Uncertainty-Aware Histopathology Survival Analysis

Comparing MC-Dropout, Deep Ensembles, and SNGP as uncertainty estimators for survival prediction from whole-slide pathology images, on TCGA-GBMLGG (glioma).

All three use the same backbone: frozen UNI v2 patch features, gated-attention MIL pooling, and a Cox proportional-hazards head. The comparison isolates the uncertainty method, not the architecture.

The three are indistinguishable on ranking accuracy (C-index $\approx$ 0.76), so the differences are in the quality and cost of their uncertainty. SNGP has the most informative uncertainty and the best calibration in one forward pass, against 100 for MC-dropout and 5 trained models for ensembles. Its uncertainty is also the least independent of its own risk score.

Results

5-fold, patient-level, event-stratified cross-validation over 875 patients (175 per fold, 445 events). All numbers are out-of-fold.

Method	C-index (fold mean $\pm$ sd)	Pooled C-index (95% CI)	MCE $downarrow$	Selective area $\uparrow$	C-index @ 20% coverage	Models trained	Passes at inference
MC-Dropout	0.758 $\pm$ 0.019	0.758 (0.735–0.780)	0.054	0.786	0.849	1	100
Deep Ensembles	0.765 $\pm$ 0.020	0.765 (0.744–0.786)	0.042	0.786	0.802	5	5
SNGP	0.763 $\pm$ 0.026	0.763 (0.742–0.784)	0.038	0.809	0.852	1	1

C-index: fraction of comparable patient pairs ordered correctly (0.5 = chance). MCE: mean calibration error against a Breslow baseline, averaged over 1/3/5-year horizons. Selective area: accuracy gain as the least-confident patients are withheld, floored at 20% coverage.

Discrimination

All three land at C-index $\approx$ 0.76 and are stable across folds. They share a backbone, so this measures the shared model more than the uncertainty method.

Risk Stratification

Predicted-risk tertiles separate observed survival in the correct order for every method. Median survival is 8.8 / 2.6 / 1.1 years for low / mid / high risk, log-rank p < 1e-72. GBMLGG spans two biologically distinct diseases and n is large, so these p-values are a sanity check rather than an effect size, and they do not rank the three methods.

Selective Prediction

Withholding the patients each model is least confident about raises accuracy for all three, above a random-subset null. SNGP climbs highest (area 0.809; C-index 0.852 at 20% coverage).

Uncertainty vs. Risk

If uncertainty is only a proxy for mid-range risk, then filtering by confidence keeps the easy patients and the UQ adds nothing. Regressing the risk-predictable component out of each uncertainty and re-ranking on the residual:

Method	p(Uncertainty, Risk)	Var. Explained by Risk	Selective Area After Removing Risk
MC-Dropout	+0.34	12%	0.763
Deep Ensembles	+0.08	$\approx$0%	0.782
SNGP	+0.46	64%	0.769

SNGP has the biggest lift but the least risk-independent uncertainty. Deep ensembles have the most independent uncertainty, but a risk-only baseline nearly matches their lift.

Pipeline

flowchart TD
    A["① Data Preparation<br/>GDC clinical → patient-level survival table<br/>patient-level, event-stratified splits"]
    B["② Preprocessing · TRIDENT + UNI v2<br/>segmentation → patching → feature extraction<br/>256×256 px @ 20× · 1536-dim · one .h5 bag per slide"]
    C["③ MIL Aggregation · ABMIL<br/>gated attention pooling → 128-dim slide embedding<br/>≤1024 patches per slide · linear in patch count"]
    D["④ Survival Head · Cox<br/>Cox partial-likelihood loss<br/>best epoch selected by validation C-index"]
    E["⑤ Uncertainty Estimation<br/>MC-Dropout vs Deep Ensembles vs SNGP<br/>same backbone, three uncertainty mechanisms"]
    F["⑥ Evaluation<br/>C-index · Kaplan-Meier · calibration (MCE)<br/>selective prediction · risk-confound diagnostics"]

    A --> B --> C --> D --> E --> F

    style A fill:#f0f0f0,stroke:#999
    style B fill:#e8f5f5,stroke:#6bc
    style C fill:#ede8f5,stroke:#96c
    style D fill:#fdecea,stroke:#e88
    style E fill:#fef6e4,stroke:#e6a817
    style F fill:#eaf5ea,stroke:#6a6

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Model

Component	Setting
Patch encoder	UNI v2, frozen $\cdot$ 1536-dim per patch $\cdot$ 256×256 px @ 20×
Patches per slide	$\le$ 1024
MIL pooling	ABMIL, gated attention $\cdot$ attention dim 128 $\cdot$ dropout 0.25 $\cdot$ LayerNorm on raw patch features
Slide embedding	128-dim
Head	Linear $\rightarrow$ scalar Cox risk score
Loss	Cox negative partial log-likelihood
Optimiser	AdamW $\cdot$ lr 5e-5 $\cdot$ weight decay 1e-3 $\cdot$ grad clip 1.0
Schedule	$\le$ 50 epochs $\cdot$ min 3 $\cdot$ early stopping patience 5 on validation C-index
CV	5-fold, patient-level, event-stratified $\cdot$ 25% of train held out for validation $\cdot$ seed 42

MC-Dropout keeps dropout active at inference and takes 100 samples. Deep Ensembles trains 5 independent models from different seeds. SNGP replaces the head with a Gaussian-process output layer (1024 random features, ridge penalty 1.0) over a spectral-normalised backbone (norm bound 0.95), giving uncertainty in a single deterministic pass.

