STREAM: A data-driven framework for physiological state monitoring in ICU patients

Abstract

Intensive care unit (ICU) monitoring systems face a critical gap: translating continuous physiological data into interpretable patterns that support clinical assessment. Existing approaches rely on static thresholds or severity scores that fail to capture dynamic disease progression patterns and provide limited insight into why patients change over time. We developed STREAM (State Trajectory Representation and Evolution-Aware Monitoring), which models each patient as a point in a multidimensional physiological space and applies geometric analysis of routine ICU data to track physiological instability. STREAM analyzes 26 routinely collected clinical measurements using optimal transport theory to discover data-derived physiological states without predefined categories and maps each patient to their nearest state. We evaluated STREAM using the multicenter eICU Collaborative Research Database (N = 158,294) for development and MIMIC-IV (N = 84,517) for external validation. STREAM identified five reproducible data-derived physiological states with distinct clinical signatures. Patients who spent less than 10% of their ICU stay within their expected state (state outliers) had ICU mortality of 37.6%, 16-fold higher than those who remained within their assigned states (2.3%). Mortality prediction achieved an area under the receiver operating characteristic curve of 0.863 at 8 hours and 0.903 at 72 hours, with excellent calibration (expected calibration error of 0.002). External validation on MIMIC-IV maintained robust performance (0.798 and 0.857, respectively), with state outliers exhibiting 10-fold higher mortality (33.5% vs. 3.2%). Feature importance analysis identified which laboratory values and vital signs are associated with movement toward higher-risk states, providing interpretable clinical explanations. STREAM provides transparent monitoring across data-derived physiological states, linking state dynamics with outcome prediction. Strong discrimination, calibration, and reproducibility across multicenter datasets support the method’s potential for prospective evaluation.

Author summary

We created STREAM, a monitoring system that tracks how critically ill patients move through different data-derived physiological states during their intensive care unit stay. Current monitoring approaches compress complex patient data into single scores that lose important information about how different organ systems interact and change over time. STREAM uses a mathematical approach called optimal transport to identify distinct patterns in routine blood tests and vital signs, then tracks each patient’s movement through these patterns. We found that patients whose measurements consistently fall outside their expected pattern, even when no single measurement is extreme, face dramatically higher mortality risk. In our largest dataset of over 158,000 patients, these outlier patients had 16 times higher mortality than those who remained within expected patterns. Importantly, STREAM explains which specific measurements are most associated with each patient’s trajectory, giving clinicians interpretable information rather than just a risk number. When tested on an independent dataset of over 84,000 patients from a different hospital, the system maintained strong performance without any retraining, suggesting it captures fundamental patterns of critical illness that generalize across institutions.

Introduction

Critical care monitoring faces a fundamental challenge: translating continuous streams of laboratory results, vital signs, and physiological measurements into clinically interpretable insights that support patient assessment. Current ICU monitoring largely depends on threshold-based alerts for individual parameter abnormalities and composite severity scores (APACHE II, SOFA) that summarize complex physiology into a single daily value [1,2]. While these approaches provide standardized risk assessment, they have critical limitations for timely clinical decision-making. First, traditional severity scores typically require 24 hours of data collection, delaying risk assessment during the crucial early hours of ICU admission when many therapeutic decisions are made [3]. Second, they compress multidimensional physiology into one score, losing information about relationships between organ systems that characterize complex critical illness. Third, they provide static risk estimates without revealing disease trajectory or progression patterns that could guide proactive interventions [4].

Machine learning has produced sophisticated ICU outcome prediction models, with deep learning approaches achieving strong discriminative performance for mortality prediction by processing high-dimensional temporal data [5]. However, many of these models function as “black boxes” that output risk probabilities without clinical explanations, limiting their utility for bedside decision-making. Although techniques like SHapley Additive exPlanations (SHAP) provide post-hoc feature importance scores, these model-specific interpretations remain difficult to translate into clear clinical states or interpretable physiological insights for individual patients [6–8]. Even when such models achieve high predictive performance, clinicians struggle to understand why predictions change over time or which specific interventions would improve patient outcome.

Beyond simply predicting risk (e.g., mortality), clinicians need systems or models that provide a clear structure for understanding how a disease evolves over time, so they can make informed decisions about treatment and intervention. They recognize that critically ill patients follow different pathways through illness: some experience steady improvement, others show gradual deterioration, and some undergo rapid decompensation or unexpected recovery. However, existing monitoring systems lack methods for systematically identifying these progression patterns or predicting when patients might transition between different phases of illness. This gap between clinical intuition about disease progression and available monitoring tools leaves deterioration signals undetected until physiological decompensation becomes clinically apparent, frequently too late for optimal intervention [9,10].

We developed STREAM (State Trajectory Representation and Evolution-Aware Monitoring), a state-based analysis method that addresses these limitations by applying optimal transport theory [11] to identify distinct multidimensional data-derived physiological states from routine ICU data. Unlike approaches that cluster patients once at baseline and then track deviations, STREAM continuously identifies physiological states across time using temporal snapshots of clinical data. A consensus voting algorithm based on optimal transport distances detects meaningful changes in population patterns, indicating state transitions. STREAM's core innovation lies in mapping individual patients onto these population-derived states to create personalized state progression profiles. This approach enables identification of patients who deviate substantially from typical illness patterns by consistently remaining outside their expected state boundaries. Such state outliers may represent high-risk populations experiencing atypical physiological patterns. This approach preserves multidimensional physiology, discovers states from data without predetermined categories, and explains which variables are most associated with state assignments and transitions.

We evaluate STREAM using the multicenter electronic ICU Collaborative Research Database (eICU-CRD; N = 158,294) for development and the single-center Medical Information Mart for Intensive Care IV (MIMIC-IV; N = 84,517) database for external validation. STREAM demonstrates strong predictive performance while providing interpretable explanations for each patient's state progression, identifying high-risk state transitions and the physiological factors associated with them. These retrospective findings may warrant prospective evaluation.

