs. (20), (22), (24); Appendix B.2] The IPCW estimators use the marginal censoring survival function G(t)=P(C>t), but under Assumption 2.1 censoring may depend on the observed covariates X while remaining independent of T given X. In Eq. (24), the first term has conditional expectation E[1(T<=t, delta=1)(0-S_hat)^2/G(T) | X] = 1(T<=t) * P(C>T|X) * (0-S_hat)^2 / G(T), which equals the desired unweighted term only if P(C>T|X)=G(T). The same issue affects the C-index estimator in Eq. (22) and the dynamic estimators in Appendix B.2. Consequently, the numerical comparisons in Tables 1-2 and the correlation in Figure 3 can be biased under covariate-dependent censoring. The paper should either impose the stronger marginal independence assumption, use conditional IPCW weights P(C>t|X), or provide evidence that the marginal-weight estimators are unbiased for the datasets used.
[Table 1 and Section 5.3] The text claims that MITRA and XGBoost 'outperform classical and neural survival baselines across all metrics on average,' but Table 1 shows CoxPH with a higher average C-index (0.682, SE 0.017) than MITRA (0.677, SE 0.016). The C-index raw value for XGBoost is also higher than MITRA. This contradicts the unqualified 'across all metrics' claim. The authors should either restrict the claim to the ranking/ELO summaries, report paired significance tests, or revise the wording to reflect that MITRA is not best on all raw metric averages.
[Section 5.4 and Table 2] The dynamic empirical claim that MITRA dominates is fragile given only 5 datasets and large standard errors. For example, MITRA's C-index is 0.650 +/- 0.043 versus 0.647 +/- 0.051 for the Joint Model, and the Joint Model has a better C-index rank (3.4 vs 3.8) and ELO (1018 vs 1005). The text admits this, but the overarching claim of superiority overstates the evidence. Per-dataset results and paired comparisons are needed before claiming that MITRA is the best dynamic survival model.

minor comments (4)

[Abstract and Section 5] The abstract at the top of the submission says 48 datasets (43 static and 5 dynamic), while the abstract in the full text and the contributions list say 53 datasets. The body reports 43+5=48; please reconcile this inconsistency.
[Section 3.3, Eq. (10)] Equation (10) sums k from 1 to K, but the labels Y_{i,k} are defined only for k=1,...,K-1. The proof in Eq. (15) correctly uses K-1; the index in Eq. (10) should be corrected.
[Contributions and Appendix D.3] Contribution (1) states that the framework works without hyperparameter tuning, but Appendix D.3 describes tuning the binary flags 'quantile_info' and 'time_since' for the dynamic classification models. Please qualify this claim to 'no additional tuning beyond the temporal feature flags' or similar.
[Appendix B] The phrase 'See our codebase' appears without a repository URL. Adding the code link would substantially improve reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the consistency theorem is derived from the censored BCE loss with Assumption 2.1 as the only substantive premise, and the benchmark comparisons use external datasets and models.

full rationale

The derivation chain is self-contained. Theorem 3.1 computes the population minimizer of the censored BCE loss in Eq. (10) by iterated expectation; Assumption 2.1 is used only to factor P(C_i > t_k | X_i,0) out of the conditional BCE, and the positivity condition ensures the pointwise minimizer remains P(Y_i,k = 1 | X_i,0) via Lemma A.1. The final identification P(Y_i,k = 1 | X_i,0) = 1 - S(t_k | X_i,0) is the definition Y_i,k = 1(T_i <= t_k), which the paper explicitly acknowledges rather than smuggling in. The dynamic theorem, Theorem A.2, follows the same argument under Assumption 2.2. No fitted constant is renamed as a prediction, and no load-bearing conclusion is justified by a self-citation: MITRA and TabPFN are used as externally pretrained off-the-shelf classifiers, and the empirical comparison uses SurvSet datasets and standard baseline implementations. The one substantive concern in the manuscript is that the Appendix B.1.1 IPCW estimators use the marginal censoring function G(t) = P(C > t), which is not implied by Assumption 2.1 when censoring depends on covariates; this is an evaluation-validity issue, not a circularity, because the estimators are not inputs to the consistency theorem and the reported benchmarks are external comparisons.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central theory rests on the conditional independent censoring assumption, which the paper itself acknowledges is required for identifiability. The metrics additionally assume IPCW consistency, including the use of a marginal censoring estimator. The only hand-set modeling choice in the method is the number of bins K; the paper averages over a range of K to show robustness. No invented entities are introduced.

