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Toward Conditional Distribution Calibration in Survival Prediction
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Proposes CiPOT, a conformal post-processing method that uses the predicted survival probability at each subject's observed time as the conformity score, improving marginal and conditional distribution calibration of survival models without hurting discrimination.
Problem
Survival models trained on censored data are typically calibrated only marginally and often lose discrimination when calibration losses are added; conditional calibration across feature subgroups is largely unaddressed, and the existing conformal method CSD struggles with Kaplan-Meier tails under hi
Approach
Conformal post-processing that vertically rescales predicted ISD curves using percentiles of the individual survival probability at observed time (iPOT); censored subjects are handled by pseudo-uniform sampling over [0, S(c_i|x_i)], avoiding KM-based sampling and preserving monotonicity and per-time AUROC.
Key results
- CiPOT improved marginal calibration over the baseline survival models in 95 of 104 comparisons (50 significantly).
- CiPOT improved conditional (worst-slab) calibration in 64 of 69 comparisons against baselines and 51 of 69 against CSD.
- CiPOT matched baseline C-index in 75 of 104 comparisons and outperformed in 7, retaining discrimination in about 79% of cases.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Apply CiPOT post-processing rather than leaving baseline predictions unprocessed | Survival models · 15 datasets | C-index: 7 wins, 22 losses, 75 ties | Mixed |
| Apply CiPOT post-processing rather than leaving baseline predictions unprocessed | Survival models · 15 datasets | Cal_margin: 95 wins, 9 losses | Helped |
| Apply CiPOT post-processing rather than leaving baseline predictions unprocessed | Survival models · 10 larger datasets | Cal_ws: 64 wins, 5 losses | Helped |
| Apply CiPOT post-processing rather than leaving baseline predictions unprocessed | Survival models · 15 datasets | IBS: 63 wins, 23 losses, 18 ties | Mixed |
| Apply CiPOT post-processing rather than leaving baseline predictions unprocessed | Survival models · 15 datasets | MAE-PO: 54 wins, 17 losses, 33 ties | Mixed |
| Use CiPOT instead of CSD | Survival models · 15 datasets | C-index: 11 wins, 26 losses, 67 ties | Mixed |
| Use CiPOT instead of CSD | Survival models · 15 datasets | Cal_margin: 68 wins, 36 losses | Mixed |
| Use CiPOT instead of CSD | Survival models · 10 larger datasets | Cal_ws: 51 wins, 18 losses | Helped |
| Use CiPOT instead of CSD | Survival models · 15 datasets | IBS: 53 wins, 35 losses, 16 ties | Mixed |
| Use CiPOT instead of CSD | Survival models · 15 datasets | MAE-PO: 39 wins, 39 losses, 26 ties | Mixed |
Surprising findings
- CiPOT does not guarantee Harrell's C-index preservation; a counterexample shows vertical rescaling can reverse median-survival ordering.
- CiPOT's marginal calibration is worse than CSD in 36 of 104 comparisons, mainly when the base model is heavily miscalibrated (DeepHit, CQRNN).
Limitations
- Conditional calibration guarantee is only asymptotic and relies on consistent base survival estimators and smoothness assumptions; no finite-sample guarantee.
- Does not preserve Harrell's C-index, and underperforms CSD on marginal calibration for heavily miscalibrated base models.
- Conditional calibration evaluated only on 10 larger datasets (69 comparisons) because small-sample slabs were unbalanced.
Experimental setup
Datasets: 15 real-world right-censored survival datasets including HFCR, FLCHAIN, Employee, MIMIC-IV
Benchmarks: 15 survival datasets (HFCR, FLCHAIN, Employee, MIMIC-IV, among others)
Metrics: Harrell's C-index marginal calibration score (Cal_margin) worst-slab calibration score (Cal_ws) integrated Brier score MAE-PO
Baselines: AFT GB DeepSurv N-MTLR DeepHit CoxTime CQRNN CSD Kaplan-Meier
Builds on: CSD (conformalized survival distribution) conformalized quantile regression split conformal prediction Kaplan-Meier sampling
Closest papers by meaning
- Conformalized Survival Distributions: A Generic Post-Process to Increase Calibration (ICML 2024 · similarity 0.93)
- Doubly Robust Conformalized Survival Analysis with Right-Censored Data (ICML 2025 · similarity 0.89)
- History-Aware Conformal Prediction Sets for Censored Time-to-Event Outcomes (NeurIPS 2026 · similarity 0.87)
- SurvivalPFN: Amortizing Survival Prediction via In-Context Bayesian Inference (NeurIPS 2026 · similarity 0.87)
- Deep Copula-Based Survival Analysis for Dependent Censoring with Identifiability Guarantees (AAAI 2024 · similarity 0.86)
- Probabilistic Conformal Prediction with Approximate Conditional Validity (ICLR 2025 · similarity 0.86)
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