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PGP-Clinical-TimeKAN: Prior-Guided Joint Probabilistic Forecasting of Clinical Trajectories

Weizhi Nie, Rihao Chang, Weijie Wang, Yuting Su

arXiv:2609.05488v1cs.AI

TL;DR

Clinical deterioration involves coupled, partially observed physiological trajectories that scalar endpoint models do not expose. PGP-Clinical-TimeKAN forecasts their joint distribution using missingness-aware temporal modeling, prior-guided relations, nonlinear messages, and a Student-t head. On a frozen MIMIC-IV-derived cohort, it delivers strong point and probabilistic forecasting results, but its trajectory-derived event score remains weaker than a dedicated classifier and is not a clinically validated sepsis predictor.

  • Problem

    Scalar early-warning models do not expose the physiological course, while clinical measurements are irregular, informative missingness is common, and future variables and horizons are coupled.

  • Method

    PGP-Clinical-TimeKAN combines missingness-aware temporal encoders, a soft organ-system prior, patient-specific relations, nonlinear KAN messages, and a low-rank multivariate Student-t forecast.

  • Results

    PGP-Clinical-TimeKAN achieves the lowest RMSE and second-lowest MAE among 13 models, improves all reported proper scores over evaluated probabilistic alternatives, and benefits most from relational structure.

  • Takeaways & Limitations

    Joint trajectory forecasting provides an inspectable intermediate representation of future physiology and uncertainty, but accurate forecasts alone do not ensure a calibrated event detector.

  • Takeaways & Limitations

    The dataset-defined terminal-positive label lacks independently reconstructed infection evidence and full SOFA variables, while the secondary event score is not accurate or calibrated enough for deployment.

Abstract

from arXiv · show

Clinical deterioration unfolds through coupled, partially observed trajectories, not a single diagnostic label. We introduce PGP-Clinical-TimeKAN, a trajectory-first framework for joint probabilistic forecasting of multivariate physiology. It combines missingness-aware temporal encoders, a soft organ-system prior, patient-specific relations, nonlinear Kolmogorov-Arnold messages, and a low-rank multivariate Student-t head. We evaluate 24-hour histories and six-hour forecasts on a frozen MIMIC-IV-derived cohort of 6,882 patients and 54,694 windows. Across five seeds and 13 models, PGP-Clinical-TimeKAN obtains the second-lowest normalized MAE (0.37727 +/- 0.00029) and the lowest RMSE (0.52656 +/- 0.00034). It reduces MAE by 0.52% relative to deterministic TimeKAN. For probabilistic forecasting, it reaches a marginal NLL of 0.66380 and a CRPS of 0.27301. Empirical coverage is 0.533, 0.831, and 0.958 for nominal 50%, 80%, and 95% intervals. Removing relational structure causes the largest ablation loss. Increasing covariance rank improves joint likelihood but has little effect on point accuracy. A trajectory-derived risk score remains weaker than a dedicated GRU-D classifier (AUROC 0.603 versus 0.650), which limits the present clinical claim. Joint trajectory forecasting therefore provides an inspectable intermediate task, but accurate physiology forecasts alone do not ensure a calibrated event detector.

1 Introduction

Clinical deterioration is better framed as forecasting coupled physiological trajectories than as assigning a single early-warning label. PGP-Clinical-TimeKAN makes this intermediate forecast probabilistic and inspectable, while the evaluation retains a clear downstream risk limitation.

  • Direct history-to-label models indicate event likelihood but do not expose which variables may change, when thresholds may be crossed, or whether organ systems deteriorate together.
  • Trajectory forecasting separates reliable future-physiology prediction from the question of whether those forecasts support calibrated warnings.
  • Irregular informative missingness, different physiological timescales, cross-organ interactions, and joint uncertainty make multivariate clinical forecasting difficult.
  • PGP-Clinical-TimeKAN combines missingness-aware temporal encoding, a soft organ-system prior, patient-specific relations, nonlinear KAN messages, and a low-rank multivariate Student-t forecast.
  • The frozen evaluation shows competitive point accuracy, stronger probabilistic scores than evaluated distributional baselines, and weaker downstream event discrimination.

