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Survival Analysis via Density Estimation

ICML 2025 · Probabilistic and scientific modeling › Variational and generative sampling · approach: Likelihood-free and graphical model estimation

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Reduces survival analysis with competing risks to density estimation by post-processing cumulative incidence estimates through a copula, with a new strictly proper scoring rule (NLL-SC) and upper/lower bounds for individual survival functions.

Problem

Survival analysis with K competing risks typically relies on conditional independence or proportional hazards assumptions, lacks identifiability-aware bounds without copula knowledge, and has no strictly proper scoring rule for K>2.

Approach

A two-step algorithm estimates the conditional cumulative incidence functions via any density estimation model, then post-processes the discretized CJD probability masses into individual CDFs by solving copula-based equations; upper and lower bounds follow from redistributing mass without a copula, and NLL-SC is a copula-based strictly proper scoring rule.

Key results

• On Dialysis and oldmort (B=32), TS-LGB shows comparable or superior performance to DeepHit on cen-log, calibration and NLL-SC metrics, and DeepHit outperforms Cox and RSF among baselines.
• The two-step framework combined with LightGBM is reported to be the most effective model on the Dialysis and oldmort datasets.
• The paper proves that for K=2 the two-step algorithm estimates survival functions with small error when density estimation error is arbitrarily small (under plausible assumptions).

Surprising findings

• Neural network models like DeepHit typically need longer training than tree-based models, while TS-LGB matches or beats DeepHit.

Limitations

• Requires prior knowledge of the copula for point estimates; without it only bounds are obtained
• Experiments limited to two small public datasets in the main text
• Identifiability of copula and survival function requires extra assumptions for parameterized copulas

Experimental setup

Datasets: Dialysis oldmort

Benchmarks: Dialysis oldmort

Metrics: Cen-log D-calibration KM-calibration NLL-SC CJD-Brier CJD-Logarithmic CJD-KS

Baselines: Cox model Random survival forest DeepHit DSM DeSurv Neural Fine-Gray

Builds on: DeepHit Random survival forests Copula-graphic estimator Rindt et al. 2022 monotone neural network survival model Sklar's theorem

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