Results

Data and cohort overview

Fig 1 summarizes the STREAM workflow from raw clinical data to state detection, patient mapping, and downstream applications including early warning signals and outcome prediction. STREAM was developed and evaluated using 158,294 ICU admissions from the multicenter eICU-CRD for model development and 84,517 ICU admissions from the single-center MIMIC-IV database for external validation (S1 Table). Both cohorts had similar demographic characteristics and severity of illness distributions, supporting the validity of cross-dataset comparison.

Fig 1. STREAM clinical workflow.

Schematic representation of the STREAM framework for processing new patient data. (1) Patient Data Input: laboratory values (Labs), vital signs (Vitals) are collected and processed at each time window (8h, 24h, 48h, etc.). (2) State Assignment: each patient snapshot is assigned to one of five population states (S1-S5) using Mahalanobis distance (MD) to state centroids; the state with minimum MD is selected (example shows S2 selected with MD = 1.8). (3) State Movement and Feature Importance: At each snapshot, the patient's state assignment (example: S4 → S1 → S2 → S5) and feature importance (e.g., GCS, lactate, creatinine at 48hrs) are determined. (4) Downstream Applications: STREAM outputs support three clinical functions: risk alerts based on state outlier detection, mortality prediction via XGBoost models using 34 features, and interpretability through feature importance analysis. Abbreviations: MD, Mahalanobis distance; S1-S5, data-derived physiological states 1-5; GCS, Glasgow Coma Scale; Lac, lactate; Cr, creatinine.

Twenty-six routinely collected clinical measurements spanning organ function (kidney, liver, hematologic), metabolic status (glucose, electrolytes, acid–base balance), and monitored physiology (hemodynamics, respiratory function, neurologic status) were used to develop STREAM (Table 1). Each ICU stay was represented by time-based snapshots covering a pre-admission window, followed by snapshots at 8, 16, and 24 hours, then at 48 and 72 hours, and daily from day 4 to day 10, yielding longitudinal profiles of each patient's clinical data. These longitudinal profiles formed the foundation for state discovery and individualized patient mapping reported below.

Table 1. Clinical features used in STREAM.

Category	Feature	Unit	Description
Kidney Function
	Creatinine	mg/dL	Serum creatinine level
	Blood Urea Nitrogen (BUN)	mg/dL	Blood urea nitrogen level
Hematology
	Hemoglobin	g/dL	Blood hemoglobin concentration
	Hematocrit	%	Red blood cell volume percentage
	Platelets	×10³/µL	Platelet count
	White Blood Cells (WBC)	×10³/µL	White blood cell count
	Red Blood Cells (RBC)	×10⁶/µL	Red blood cell count
	Mean Corpuscular Hemoglobin (MCH)	pg	Average hemoglobin per RBC
	Mean Corpuscular Volume (MCV)	fL	Average RBC volume
	MCHC	g/dL	Mean corpuscular hemoglobin concentration
	Red Cell Distribution Width (RDW)	%	Variation in RBC size
Electrolytes
	Sodium	mEq/L	Serum sodium level
	Potassium	mEq/L	Serum potassium level
	Chloride	mEq/L	Serum chloride level
	Calcium	mg/dL	Serum calcium level
	Bicarbonate	mEq/L	Serum bicarbonate level
Metabolism
	Glucose	mg/dL	Blood glucose level
	Anion Gap	mEq/L	Calculated anion gap
	Lactate	mmol/L	Blood lactate level
Vital Signs
	Heart Rate Maximum	bpm	Highest heart rate in window
	Heart Rate Minimum	bpm	Lowest heart rate in window
	Mean Arterial Pressure (MAP)	mmHg	Average arterial pressure
	SpO2 Minimum	%	Lowest oxygen saturation
	Respiratory Rate Maximum	breaths/min	Highest respiratory rate
Neurologic
	Glasgow Coma Scale Maximum	3–15	Best neurologic status
	Glasgow Coma Scale Minimum	3–15	Worst neurologic status

26 routinely collected clinical measurements spanning organ function (kidney), hematology, electrolytes, metabolism, vital signs, and neurologic status. Demographics (age and gender) are included as separate features for a total of 28 base features. All features are available in standard ICU electronic health records.

STREAM physiological state discovery

Five distinct data-derived physiological states were identified across the ICU course in eICU-CRD (Fig 2A) using a voting system that combines three distance metrics from optimal transport theory. These states represent physiological patterns detected at different snapshots and are not hierarchical in nature. The first transition between states was detected within 24 hours of ICU admission, with subsequent transitions occurring at day 3 (72 hours), 6 and 8 of the ICU stay.

Fig 2. Physiological state discovery and characterization in eICU-CRD.

(A) Unsupervised state discovery. STREAM identifies five recurrent data-derived physiological states (States 1–5) across ICU snapshots from pre-admission through day 10. (B) State clinical signatures. Bar plots show the top variables characterizing each state. State 1: calcium, platelets, chloride, MCH, MCV. State 2: BUN, bicarbonate, creatinine, anion gap, RDW. State 3: bicarbonate, WBC, potassium. State 4: platelets, MCHC, BUN, RDW. State 5: platelets, GCS minimum, SpO₂ minimum, creatinine. Abbreviations: BUN, blood urea nitrogen; WBC, white blood cell count; MCHC, mean corpuscular hemoglobin concentration; GCS, Glasgow Coma Scale; SpO₂, oxygen saturation; MCH, mean corpuscular hemoglobin; MCV, mean corpuscular volume; RDW, red cell distribution width.

Each state exhibited a distinct clinical signature reflecting characteristic patterns of critical illness progression (Fig 2B). State 1 was characterized by electrolyte and hematologic abnormalities including calcium, chloride disturbances, and red cell indices (MCH, MCV, platelets) [12]. State 2 showed elevations in renal and metabolic markers including BUN, creatinine, bicarbonate, anion gap, and RDW. State 3 was characterized by inflammatory and metabolic features including elevated WBC count, bicarbonate, and potassium abnormalities [13]. State 4 demonstrated hematologic changes with platelets, MCHC, BUN, and RDW elevations. State 5 showed multi-organ involvement with depressed Glasgow Coma Scale scores, low SpO₂, elevated creatinine, and platelet abnormalities [14,15].