free parameters (2)

number of discretization bins K = 4, 5, 10, 15, 20 (static; 5 for dynamic)
Hand-chosen time grid; the paper averages results over K to show robustness, so it does not bias the headline claim.
dynamic feature flags (quantile_info, time_since) = selected per dataset on validation split (binary)
Two binary flags control whether the horizon index and elapsed time since last observation are added as features; tuned on validation C-index for the classifier-based dynamic models.

assumptions (4)

domain assumption Assumption 2.1 (Conditionally Independent Censoring): Ti ⊥⊥ Ci | Xi,0
Needed in proof of Theorem 3.1 (Eq. 15, step (c)) to factor the censoring indicator out of the label expectation; also grounds IPCW metric validity.
domain assumption Assumption 2.2 (Dynamic Conditionally Independent Censoring): Ti ⊥⊥ Ci | (Hi,t, Ti > t)
Used in the dynamic consistency theorem (Theorem A.2, Eq. 17, step (c)).
standard math BCE is uniquely minimized by the conditional label probability (Lemma A.1)
Standard convexity argument for Bernoulli cross-entropy; the paper proves it in Lemma A.1.
domain assumption IPCW estimators with marginal censoring KM G(t) are consistent for the reported metrics
The paper uses G(t)=P(C>t) estimated by KM for C-index, AUC, and Brier score; this is only justified when censoring is independent of covariates or a conditional censoring model is used, which is not discussed.

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Cite this review

Pith. "Pith review of Tabular Foundation Models Can Do Survival Analysis." pith.science (2026). https://pith.science/paper/N5NYDYKY

@misc{pith2026260122259,
  author       = {Pith},
  title        = {Pith review of: Tabular Foundation Models Can Do Survival Analysis},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/N5NYDYKY}},
  note         = {Machine review of arXiv:2601.22259}
}

read the original abstract

While tabular foundation models have achieved remarkable success in classification and regression, adapting them to model time-to-event outcomes for survival analysis is non-trivial due to right-censoring, where data observations may end before the event of interest occurs. We utilize a classification-based framework that reformulates both static and dynamic survival analysis as a series of binary classification problems by discretizing event times. Censored observations are naturally handled as examples with missing labels at certain time points. This classification formulation enables existing tabular foundation models (TFMs) to perform survival analysis through in-context learning without explicit training. In contrast to classical approaches that use binary classifiers to model discrete-time hazards, our approach directly models cumulative failure probabilities, which we find empirically to be more robust to the number of discretization bins by avoiding multiplicative accumulation of per-bin errors. We prove that under standard censoring assumptions, minimizing our binary classification loss recovers the true survival probabilities as the training set size increases. We demonstrate through evaluation across 48 real-world datasets (43 static and 5 dynamic) that off-the-shelf TFMs with this classification formulation outperform classical and deep learning baselines on average over multiple survival metrics.

Figures

Figures reproduced from arXiv: 2601.22259 by the authors.

**Figure 1.** Transforming of survival data into a binary classification dataset (static setting). The pink panel (top left) illustrates the original time-to-event data (Xi,0, Ti, Ci, δi), where event times Ti and censoring times Ci are continuous. For second example, the event remains latent (T2 =?) after the censoring time C2. The blue panel (top right) displays the discretization of time into 5 intervals {τk} 5 k=1, where bina… view at source ↗

**Figure 2.** Performance heterogeneity in the static setting. Distribution of C-index, Integrated AUC, and IBS for the top four models across the 43 static datasets. Individual points represent specific datasets, while violin plots and vertical bars indicate the density, median, and interquartile range. Results are shown for K = 5 discretization bins. MITRA and XGBoost exhibit the highest median performance across all metrics. N… view at source ↗

**Figure 3.** Correlation between classification and survival metrics (static). Each point represents a classification model evaluated on 1 of the 43 datasets. Results are shown for the test set and averaged over time-discretization granularities K ∈ {4, 5, 10, 15, 20}. We observe a strong correlation (r = 0.89) between the binary cross entropy loss and the integrated Brier score. This empirically supports our Theorem 3.1 that … view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: Performance over time in the dynamic setting. Timepoint-wise performance across the five longitudinal datasets at timepoints t1, t2, t3 (K = 5 discretization bins). MITRA consistently outperforms both traditional landmarking baselines, joint modeling, and dynamic neura…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

