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Toward a Well-Calibrated Discrimination via Survival Outcome-Aware Contrastive Learning
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Proposes ConSurv, a contrastive learning method for deep survival analysis that weights negatives by event-time difference (importance sampling) and combines it with NLL, improving discrimination while preserving calibration.
Problem
Deep survival models that add ranking losses to NLL improve discrimination (C-index) but tend to degrade calibration; the paper seeks discrimination gains without sacrificing calibration.
Approach
A survival-outcome-aware NCE loss (SNCE) where negatives are importance-weighted by the absolute difference in event/censoring times (Laplacian-style weight), so samples with similar survival times are penalized less as false negatives; contrastive loss acts on embeddings rather than model outputs, and is added to NLL. Censoring-aware comparability rules and a time margin alpha are applied.
Key results
- On METABRIC, ConSurv reaches CI 0.688 vs 0.660 for the NLL+InfoNCE variant and 0.658 for X-CAL, with IBS 0.183 (comparable to CoxPH 0.170).
- On NWTCO, ConSurv achieves CI 0.729 and D-CAL 10/10 seeds, the best among compared models.
- Across datasets, ConSurv attains the highest CI on most benchmarks, e.g. SEER CI 0.865 and SEER IBS 0.004, while maintaining calibration competitive with DCS and X-CAL.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add survival-outcome-weighted contrastive loss (SNCE) to NLL (ablation) | ConSurv · METABRIC, NWTCO, GBSG, FLCHAIN, SUPPORT, SEER | CI: 0.608_{\pm0.046} -> 0.688_{\pm0.017}; 0.711_{\pm0.051} -> 0.729_{\pm0.052}; 0.675_{\pm0.018} -> 0.696_{\pm0.006}; 0.794_ | Helped |
| Replace equal-weight negative sampling with survival-time-weighted negative sampling (ablation) | NLL + contrastive learning · METABRIC, NWTCO, GBSG, FLCHAIN, SUPPORT, SEER | CI: 0.660_{\pm0.002} -> 0.688_{\pm0.017}; 0.716_{\pm0.048} -> 0.729_{\pm0.052}; 0.687_{\pm0.008} -> 0.696_{\pm0.006}; 0.797_ | Helped |
| Replace SNCE with ranking loss (ablation) | NLL + contrastive learning · METABRIC, NWTCO, GBSG, FLCHAIN, SUPPORT, SEER | IBS: 0.183_{\pm0.019} -> 0.267_{\pm0.025}; 0.090_{\pm0.011} -> 0.210_{\pm0.026}; 0.175_{\pm0.002} -> 0.342_{\pm0.034}; 0.072_ | Hurt |
| Replace SCARF augmentation with noise injection (NI) (ablation) | ConSurv · METABRIC, NWTCO, GBSG, FLCHAIN, SUPPORT, SEER | CI: 0.650 -> 0.688; 0.704 -> 0.729; 0.681 -> 0.696; 0.788 -> 0.810; 0.612 -> 0.625; 0.842 -> 0.854 | Hurt |
| Set the margin to 0 instead of 10 (ablation) | ConSurv · METABRIC, NWTCO, GBSG, FLCHAIN, SUPPORT, SEER | CI: 0.707 -> 0.695; 0.773 -> 0.765; 0.695 -> 0.691; 0.783 -> 0.779; 0.610 -> 0.592; 0.889 -> 0.883 | Mixed |
| Increase contrastive-loss coefficient from β=0.01 to β=1.0 (ablation) | ConSurv · METABRIC, NWTCO, GBSG, FLCHAIN, SUPPORT, SEER | CI: 0.673 -> 0.706; 0.747 -> 0.773; 0.655 -> 0.703; 0.746 -> 0.816; 0.594 -> 0.610; 0.831 -> 0.854 | Helped |
Surprising findings
- Ranking-loss models (DeepHit, DRSA) show poor calibration (e.g., D-CAL 0 on METABRIC), while contrastive learning without any calibration loss keeps calibration competitive.
- On FLCHAIN, ConSurv's D-CAL-based calibration is strong but ConSurv does not win every calibration metric; on GBSG its D-CAL is 0 despite best CI.
Limitations
- Calibration results are mixed across datasets and metrics (e.g., GBSG D-CAL 0, FLCHAIN DDC not best).
- Sensitivity to margin alpha and balancing coefficient beta; poor results at small beta.
- Relies on the ignorable censoring assumption underlying NLL-based MLE.
Experimental setup
Datasets: METABRIC NWTCO GBSG FLCHAIN SUPPORT SEER
Benchmarks: METABRIC NWTCO GBSG FLCHAIN SUPPORT SEER
Metrics: integrated time-dependent C-index integrated Brier score distributional divergence for calibration (DDC) D-calibration p-value time-dependent C-index time-dependent Brier score Wasserstein distance to Kaplan-Meier curves
Baselines: CoxPH DeepSurv DeepHit DRSA DCS X-CAL NLL only NLL + InfoNCE NLL + ranking loss
Builds on: InfoNCE SCARF DeepHit DeepSurv X-CAL
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