Patient state mapping, alignment, and feature importance

Throughout the ICU stay, patients were assigned to the nearest state based on Mahalanobis distance from state centroids at every snapshot, creating a state progression pathway. For each state, we identified all unique patients who entered that state at any time during their ICU course and calculated the proportion who died in ICU. State 1 had the highest mortality rate (5.5%), followed closely by State 5 (5.2%) (Fig 3A). States 2, 4, and 3 had lower mortality rates (2.5%, 2.0%, and 3.7%, respectively). Notably, although States 1 and 5 showed similar mortality rates, their clinical signatures differ markedly (Fig 2B): State 1 is characterized by hematologic and electrolyte abnormalities, whereas State 5 reflects multi-organ failure with neurologic and respiratory compromise. Optimal-transport segmentation produced higher mortality discrimination than classical change-point detection (AUROC 0.863 to 0.932 vs 0.828 to 0.906 across horizons; S7 Table). Gaussian mixture models identified only three states and, operating in reduced principal component space, could not yield the feature-importance geometry on which STREAM depends (S6 Fig). Unlike both alternatives, optimal transport does not require the number of states to be specified in advance.

Fig 3. State mortality and geometric alignment patterns in eICU-CRD.

(A) ICU mortality by states visited during the ICU course. State 1 (5.5%), State 5 (5.2%), State 3 (3.7%), State 2 (2.5%), State 4 (2.0%). (B) Mortality versus state alignment. ICU mortality increases as alignment to assigned state clouds decreases (percent of ICU time inside the 95% state boundaries). State outliers (0–10% alignment) have 37.6% ICU mortality versus 2.3% for patients with 90–100% alignment (16-fold difference). State-specific outlier rates are in Section S.R.4 in S1 Text.

In addition to patient state assignment, we determined how well each patient's measurements matched their assigned state. We defined state outliers as patients who fell outside the 95% confidence boundary of their assigned state, indicating physiological patterns that deviated substantially from typical state characteristics. ICU mortality was 37.6% in patients with 0–10% alignment compared with 2.3% for patients who remained inside state boundaries (90–100% alignment). Mortality decreased progressively as alignment increased (Fig 3B). The five-state structure was stable across consensus thresholds from 0.45 to 0.55, with the value used (0.5) lying within this range (S4 Fig), and the outlier-mortality association was likewise stable across confidence boundaries from the 90th to the 99th percentile (S5 Fig). Notably, state outliers showed elevated mortality across all five states, regardless of whether the state itself was low-risk or high-risk (Section S.R.4 in S1 Text).

Fig 4 illustrates a representative patient that demonstrates a high-risk state progression with feature importance profiles. At ICU admission, the patient was assigned to State 1 as a state outlier, remaining outside state boundaries during the first 24 hours with high Mahalanobis distance, where the features most associated with this state reflected metabolic stress (potassium and bicarbonate abnormalities) (Fig 4A–4B). By day 3, the patient transitioned to State 5; over the subsequent days, falling hemoglobin and platelet counts emerged as dominant features. Although the patient was in State 4 and within its state boundaries on days 4 and 5, conditions returned to State 5 (days 6–8), where the patient remained until death. Feature importance profiles reveal the features most associated with risk at each snapshot. Notably, feature importance changed even when the patient remained in the same state. While in State 1, for example, dominant features shifted from potassium and RDW at admission to glucose and anion gap by day 3, demonstrating that STREAM can detect evolving pathophysiology before state transitions occur.

Fig 4. Patient history panel generated by STREAM.

Example high-risk patient state movement.(A) State progression across ICU intervals (State 1 → State 5 → State 4 → State 5) with death. (B) Geometric alignment over time. Mahalanobis distance to the assigned state centroid with in-cloud status (inside/outside the 95% state boundary). (C) Time-resolved feature importance highlighting variables associated with state maintenance or shifts at selected intervals. Feature colors denote physiological domains (hematologic, hemodynamic, neurologic, respiratory, electrolyte). The patient shown is a real, de-identified eICU-CRD patient, not a synthetic or schematic example; ‘expired’ refers to ICU mortality.

Mortality prediction using gradient boost model

XGBoost (extreme gradient boosting) models trained with STREAM-derived state geometry features predicted ICU mortality in eICU-CRD (S2 Table) cohort. To ensure that predicted probabilities reflected observed outcome frequencies, we applied post-hoc calibration to our model using Platt scaling and isotonic regression. Calibration substantially improved, with expected calibration error decreasing from 0.037 (uncalibrated) to 0.005 with Platt scaling and to 0.002 with isotonic regression (Section S.R.1 in S1 Text; S1 Fig). Discriminative performance was strong across time horizons: area under the receiver operating characteristic curves (AUROC) was 0.863 at 8 hours, 0.873 at 24 hours, 0.890 at 48 hours, 0.903 at 72 hours, and 0.932 using complete ICU stay data (Table 2). Corresponding area under the precision-recall curve (AUPRC) ranged from 0.368 at 8 hours to 0.561 for full stay. At prespecified Youden-optimal thresholds, the model maintained high sensitivity (0.77 to 0.84) and very high negative predictive value (0.98 to 0.99) across horizons, with positive likelihood ratios rising from 3.47 at 8 hours to 6.69 for the full stay (Table 2). The modest positive predictive value (0.18 to 0.28) reflects the low prevalence of ICU mortality rather than poor performance; the prevalence-independent likelihood ratios confirm useful discrimination. External validation in MIMIC-IV showed the same pattern (Table 3).

Table 2. Predictive performance of STREAM-based ICU mortality models in eICU-CRD.