C-index is not the training objective: it counts pairwise comparisons and has no usable gradient. The Cox partial likelihood is a differentiable surrogate for the same ranking goal, and C-index only selects the best epoch.

The SurvRNC rank-N-contrast loss is implemented in src/losses/survrnc.py as an auxiliary embedding loss (L = L_cox + β·L_survrnc), but is disabled for every result reported here (LAMBDA_RNC = 0.0).

Datasets

Diagnostic whole-slide images were downloaded from the NCI Genomic Data Commons using open-access, SVS, slide-image, and diagnostic-slide filters. Filtering criteria and cohort composition: data/README.md.

Dataset	Projects	Cases	Slides	Manifest	Status
TCGA Glioma	TCGA-GBM, TCGA-LGG	879	1,703	gdc_manifest_full_gbmlgg_dx.txt	Reported above (one slide per patient; 875 patients across 5 folds)
TCGA Lung Adenocarcinoma	TCGA-LUAD	478	541	gdc_manifest_full_luad_dx.txt	Preprocessed; not part of the current results

Repository layout

src/          Importable package: data → model → loss → train → eval  (see src/README.md)
scripts/      Runnable stages: data prep, feature extraction, training, tuning, eval
notebooks/    Analysis; publication_figures.ipynb regenerates every figure above
results/      Per-method CV predictions, summaries, figures, and diagrams
data/         Survival tables, splits, and (gitignored) slides + features
manifests/    GDC download manifests
TRIDENT/      Vendored WSI preprocessing toolkit

Contributors

Name	University	Profile
Robert Pearce	University of Nevada, Las Vegas	robertxpearce.com
Sejun Park	Gyeonggi Science Technology University	LinkedIn
Hailey (Heejae Kwon)	Sookmyung Womens University	LinkedIn
HyeonKyeong Lee	Gyeongsang National University	LinkedIn

Acknowledgments

This project was completed during the International AI & Machine Learning Summer Camp hosted by the University of Nevada, Las Vegas. Resources and guidance were provided by Dr. Mingon Kang.

References

Zhang, Andrew, et al. "Accelerating data processing and benchmarking of ai models for pathology." arXiv preprint arXiv:2502.06750 (2025).

Chen, Richard J et al. “Towards a general-purpose foundation model for computational pathology.” Nature medicine vol. 30,3 (2024): 850-862. doi:10.1038/s41591-024-02857-3

Lu, Ming Y et al. “A visual-language foundation model for computational pathology.” Nature medicine vol. 30,3 (2024): 863-874. doi:10.1038/s41591-024-02856-4

Ilse, M., Tomczak, J. & Welling, M.. (2018). Attention-based Deep Multiple Instance Learning. Proceedings of the 35th International Conference on Machine Learning, in Proceedings of Machine Learning Research 80:2127-2136

Shao, Zhuchen, et al. ‘TransMIL: Transformer Based Correlated Multiple Instance Learning for Whole Slide Image Classification’. Advances in Neural Information Processing Systems, edited by M. Ranzato et al., vol. 34, Curran Associates, Inc., 2021, pp. 2136–2147, proceedings.neurips.cc/paper_files/paper/2021/file/10c272d06794d3e5785d5e7c5356e9ff-Paper.pdf.

Saeed, Numan, et al. ‘SurvRNC: Learning Ordered Representations for Survival Prediction Using Rank-N-Contrast’. arXiv [Cs.CV], 2024, arxiv.org/abs/2403.10603. arXiv.

Liu, Jeremiah Zhe, et al. ‘Simple and Principled Uncertainty Estimation with Deterministic Deep Learning via Distance Awareness’. CoRR, vol. abs/2006.10108, 2020, arxiv.org/abs/2006.10108.

Meleti, Uma, and Jeffrey J. Nirschl. ‘Uncertainty-Aware Image Classification in Biomedical Imaging Using Spectral-Normalized Neural Gaussian Processes’. 2026 IEEE 23rd International Symposium on Biomedical Imaging (ISBI), IEEE, 2026, pp. 1–4, https://doi.org/10.1109/isbi61048.2026.11515555.

Gal, Yarin, and Zoubin Ghahramani. ‘Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning’. arXiv [Stat.ML], 2016, arxiv.org/abs/1506.02142. arXiv.

Lakshminarayanan, Balaji, et al. ‘Simple and Scalable Predictive Uncertainty Estimation Using Deep Ensembles’. arXiv [Stat.ML], 2017, arxiv.org/abs/1612.01474. arXiv.