2 Related work

Prior work spans endpoint-oriented clinical warning systems, irregular-time sequence models, multivariate forecasters, graph methods, and probabilistic distributions. This paper positions its approach as a complementary, explicitly noncausal forecast of joint future physiology.

  • Earlier sepsis systems generally map EHR histories directly to diagnostic endpoints, with evaluation concerns spanning timely alerts, false alarms, deployment, and cohort heterogeneity.
  • Recent endpoint models add temporal, relational, or causal structure, whereas this work forecasts future physiology before deriving event risk.
  • Irregular-time methods represent informative missingness through masks, elapsed time, learned imputation, continuous dynamics, or observation-path controls.
  • Multihorizon forecasting includes linear, convolutional, recurrent, and Transformer-based models, while graph forecasters learn cross-series interactions over variables treated as nodes.
  • The method blends a soft organ-system prior with patient-specific relations and evaluates the resulting KAN graph as predictive rather than causal.
  • Probabilistic forecasting methods differ in how they preserve contemporaneous multivariate dependence, motivating a flexible joint forecast distribution.

3 Problem formulation

The problem formulation represents each patient’s irregular clinical history with measurements, observation masks, and elapsed times, then models a joint distribution over future multivariate trajectories rather than only conditional means.

  • For patient i at anchor t, Xi contains D clinical variables across L hourly bins, while Mi records whether each variable was observed.
  • The elapsed-time tensor ∆i records how long it has been since each variable was last measured, with optional treatment histories and static covariates represented separately.
  • The model learns pθ(Yi | Hi,t) instead of estimating only E[Yi | Hi,t].
  • Vectorizing future targets into yi ∈ R^N enables dependencies across variables at one horizon, across horizons within a variable, and across both dimensions.

4 Data source and cohort construction

The study uses a frozen, locally prepared MIMIC-IV-derived cohort with patient-level splitting and leakage-controlled windows. Labels are dataset-defined terminal events rather than independently validated Sepsis-3 endpoints.

  • The source view contains 15,029 ICU stays, while eligibility rules leave 6,882 patients and stays, including 553 dataset-defined positives and 6,329 negatives.
  • Window construction produces 54,694 examples split into 38,591 training, 8,116 validation, and 7,987 testing windows.
  • The derivative lacks independently auditable infection-evidence fields, so the source label is treated as a dataset-defined terminal-positive event rather than a validated Sepsis-3 endpoint.
  • All stays from one patient remain in a single split, with quality-control thresholds, imputation constants, scaling statistics, and calibration models fitted only on training data.
  • The primary setting uses 24-hour histories and six-hour forecasts with one-hour bins, while outcomes based on worst hourly values remain in a separate derived view.
  • The six forecast targets are heart rate, respiratory rate, oxygen saturation, mean arterial pressure, systolic pressure, and temperature; treatment inputs are excluded from the reported main model.
  • Forward filling uses only pre-anchor observations, unseen variables receive a training-set constant, and future losses use observed targets only.

5 Method

PGP-Clinical-TimeKAN maps missingness-aware histories to coherent joint forecasts by combining variable-specific temporal encoding, prior-guided relational message passing, and a low-rank multivariate Student-t output. The pipeline then derives threshold-crossing and organ-function probabilities while retaining observed-target masking and regularized likelihood training.

  • The pipeline maps leakage-controlled histories to joint trajectory samples and downstream organ-function estimates.
  • Missingness-aware embeddings distinguish observed, imputed, and stale measurements while retaining measurement reliability and optional treatment-history information.
  • Variable-wise multi-scale TimeKAN blocks extract temporal patterns before cross-variable mixing, with alternative decompositions considered for short, nonstationary ICU trajectories.
  • A learned gate blends a soft organ-system prior with patient-specific dynamic relations, and KAN functions transform cross-variable messages nonlinearly.
  • The direct decoder predicts all horizons jointly with a low-rank multivariate Student-t distribution whose factor and diagonal terms capture shared and output-specific uncertainty.
  • Coherent samples support threshold-crossing and organ-deterioration probabilities, while complete sepsis-risk estimation requires independently validated infection evidence.

