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Dynamic Survival Analysis with Controlled Latent States
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Models the intensity of a counting process as exp of a latent state driven by a controlled differential equation, estimated either with neural CDEs or a linearized signature-based estimator (CoxSig), with risk bounds and survival experiments.
Problem
Predicting individual-specific event intensities for survival analysis from static covariates and irregularly sampled, time-dependent longitudinal features, where joint models do not scale to high-dimensional data.
Approach
The log-intensity is a linear readout of a latent state solving a controlled differential equation driven by the observed time series; this is estimated either by a neural CDE (controlled ResNet on piecewise-constant interpolation) or by a linear model on truncated signatures (CoxSig), which is shown to be a generalized Cox model with time-varying covariates.
Key results
- On the partially observed SDE experiment, CoxSig reaches average C-index 0.857 and IBS 0.091, versus 0.545 C-index for Dynamic DeepHit.
- On the churn dataset, CoxSig+ reaches average C-index 0.751 and IBS 0.129, outperforming DDH (0.570, 0.139).
- CoxSig is generally outperformed on the low-dimensional tumor growth simulation, where DDH reaches 0.941 C-index versus 0.696 for CoxSig.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use CoxSig instead of the strongest baseline | CoxSig · OU | Avg. C-Index: 0.621±0.05 -> 0.857±0.01 | Helped |
| use CoxSig instead of the strongest baseline | CoxSig · OU | IBS: 0.094±0.01 -> 0.091±0.01 | Helped |
| add the first observed time-series value to the static features (ablation) | CoxSig · OU | IBS: 0.091±0.01 -> 0.095±0.01 | Hurt |
| add the first observed time-series value to the static features (ablation) | CoxSig · Tumor Growth | Avg. C-Index: 0.696±0.02 -> 0.797±0.03 | Helped |
| use DDH instead of CoxSig | CoxSig · Tumor Growth | Avg. C-Index: 0.696±0.02 -> 0.941±0.05 | Hurt |
| add the first observed time-series value to the static features (ablation) | CoxSig · NASA | Avg. C-Index: 0.858±0.04 -> 0.867±0.04 | Helped |
| add the first observed time-series value to the static features (ablation) | CoxSig · NASA | IBS: 0.154±0.03 -> 0.154±0.03 | No clear effect |
| use CoxSig instead of the strongest baseline | CoxSig · NASA | Avg. C-Index: 0.867±0.04 -> 0.858±0.04 | Hurt |
| add the first observed time-series value to the static features (ablation) | CoxSig · Califrais | Avg. C-Index: 0.741±0.01 -> 0.751±0.01 | Helped |
| use CoxSig+ instead of the strongest baseline | CoxSig+ · Califrais | IBS: 0.139±0.01 -> 0.129±0.01 | Helped |
Surprising findings
- NCDE-based estimators tie or perform worse than competing methods, and on predictive maintenance their C-index is below random (0.541).
- Signature-based models underperform on low-dimensional data, unlike their strong results on moderate to high dimensional streams.
Limitations
- Below-average performance on low-dimensional time series.
- Signature computation scales exponentially with the dimension of the time series, making very high dimensional data prohibitive.
- Experiments limited to survival analysis; no competing risks or general counting processes.
Experimental setup
Datasets: simulated Ornstein-Uhlenbeck SDE hitting time simulated tumor growth NASA aircraft gas turbine engine simulations Califrais churn dataset (private)
Benchmarks: simulated hitting time tumor growth NASA predictive maintenance churn prediction (Califrais)
Metrics: time-dependent C-index integrated Brier score Brier score AUC
Baselines: Cox model (scikit-survival) Random Survival Forest Dynamic DeepHit SurvLatent ODE NCDE
Builds on: neural controlled differential equations Cox model with time-varying covariates signature transform Random Survival Forest Dynamic DeepHit
Closest papers by meaning
- Learning the Dynamics of Sparsely Observed Interacting Systems (ICML 2023 · similarity 0.84)
- Observable Neural ODEs for Identifiable Causal Forecasting in Continuous Time (NeurIPS 2026 · similarity 0.84)
- LogSig-SSM: Time-Series Modelling with Multi-Scale Log-Signature Compression for State-Space Models (NeurIPS 2026 · similarity 0.84)
- Orthogonal Survival Learners for Estimating Heterogeneous Treatment Effects from Time-to-Event Data (NeurIPS 2025 · similarity 0.83)
- In-Context Learning of Stochastic Differential Equations with Foundation Inference Models (NeurIPS 2025 · similarity 0.82)
- Decoupled Marked Temporal Point Process using Neural Ordinary Differential Equations (ICLR 2024 · similarity 0.82)
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