Time window	AUROC (95% CI)	AUPRC (95% CI)	Threshold	Accuracy	Sensitivity	Specificity	PPV	NPV	LR+	LR-
8 hours	0.863 (0.860-0.866)	0.368 (0.360-0.375)	0.45	0.774	0.789	0.773	0.179	0.983	3.47	0.27
24 hours	0.873 (0.868-0.878)	0.401 (0.386-0.416)	0.50	0.809	0.766	0.812	0.190	0.984	4.08	0.29
48 hours	0.890 (0.886-0.893)	0.452 (0.436-0.468)	0.43	0.803	0.811	0.802	0.189	0.987	4.10	0.24
72 hours	0.903 (0.898-0.908)	0.485 (0.474-0.495)	0.49	0.837	0.803	0.838	0.220	0.987	4.97	0.24
Full stay	0.932 (0.930-0.933)	0.561 (0.549-0.573)	0.47	0.873	0.836	0.875	0.275	0.990	6.69	0.19

Performance of XGBoost models trained on STREAM-derived state-geometry features for predicting ICU mortality in eICU-CRD, using a patient-level 80–20 train-test split, with all metrics computed on the held-out 20% test set. AUROC and AUPRC are reported with 95% bootstrap confidence intervals. Accuracy, sensitivity, specificity, PPV, NPV, and likelihood ratios are reported at the Youden-optimal operating threshold for each horizon. ICU mortality prevalence in the cohort was 5.4%; the low PPV reflects this low base rate, while the high NPV and low LR- indicate reliable identification of low-risk patients. AUROC, area under the receiver operating characteristic curve; AUPRC, area under the precision-recall curve; PPV, positive predictive value; NPV, negative predictive value; LR + , positive likelihood ratio; LR-, negative likelihood ratio.

Table 3. Generalization to MIMIC-IV: Performance of STREAM-based ICU mortality prediction.

Time window	MIMIC AUROC (95% CI)	eICU AUROC	Δ AUROC	Threshold	Accuracy	Sensitivity	Specificity	PPV	NPV	LR+	LR-
8 hours	0.798 (0.796-0.799)	0.863	-0.065	0.55	0.742	0.710	0.744	0.180	0.970	2.78	0.39
24 hours	0.815 (0.813-0.816)	0.873	-0.058	0.54	0.736	0.745	0.736	0.174	0.975	2.82	0.35
48 hours	0.836 (0.835-0.838)	0.890	-0.054	0.49	0.732	0.787	0.728	0.177	0.979	2.89	0.29
72 hours	0.857 (0.857-0.858)	0.903	-0.046	0.50	0.746	0.813	0.741	0.190	0.982	3.14	0.25
Full stay	0.899 (0.899-0.900)	0.932	-0.033	0.51	0.805	0.834	0.803	0.240	0.985	4.23	0.21

Performance of the eICU-trained STREAM models applied to MIMIC-IV without retraining. AUROC is reported with a 95% bootstrap CI, Δ AUROC shows a 3–7 percentage-point decrease from eICU, and all threshold metrics plus AUPRC (0.326, 0.348, 0.386, 0.419, and 0.516 for the 8h, 24h, 48h, 72h, and full-stay horizons) are reported at the MIMIC-IV Youden-optimal threshold. With the eICU-derived thresholds applied without re-tuning (true prospective deployment), discrimination was unchanged and sensitivity remained high (0.88 to 0.90) with excellent NPV, the lower specificity reflecting a between-site calibration shift that small local recalibration corrects. At the 6.9% MIMIC-IV ICU mortality prevalence the low PPV reflects this base rate, while the high NPV and low LR- confirm that low-risk patients are reliably identified in the external cohort.

We performed a SHapley Additive exPlanations (SHAP) analysis to identify the features that most strongly influenced mortality predictions (Fig 5; Section S.R.2 in S1 Text; S2 Fig). At 8 hours, clinical variables such as lactate dominated predictions (Fig 5 A). By 72 hours, state geometry features, particularly Mahalanobis distance, emerged as the strongest contributor (Fig 5 B), demonstrating the increasing value of longitudinal, trajectory-based information as more temporal data accrued. Across all evaluated time windows, state geometry features, including mean, minimum, and maximum Mahalanobis distance, consistently ranked among the top predictors and frequently surpassed the importance of individual physiological measurements. Age and Glasgow Coma Scale values also remained influential, alongside markers of renal function (creatinine, BUN), inflammatory markers (WBC), and metabolic stress (lactate).

Fig 5. SHAP feature importance analysis comparing early and extended prediction horizons.

(A) 8-hour mortality model. Top features by mean |SHAP| include lactate, age, MAP, GCS maximum, Mahalanobis distance, and SpO₂ minimum. (B) 72-hour mortality model. Mahalanobis distance becomes the top feature, with age, GCS, MAP, and SpO₂ remaining prominent. SHAP summary plots show per-patient contributions (x-axis) for each feature (rows), with color indicating feature value.

For completeness, we compared STREAM prediction model with a baseline model using only raw clinical features. Models that employ STREAM defined state geometry features consistently outperformed baseline models across all time horizons (S3 Table; Section S.R.6 in S1 Text). Adding state geometry features significantly improved discrimination over a raw-feature baseline at every horizon. DeLong tests were significant throughout (z = 28.1 to 31.7, all p < 0.001). The integrated discrimination improvement ranged from 0.115 to 0.152 and the category-free net reclassification improvement from 0.498 to 0.699 (all p < 0.001), confirming improved risk separation and reclassification, with the same pattern in MIMIC-IV (S3 Table).

External validation in MIMIC-IV

To assess generalizability, we applied the eICU-trained model to the independent MIMIC-IV dataset (N = 84,517). Cross-dataset application required quantile-to-quantile distribution alignment to address systematic measurement differences between datasets (Section S.R.3 in S1 Text; S4 Table).