15 extracted references · 12 canonical work pages

[1]

ˆG(Ti) 0− ˆS(t|X i,0) 2 + 1(T i >t) ˆG(t) 1− ˆS(t|X i,0) 2 # ,(24) whereG(t) is the censoring function at timet, defined in Eq. (20). We estimate the Integrated Brier Score by evaluating Eq. (24) at time pointstk,k∈{1,...,K−1}, and then integrating these values over time BS = 1 tK−1−t 1 Z tK−1 t1 cBS(t)dt. We use the trapezoidal rule to approximate the in...

work page 1958
[2]

Specifically, we refine our definition of ˆS(tk|X i,0)from Eq

Clipping survival probabilities.To ensure our survival probabilities are non-increasing in time, we apply a post-processing step that enforces monotonicity over time. Specifically, we refine our definition of ˆS(tk|X i,0)from Eq. (7) as follows: ˆS(tk|X i,0)≜min j≤k 1−ˆp(Xi,0,tk). This ensures that ˆS(t1|X i,0)≥ ˆS(t2|X i,0)≥···≥ ˆS(tK−1|X i,0). Our defin...

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W., Kim, S., You, S

Han, C., Kim, D. W., Kim, S., You, S. C., Bae, S., and Yoon, D. Large-language-model-based 10-year risk prediction of cardiovascular disease: insight from the uk biobank data.medRxiv, pp. 2023–05,

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Review of lan- guage models for survival analysis

Jeanselme, V ., Agarwal, N., and Wang, C. Review of lan- guage models for survival analysis. InAAAI 2024 Spring Symposium on Clinical Foundation Models,

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Metrics This appendix provides formal definitions, corresponding estimators and implementation details for the evaluation metrics used in thestatic settinganddynamic setting

13 Tabular Foundation Models Can Do Survival Analysis B. Metrics This appendix provides formal definitions, corresponding estimators and implementation details for the evaluation metrics used in thestatic settinganddynamic setting. All survival metrics are implemented using the sksurv library (P¨olsterl, 2020). We also briefly explain how we calculate the...

work page 2011
[13]

Specifically, DeepHit produces estimates pθ,k(Xi,0)≈P(T i∈τ k|X i,0), k= 1,...,K, whereτk = (tk−1,tk] are time bins induced by cut points 0 =t 0 <···<t K =∞

For an input Xi,0, the network outputs a probability mass function over a discretized time with K ordered time bins. Specifically, DeepHit produces estimates pθ,k(Xi,0)≈P(T i∈τ k|X i,0), k= 1,...,K, whereτk = (tk−1,tk] are time bins induced by cut points 0 =t 0 <···<t K =∞ . We obtain the risk score by computing the negative expected bin index under the p...

work page 2019
[14]

We define the time-dependent risk score at timetk as the predicted probability of experiencing the event in the next interval, ˆr(Hi,tk) = ˆptk,k+1(Hi,tk)

The implementation of Dynamic DeepHit takes as input the longitudinal history Hi,tk and outputs the estimates of the cumulative incidence distribution, ˆptk,k+∆(Hi,tk)≈P(T i≤t k+∆|Ti >t k,H i,tk),∆ = 1,...,K−k−1. We define the time-dependent risk score at timetk as the predicted probability of experiencing the event in the next interval, ˆr(Hi,tk) = ˆptk,...

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Table 3.Summary statistics for each static survival dataset

The censoring rate ranged from 6.6% to 94.4%. Table 3.Summary statistics for each static survival dataset. No. Dataset No. of covariates No. of unique samples Censoring (%) 1 Aids2 4 2839 38.0 2 Dialysis 4 6805 76.4 3 Framingham 7 4699 68.7 4 GBSG2 8 686 56.4 5 Melanoma 5 205 72.2 6 TRACE 6 1878 49.0 7 UnempDur 6 3241 38.7 8 Unemployment 5 452 43.4 9 actg...

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(21) is given by [AUC(t) = P i̸=j ˆG(Ti)−1δi 1 Ti≤t, Tj >t 1 ˆr(Xi,0)>ˆr(Xj,0) P i̸=j ˆG(Ti)−1δi 1 Ti≤t, Tj >t ,(22) whereG(t) is the censoring function at timet; see Eq

of Eq. (21) is given by [AUC(t) = P i̸=j ˆG(Ti)−1δi 1 Ti≤t, Tj >t 1 ˆr(Xi,0)>ˆr(Xj,0) P i̸=j ˆG(Ti)−1δi 1 Ti≤t, Tj >t ,(22) whereG(t) is the censoring function at timet; see Eq. (20). We evaluate Eq.(22) attk fork∈{1,...,K−1} , and compute a weighted average of the resulting A...