6 Experiments

Experiments use a frozen patient-level cohort and consistent observed-target masking across models, evaluating point, distributional, and secondary risk-prediction performance. Measurement coverage is highly uneven, especially for temperature, so raw errors require cautious interpretation.

  • The frozen experiment contains 6,882 patients and 54,694 windows, using 24-hour histories to forecast six vital signs over six hours.
  • All trainable models share the same split and observed-target masks, with results averaged over five optimization seeds.
  • The benchmark compares PGP-Clinical-TimeKAN against persistence, linear, neural, transformer, probabilistic, and deterministic TimeKAN baselines.
  • Cohort characteristics are descriptive and support no causal or group-difference claim.
  • Evaluation includes masked normalized MAE, RMSE, marginal and joint NLL, CRPS, energy score, empirical coverage, and interval width.
  • Temperature observability is 23.09% historically and 23.20% for future targets, versus more than 89% for the other vital-sign targets.

7 Results

PGP-Clinical-TimeKAN delivers competitive point and probabilistic forecasting, with errors increasing over longer horizons and varying across physiological variables. Its forecasts remain limited for abrupt blood-pressure changes.

  • Point forecasting: 0.52656 ± 0.00034 RMSE is lowest, while 0.37727 ± 0.00029 MAE is second-lowest among the compared models.GRU-D has slightly lower MAE, so the point-accuracy advantage is metric-specific.
  • Point forecasting: 0.52% lower MAE and 0.75% lower RMSE are achieved relative to deterministic TimeKAN.The paired bootstrap favors PGP-Clinical-TimeKAN over TimeKAN across all seeds.
  • Horizon and variable effects: 0.33784-to-0.40507 weighted MAE and 0.48050-to-0.55455 RMSE increases occur from +1 to +6 hours.Heart rate at +1 hour is easiest, whereas respiratory rate at +6 hours is hardest.
  • Forecast limitations: Forecast centers are smooth for stable trajectories but regress toward the mean during abrupt MAP and SBP excursions.The direction accuracy is 0.4520, indicating difficulty with short-term turning points.
  • Probabilistic forecasting: 0.66380 marginal NLL and 0.27301 CRPS are lowest among the evaluated probabilistic baselines.Coverage is 0.533, 0.831, and 0.958 for nominal 50%, 80%, and 95% intervals, respectively.

8 Ablation and further analysis

Ablations identify cross-variable relations as the clearest contributor to forecast accuracy, while covariance rank mainly improves joint likelihood. Performance worsens with longer horizons and difficult clinical settings, and trajectory-derived risk remains weaker than dedicated classifiers.

  • Relational structure: Removing cross-variable relations causes the largest ablation loss, while nonlinear KAN relations outperform isolated alternatives.A prior-only graph is insufficient, and the full model outperforms every isolated relation variant.
  • Probabilistic analysis: Raising covariance rank from 2 to 16 improves joint NLL per observed target from 0.58930 to 0.50323 while changing MAE by at most 0.00026.This indicates that covariance rank primarily affects joint dependence rather than the forecast center.
  • Sensitivity: MAE increases from 0.35860 at three forecast hours to 0.42832 at 24 hours, while extending history from 24 to 48 hours does not help.Values-only, mask, gap, and temporal variants differ only minimally in MAE.
  • Subgroup heterogeneity: High-missingness windows have MAE 0.38203 versus 0.37336 for low-missingness windows, and near-event windows reach about 0.395 versus 0.37639 for controls.Errors are also higher in TSICU and MICU/SICU, although small strata cannot establish fairness conclusions.
  • Secondary risk analysis: The trajectory-derived score reaches AUROC 0.6030, below GRU-D at 0.6503, and detects 9.16%, 32.29%, and 49.16% of positive stays at 1%, 5%, and 10% alert rates.Matched pseudo-anchors change prevalence and are not comparable with natural-window results.

9 Discussion

The results support a narrow trajectory-first claim: the model combines competitive point forecasts with stronger joint uncertainty representation, but learned relations remain predictive rather than causal. Forecast likelihood does not ensure a calibrated event detector, and errors concentrate in difficult settings.