State-specific mortality patterns replicated in MIMIC-IV (Fig 6A): State 1 showed highest mortality (6.9% vs 5.5% in eICU-CRD), followed by State 5 (6.4% vs 5.2%), while States 2 and 4 remained lowest-risk. The state outlier-mortality relationship also replicated (Fig 6B): state outliers (0–10% time inside state boundaries) had 33.5% ICU mortality versus 3.2% for patients who remained inside state boundaries (90–100%), a 10-fold difference. State outlier mortality rates were consistent across all states, confirming that state outlier status confers elevated risk independent of state assignment (Section S.R.4 in S1 Text).

Fig 6. Cross-dataset validation of state mortality and geometric alignment patterns in MIMIC-IV.

(A) ICU mortality by states visited when MIMIC-IV patients are projected onto eICU-derived state boundaries. State 1 (6.9%), State 5 (6.4%), State 3 (5.1%), State 2 (2.0%), State 4 (1.8%). (B) Mortality versus state alignment. Outliers (0–10% alignment) have 33.5% ICU mortality versus 3.2% for 90–100% alignment (10-fold difference), reproducing the alignment–mortality gradient. State-specific outlier rates are in Section S.R.4 in S1 Text.

The eICU-trained model maintained strong performance without retraining (Table 3). AUROC decreased by only 3–7% across all time windows: 0.798 at 8 hours, 0.815 at 24 hours, 0.836 at 48 hours, 0.857 at 72 hours, and 0.899 for full stay (Section S.R.4 in S1 Text). When the eICU-trained model was applied to MIMIC-IV without distribution alignment (unit conversion and scaling only), discrimination was essentially unchanged (AUROC 0.790 to 0.899, within 0.008 of the aligned results; S6 Table), indicating that the alignment did not inflate external performance. Geometric alignment features remained among top predictors in both datasets (Section S.R.5 in S1 Text; S3 Fig).

Discussion

Critical care monitoring currently relies on threshold-based alerts and composite scores that compress multidimensional physiology into a single value, limiting their ability to capture evolving patterns of organ dysfunction. STREAM offers an alternative paradigm by using optimal transport theory to define data-driven physiological states and track how individual patients move through this state space over time using routinely collected ICU variables. STREAM first assigns each patient snapshot to the nearest physiological state using Mahalanobis distance and then uses this geometry to identify state outliers, patients whose measurements deviate substantially from the characteristic pattern of their assigned state.

A unique feature of STREAM is its use of optimal transport theory to stratify clinically relevant states over time. While optimal transport has been applied in medical imaging (for example, brain morphometry classification) and computational biology (for example, single-cell trajectory inference), its use in critical care remains limited. To our knowledge, only Wang and colleagues have applied optimal transport in this setting, using Sinkhorn distance for cross-hospital sepsis domain adaptation, a fundamentally different application than physiological state identification [16]. As shown in Fig 2, five temporal physiological states were identified by unsupervised optimal-transport detection of population-level distributional shifts across consecutive ICU snapshots, each with distinct clinical signatures and mortality risks ranging from 2.0% in State 4 to 5.5% in State 1. States with similar mortality can still differ clinically; for example, States 2 and 4 have comparable mortality (2.5% versus 2.0%) but distinct signatures, with State 2 marked by elevations in BUN, bicarbonate, creatinine, anion gap, and RDW, and State 4 characterized by abnormalities in platelets, MCHC, BUN, and RDW. STREAM provides patient-specific feature importance that identifies which biomarkers are most associated with each individual's state assignment and transitions. For state transitions, STREAM quantifies which features are most associated with the change; for patients remaining in the same state, it tracks whether the feature importance profile is stable or shifting over time. This distinction is clinically meaningful: two patients in State 1 may have different profiles (for example, one dominated by thrombocytopenia and hypocalcemia, another by macrocytosis and hyperchloremia), and a single patient's profile can change substantially while state classification remains unchanged, as illustrated by the evolving feature importance pattern in Fig 4C despite periods of state maintenance.

STREAM can also be compared with other temporal state modeling approaches. Hidden Markov models represent each patient as a sequence of latent states governed by a transition matrix and assume the Markov property, whereby the next state depends only on the current one. Semi-Markov extensions relax this assumption by modeling state durations explicitly, which is relevant in critical care because the probability of transition can depend on the time already spent in a state. Both families, however, generally require the number of latent states to be fixed in advance or selected using a secondary criterion. Alaa and van der Schaar, for example, used the Bayesian Information Criterion to select a four-state hidden absorbing semi-Markov model in 6,094 hospital episodes, predicting ICU transfer 8–9 hours in advance with a higher AUPRC than conventional hidden Markov models and established clinical risk scores [17]. STREAM differs in two respects. First, states are not latent variables but explicit geometric regions of the measured feature space, each defined by a centroid and covariance structure. Each patient snapshot is assigned to its nearest state using Mahalanobis distance, allowing a patient’s state progression to be read directly from the data rather than inferred through a transition matrix. Second, the number and duration of states emerge from the optimal-transport consensus rather than from a model-selection criterion.

In addition to state assignment, STREAM also designates individual cases as state outliers. These are patients whose measurements fall outside the 95% confidence boundary of their assigned state. State outliers experienced higher ICU mortality (37.6%) compared with 2.3% for patients who remained inside state boundaries, representing a 16-fold risk difference. State outliers are atypical relative to other ICU patients in the same temporal state, not abnormal in an absolute clinical sense; even within this critically ill population, such deviation marks substantially higher risk. This represents a large separation in mortality risk. Prior phenotyping studies have reported smaller separations in other settings. However, these are not direct comparisons, because cohorts, endpoints, and study designs differ. In ARDS, Calfee et al. identified inflammatory sub-phenotypes with about a 2-fold difference in 90-day mortality, and treatment effects differed by subtype. In sepsis, temperature-trajectory sub-phenotypes showed 4-fold higher odds of mortality for the hypothermic group versus the reference group [18,19]. Prior work using routine laboratory panels shows that mortality risk is carried by the overall pattern across tests, not by any single marker alone. Lind and colleagues showed that adding a set of common clinical chemistry tests to standard risk factors improved mortality prediction in two large cohorts [20]. Our findings extend this idea to the STREAM state space. A patient can become a state outlier without one lab being severely abnormal. Several mildly abnormal values can add up and shift the patient far from the state center, capturing risk that single threshold alerts may miss. State outlier status appears to be a marker of clinical instability that replicated across both datasets (Section S.R.4 in S1 Text).