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

[1] [1]

ˆG(Ti) 0− ˆS(t|X i,0) 2 + 1(T i >t) ˆG(t) 1− ˆS(t|X i,0) 2 # ,(24) whereG(t) is the censoring function at timet, defined in Eq. (20). We estimate the Integrated Brier Score by evaluating Eq. (24) at time pointstk,k∈{1,...,K−1}, and then integrating these values over time BS = 1 tK−1−t 1 Z tK−1 t1 cBS(t)dt. We use the trapezoidal rule to approximate the in...

work page 1958

[2] [2]

Specifically, we refine our definition of ˆS(tk|X i,0)from Eq

Clipping survival probabilities.To ensure our survival probabilities are non-increasing in time, we apply a post-processing step that enforces monotonicity over time. Specifically, we refine our definition of ˆS(tk|X i,0)from Eq. (7) as follows: ˆS(tk|X i,0)≜min j≤k 1−ˆp(Xi,0,tk). This ensures that ˆS(t1|X i,0)≥ ˆS(t2|X i,0)≥···≥ ˆS(tK−1|X i,0). Our defin...

work page 1972

[3] [3]

W., Kim, S., You, S

Han, C., Kim, D. W., Kim, S., You, S. C., Bae, S., and Yoon, D. Large-language-model-based 10-year risk prediction of cardiovascular disease: insight from the uk biobank data.medRxiv, pp. 2023–05,

work page 2023

[4] [5]

Review of lan- guage models for survival analysis

Jeanselme, V ., Agarwal, N., and Wang, C. Review of lan- guage models for survival analysis. InAAAI 2024 Spring Symposium on Clinical Foundation Models,

work page 2024

[5] [9]

Metrics This appendix provides formal definitions, corresponding estimators and implementation details for the evaluation metrics used in thestatic settinganddynamic setting

13 Tabular Foundation Models Can Do Survival Analysis B. Metrics This appendix provides formal definitions, corresponding estimators and implementation details for the evaluation metrics used in thestatic settinganddynamic setting. All survival metrics are implemented using the sksurv library (P¨olsterl, 2020). We also briefly explain how we calculate the...

work page 2011

[6] [13]

Specifically, DeepHit produces estimates pθ,k(Xi,0)≈P(T i∈τ k|X i,0), k= 1,...,K, whereτk = (tk−1,tk] are time bins induced by cut points 0 =t 0 <···<t K =∞

For an input Xi,0, the network outputs a probability mass function over a discretized time with K ordered time bins. Specifically, DeepHit produces estimates pθ,k(Xi,0)≈P(T i∈τ k|X i,0), k= 1,...,K, whereτk = (tk−1,tk] are time bins induced by cut points 0 =t 0 <···<t K =∞ . We obtain the risk score by computing the negative expected bin index under the p...

work page 2019

[7] [14]

We define the time-dependent risk score at timetk as the predicted probability of experiencing the event in the next interval, ˆr(Hi,tk) = ˆptk,k+1(Hi,tk)

The implementation of Dynamic DeepHit takes as input the longitudinal history Hi,tk and outputs the estimates of the cumulative incidence distribution, ˆptk,k+∆(Hi,tk)≈P(T i≤t k+∆|Ti >t k,H i,tk),∆ = 1,...,K−k−1. We define the time-dependent risk score at timetk as the predicted probability of experiencing the event in the next interval, ˆr(Hi,tk) = ˆptk,...

work page 2010

[8] [160]

Table 3.Summary statistics for each static survival dataset

The censoring rate ranged from 6.6% to 94.4%. Table 3.Summary statistics for each static survival dataset. No. Dataset No. of covariates No. of unique samples Censoring (%) 1 Aids2 4 2839 38.0 2 Dialysis 4 6805 76.4 3 Framingham 7 4699 68.7 4 GBSG2 8 686 56.4 5 Melanoma 5 205 72.2 6 TRACE 6 1878 49.0 7 UnempDur 6 3241 38.7 8 Unemployment 5 452 43.4 9 actg...

work page 1931