  • Scope of gains: PGP-Clinical-TimeKAN has the lowest RMSE and improves over deterministic TimeKAN, but it does not beat every point baseline.Its contribution is a competitive forecast center paired with better joint future uncertainty representation.
  • Dependence modeling: Cross-variable relations are the clearest source of improvement, while higher covariance rank improves joint likelihood with little change in point error.Nonzero off-diagonal correlations support dependence across variables and horizons.
  • Interpretation: Predictive relation graphs encode associations rather than causal mechanisms, because learned edges can mix biology, measurement policy, treatment effects, and cohort-specific correlations.Efficiency values are GPU microbenchmarks rather than end-to-end deployment latency.
  • Downstream risk: The trajectory-derived score is less discriminative and calibrated than dedicated classifiers, showing that future-physiology likelihood does not ensure preservation of rare event-predictive features.Endpoint-aware representations may therefore be needed for forecast–assess models.
  • Error structure: Errors grow with missingness, near-event timing, some ICU strata, and forecast distance, while representative forecasts smooth abrupt hemodynamic changes.External validation should cover different measurement policies and patient mixtures.

10 Limitations, ethics, and broader impact

The study’s clinical interpretation is constrained by retrospective single-center data, a narrow six-vital-sign target, an unvalidated endpoint, and exploratory subgroup analyses. The trajectory-derived score is not accurate or calibrated enough for deployment, and operational benchmarks omit important clinical-system delays.

  • Data and scope: The study uses a single-center database and forecasts six vital signs, while excluding treatment-input results from its claims.Static covariates are available, but their ablation gain is small.
  • Endpoint validity: The dataset-defined terminal-positive label is not an independently validated Sepsis-3 endpoint and cannot reconstruct infection timing or the full six-organ SOFA state.Positive-window prevalence is only 1.039%, making AUPRC and alert metrics sensitive to anchor construction.
  • Fairness and validation: Subgroup analyses are exploratory, and small strata may reflect sample size, disease mix, ICU workflow, or measurement frequency rather than demographic effects.External, temporal, and multi-site validation is required before clinical use.
  • Clinical deployment: The trajectory-derived score is not accurate or calibrated enough for deployment, with false reassurance and alert fatigue identified as plausible harms.A prospective system should retain human oversight and support abstention or escalation for out-of-distribution inputs.
  • Operational scope: The GPU benchmark omits extraction, preprocessing, interface, and clinician-response delays.Reported latency therefore does not represent full clinical-system performance.

11 Conclusion

PGP-Clinical-TimeKAN provides a prior-guided framework for joint probabilistic forecasting of short-horizon clinical trajectories. It achieves strong point and probabilistic forecasting results, but downstream event prediction remains weaker than dedicated classifiers, so clinical translation requires stronger endpoint evidence, calibration, and data coverage.

  • Conclusion: On a frozen cohort of 6,882 patients, PGP-Clinical-TimeKAN obtains the lowest RMSE and second-lowest MAE among 13 models.It also improves consistently over deterministic TimeKAN and achieves the best evaluated probabilistic scores.
  • Clinical interpretation: The resulting trajectories form an inspectable intermediate representation, but the secondary event score remains weaker than dedicated classifiers and is not a clinically validated sepsis predictor.Joint trajectory modeling is useful in its own right, while clinical translation still requires stronger endpoint evidence, calibration, and data coverage.

A Detailed experimental results

The paper reports an empirical forecasting study with documented evaluation procedures, while explicitly limiting interpretation of its secondary risk analysis and subgroup findings.

  • Limitations: The secondary risk outcome is dataset-defined terminal positivity because infection evidence and full SOFA variables were unavailable.
  • Study scope: The study is empirical and does not claim new theoretical results or formal proofs.
  • Reproducibility: The evaluation documentation covers cohort construction, splits, variables, optimization, seeds, metrics, baselines, ablations, and patient-level bootstrap procedures.
  • Limitations: Subgroup estimates describe evaluation heterogeneity and cannot establish demographic causation or fairness.
  • Broader impact: The paper discusses inspectable forecasting as a potential benefit alongside false reassurance, alert fatigue, subgroup heterogeneity, and workflow-shift risks.
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