STREAM’s predictive performance compares well with contemporary machine learning early warning approaches when viewed in the context of published results (Table 4). At 8 hours, STREAM achieved AUROC 0.863 (95% CI 0.860 to 0.866), providing risk stratification before traditional severity scores can be calculated. Reported AUROCs in related studies include PICTURE (AUROC 0.819) [21], eCART (AUROC 0.801) [22], HAVEN (AUROC 0.901) [23], and iMORS (internal AUROC 0.964, external 0.870–0.890) [24]. STREAM showed a modest reduction on external validation. This magnitude of drop is smaller than reductions reported in other cross cohort settings, including an 18% AUROC reduction reported by Chen et al. [25] for sepsis associated acute kidney injury prediction and a 7–10% reduction reported for iMORS across external cohorts. STREAM decreased by only 3–7% between eICU-CRD and MIMIC-IV. These values are not direct comparisons, because the studies use different endpoints, prediction windows, and cohorts. Taken together, this level of detail suggests potential clinical applications, such as characterizing which organ system is most strongly associated with deterioration and supporting interpretable communication about a patient’s trajectory. However, these applications remain hypotheses generated by retrospective analysis and would require prospective evaluation before clinical use.

Table 4. Comparison of STREAM with existing ICU risk prediction models.

Model	Year	Internal AUROC	External AUROC	Δ AUROC	Key Feature
STREAM (72 h)	2026	0.903	0.857	~5%	State Based OT
STREAM (8 hours)	2026	0.863	0.798	~7.5%	Early prediction
iMORS	2024	0.964	0.870–0.890	~7–10%	Ensemble DL+LGBM
XMI-ICU [26]	2025	0.910	0.85–0.88	~5%	MI patients only
eCART	2014	0.801	0.75–0.80	~5%	Ward patients
PICTURE	2021	0.819	—	—	XGBoost+SHAP
HAVEN	2021	0.901	~0.88	~3%	UK hospitals
Epic EDI [27]	2020	0.65–0.80	Variable	Variable	Proprietary
APACHE II	1985	0.58–0.74	0.58–0.74	—	14 variables
APACHE IV	2006	0.76–0.88	0.76–0.88	—	142 variables
SOFA	1996	0.69–0.82	0.69–0.82	—	6 organ systems

Abbreviations: OT, optimal transport; DL, deep learning; LGBM, LightGBM; MI, myocardial infarction; EDI, Epic Deterioration Index. Values for comparator models extracted from original publications. STREAM rows highlighted in green.

We acknowledge limitations to this study. We used only retrospective data from US databases, so generalization to international populations and prospective clinical settings will require further evaluation, especially because temporal, geographical, and domain generalizability represent distinct validation requirements. In addition, the current framework analyzes only routinely collected structured clinical data and does not incorporate richer sources such as ventilator waveforms, medical imaging, or unstructured clinical documentation, including physician progress notes and nursing documentation, that might further refine state definitions. With strong predictive performance, calibration, and external validation, these retrospective findings support geometric, state-based monitoring as a promising approach to bedside decision support, while underscoring the need for prospective evaluation before clinical implementation.

STREAM demonstrates the feasibility of state-based geometric analysis as a framework for characterizing patient trajectories and supporting interpretable clinical monitoring. By combining optimal transport-derived states, patient-level mapping, feature importance, and state outlier detection, STREAM links risk stratification to the clinical measurements that define each physiological pattern. Strong and well-calibrated predictive performance, limited loss of accuracy on external validation, and a consistent association between state alignment and mortality support the potential of state-aware, geometry-based monitoring to complement static severity scores and single-parameter alerts. Because STREAM relies exclusively on routinely collected longitudinal clinical data, the framework is, in principle, extensible to settings such as emergency departments, general wards, chronic disease management, and post-surgical recovery. However, state geometries would need to be learned and validated separately for each new clinical context. Future prospective studies should test whether integrating STREAM into clinical workflows, particularly by identifying state outliers and their associated features, can support earlier and more targeted clinical attention and may improve care efficiency in critical care.

Materials and methods

Ethics statement

This study was a secondary analysis of two de-identified, credentialed-access critical care databases available through PhysioNet: the eICU Collaborative Research Database (eICU-CRD v2.0) and the Medical Information Mart for Intensive Care IV (MIMIC-IV v3.1). eICU-CRD was de-identified in accordance with the Safe Harbor provision of the US Health Insurance Portability and Accountability Act, and its re-identification risk was certified by Privacert as meeting Safe Harbor standards (Cambridge, MA; HIPAA Certification no. 1031219–2). The collection and release of MIMIC-IV were reviewed and approved by the Institutional Review Board of Beth Israel Deaconess Medical Center, which granted a waiver of informed consent; secondary analyses of these de-identified records are exempt from further review. Access to both databases requires completion of human-subjects research training and acceptance of the PhysioNet Credentialed Health Data Use Agreement, both of which were completed by the authors. Because this study used only pre-existing, de-identified data, it did not constitute human subjects research and required no additional institutional review board approval. The authors made no attempt to re-identify individuals or redistribute the data. No new patient-level data were generated [28,29].

Data sources and study population

We used eICU-CRD version 2.0 for model development and internal validation. This multicenter database contains 200,859 ICU admissions from 335 ICUs across 208 US hospitals between 2014 and 2015, representing diverse practice settings including academic medical centers, community hospitals, and specialty facilities spanning medical, surgical, cardiac, and neurological intensive care units. The database includes minute-by-minute vital signs, laboratory results, medications, and clinical notes, with a median ICU length of stay of 1.9 days (IQR: 1.0-3.8 days). We included adult patients (≥18 years) with ICU stays exceeding 8 hours, yielding 158,294 ICU admissions for analysis. We selected this dataset to demonstrate STREAM's capability to identify data-derived physiological states and predict outcomes using only routine clinical measurements available in standard ICU care, without requiring specialized monitoring or research-grade data collection. MIMIC-IV 3.1 was used exclusively for external validation. This single-center database contains 86,540 ICU admissions from Beth Israel Deaconess Medical Center (Boston, MA) between 2008 and 2019, representing a large academic medical center with medical, surgical, trauma, and cardiac ICUs. After applying identical inclusion criteria (age ≥ 18 years, ICU stay >8 hours), we analyzed 84,517 ICU admissions. MIMIC-IV provides an independent test of validation across different hospitals, geographic regions, patient populations, and time periods. The primary endpoint was ICU mortality, defined as death during the ICU admission, determined from the unit discharge status (unit_expire_flag) in eICU-CRD and the equivalent ICU mortality flag (icu_expire_flag) in MIMIC-IV.

Feature selection and temporal structure

Clinical measurements.

We analyzed 26 routinely collected clinical measurements to represent critical organ systems without requiring specialized equipment (Table 1). To identify the most frequently measured parameters, we ranked all laboratory tests by measurement frequency across the eICU-CRD cohort. We selected the top 19 most frequently measured laboratory values, then added routinely monitored vital signs and neurologic assessments including heart rate extrema (maximum and minimum), mean arterial pressure, oxygen saturation minimum, respiratory rate maximum, and Glasgow Coma Scale extrema (maximum and minimum). This yielded 26 features spanning kidney function (creatinine, blood urea nitrogen), hematology (hemoglobin, hematocrit, platelets, white blood cells, red blood cells, red cell indices), electrolytes (sodium, potassium, chloride, calcium, bicarbonate), metabolism (glucose, anion gap, lactate), and cardiorespiratory-neurologic status. Among demographic data, age and gender were selected. We excluded composite severity scores (APACHE, SOFA) and outcome indicators to prevent the model from learning direct associations with labels rather than underlying physiological patterns.

Snapshot creation.

Each patient's timeline began at ICU admission (time zero) and was expressed in hours. We divided each ICU stay into time-based snapshots: one pre-admission snapshot (−24–0 hours, capturing emergency department or ward data, if available), snapshots at 8, 16, and 24 hours, followed by snapshots at 48 and 72 hours, and daily snapshots from day 4 to day 10. This structure provides fine temporal resolution during the critical first day when many clinical decisions occur, followed by daily resolution to track longer-term trajectories. Clinical measurements were assigned to snapshots based on timestamp, and all values within each snapshot were averaged per feature to create one physiologic profile per snapshot.

Data preprocessing

Missing data imputation.

ICU data contain substantial missingness due to selective laboratory ordering based on clinical need. For the unsupervised state-discovery pipeline, we used Multiple Imputation by Chained Equations (MICE) to estimate missing values while preserving relationships between variables [30]. For each feature type, we applied appropriate imputation methods: continuous laboratory values used predictive mean matching, categorical variables used mode-based selection, ordinal variables used proportional odds models, and binary indicators used logistic regression. For time-varying measurements such as Glasgow Coma Scale and vital signs, interior gaps were filled by linear interpolation, and the most recent value was extended forward or the earliest value backward to maintain clinical continuity (Section S.M.1 in S1 Text).

Feature standardization.

After imputation, we standardized all features to comparable scales. Continuous laboratory values and vital signs were scaled to [0,1] using minimum and maximum values observed in the eICU-CRD cohort. Ordinal features (e.g., categorical laboratory interpretations) were mapped to [0,1] according to their natural ordering. Binary features remained as 0 or 1. All standardization parameters (minimum, maximum, means) were calculated exclusively from eICU-CRD training data [31].

Distance-based state detection

Overview.

STREAM detects when the population transitions between data-derived physiological states by monitoring changes at three different levels: individual laboratory values, overall patient condition, and patient similarity patterns. We call this the 3-OT (Triple Optimal Transport) system, which operates like three independent judges examining the same data from different perspectives.

The three detection methods.

OT-1D uses 1-Wasserstein distance computed separately for each of the 26 clinical features between consecutive snapshots [32].This univariate optimal transport metric quantifies distributional shifts in individual biomarkers across the population, detecting feature-specific transitions such as systematic increases in lactate distributions or widening of mean arterial pressure distributions. OT-2D uses the 2-Wasserstein distance to measure movement in the complete 26-dimensional physiological space between consecutive snapshots [33]. This multivariate optimal transport metric quantifies the minimum work required to transform one snapshot's patient distribution into the next, capturing coordinated changes across multiple organ systems simultaneously. OT-Geometric uses Gromov-Wasserstein distance to measure changes in the internal geometric structure of patient populations across consecutive snapshots [34].

Consensus voting system.

Each method generates a distance between consecutive snapshots. To determine which time points represent true state transitions rather than random fluctuations, each method independently applies three unsupervised threshold-detection algorithms: KneeLocator (elbow detection) [35], Gaussian Mixture Models (cluster intersection) [36], and K-means clustering (midpoint boundaries) [37]. Each algorithm produces a binary (yes/no) vote for each snapshot. The three algorithm votes are aggregated to produce one single vote per detection method. Final transition decisions are made by combining the three OT method votes using confidence-weighted consensus score, defined as:

$$\begin{array}{c}\text{ConsensusScore}(t)=\frac{{\sum }_i{w}_i·c_i·v_i(t)}{{\sum }_i{w}_i·c_i}\end{array}$$

where V_i(t)∈{0,1} is the binary vote from method i at snapshot t, W_i is the base weight, and C_i is a confidence score calculated from each method's signal dynamic range and consistency across snapshots. A state transition is recorded when ConsensusScore(t) > 0.5, corresponding to agreement from at least two of the three methods.

Implementation for eICU-CRD.

For the multicenter eICU-CRD cohort, we used a consensus threshold of 0.5, requiring agreement from at least two of the three methods. This choice accounts for heterogeneity across hospitals and patient populations while balancing sensitivity to avoid false positives driven by isolated fluctuations in individual methods. Mathematical formulations for the 3-OT consensus voting system are provided in Section S.M.2 in S1 Text.

Comparison with alternative segmentation methods.

To assess whether optimal transport contributes beyond simpler unsupervised alternatives, we compared the 3-OT consensus segmentation against two alternatives: classical change-point detection by binary segmentation on the multivariate population signal [38], and Gaussian mixture models fitted in a three-component principal component space with the number of components selected by the Bayesian Information Criterion [39,40]. For classical change-point detection, we re-derived the state boundaries, recomputed the state centroids and geometry features, and retrained the XGBoost models with identical hyperparameters and cross-validation. Gaussian mixture models were evaluated at the state-identification stage only; because they operate in a reduced principal component space, per-feature importance scores cannot be computed, so this comparison is reported at the level of the number and placement of detected states rather than downstream prediction.

Sensitivity analyses.

We tested the stability of the five-state structure by varying the consensus threshold from 0.25 to 0.60 and re-deriving the states at each value, and the stability of the outlier definition by varying the confidence boundary from the 90th to the 99th percentile and recomputing outlier and inside-state mortality.

Individual patient mapping and state assignment

After identifying population-level states using the 3-OT voting system, each patient snapshot was assigned to its nearest state to track individual state progressions through the ICU course. For each detected state, a centroid (mean feature vector) was calculated in the 26-dimensional feature space, and an inverse covariance matrix was computed to capture the state's characteristic variance structure.

Patient assignment used Mahalanobis distance to account for feature correlations and variable scales within each state [41]. For each patient at each snapshot, Mahalanobis distance was calculated from the patient's feature vector to each state centroid. Patients were assigned to the state with the smallest Mahalanobis distance, generating a sequence of state labels over time that constitutes the patient's state progression pathway.

Patient-level alignment metrics were computed to quantify how well each patient matched their assigned state. At each snapshot, we calculated the normalized Mahalanobis distance and determined whether the patient fell inside or outside the 95% confidence boundary of their assigned state. A snapshot was classified as outside its assigned state when its squared Mahalanobis distance exceeded the 95th-percentile quantile of the chi-squared distribution with degrees of freedom equal to the number of state-discovery features [26]; the per-state covariance was estimated empirically with ridge regularization and a pseudo-inverse for numerical stability. The 95% boundary assumes approximate multivariate Gaussianity within each state; given the skewness of ICU data this is an approximation, and the outlier metric is interpreted as an empirical risk indicator rather than a formal test. Alignment was defined as the percentage of snapshots in which a patient remained inside the boundaries of their assigned states across their ICU stay. State outliers were defined as patients who fell outside the 95% confidence boundary of their assigned state.

Feature importance calculation

Following state assignment at each snapshot, we computed snapshot-specific feature importance scores to quantify each clinical variable's contribution to individual patient state progressions. We developed a hybrid importance scoring system that adapts to different state progression patterns while maintaining interpretability [42].

The system distinguishes between two clinical scenarios. For patients who remained in the same state across consecutive snapshots, maintenance importance quantifies which features characterize a stable physiological pattern. For each feature, maintenance importance measures how strongly that feature distinguishes the patient's assigned state from alternative states, calculated as the ratio of the distance to the assigned state centroid to the average distance to other state centroids. Features with high maintenance importance indicate strong specificity for the current state assignment.

For patients transitioning between states, transition importance measures how each feature contributed to movement from the previous state toward the new state. Transition importance combines changes in the feature that increase distance from the previous state centroid with simultaneous movement toward the new state centroid. Features exhibiting large, coordinated changes aligned with the transition direction receive higher scores. All feature importance scores were normalized to sum to 1.0 for each patient at each time snapshot, enabling interpretation as percentage contributions. This normalization ensured compatibility across patients with different state progression patterns and levels of clinical severity. Mathematical formulations are provided in Section S.M.3 in S1 Text.

Predictive modeling and performance validation

Model architecture and feature engineering.

To evaluate the predictive capability of state-based features, we trained XGBoost gradient boosting models for mortality prediction across multiple prediction horizons [43]. The feature matrix for each patient included 26 clinical variables (Table 1), 2 demographic variables (age, gender), and 6 state geometry descriptors (first state, last state, current Mahalanobis distance, and mean/minimum/maximum Mahalanobis distances), totaling 34 features.

Model training.

Models employed binary logistic objective with conservative hyperparameters to limit overfitting: learning rate 0.05, maximum 64 leaves per tree, minimum child weight 6, L1 regularization (alpha) 0.8, and gamma 0.1. We used GPU-accelerated histogram-based tree construction for 2000 boosting rounds with early stopping patience of 100 rounds. We implemented patient-level train-test splits (80–20) with outcome stratification to ensure that no individual patient's data appeared in both training and test sets. Class imbalance was addressed by setting the XGBoost scale_pos_weight parameter to (1 − p)/p, where p represents the mortality rate in the training set. Complete hyperparameter details are provided in Section S.M.4 in S1 Text. Data leakage prevention measures are summarized in S5 Table.

Probability calibration.

To ensure reliable probability estimates for clinical application [44], we reserved 20% of the training data as a calibration set and applied two post-hoc calibration methods: Platt scaling (logistic regression on model scores) and isotonic regression. Calibration quality was assessed using Expected Calibration Error (ECE), which measures the weighted average deviation between predicted probabilities and observed frequencies across probability bins [45], and Hosmer-Lemeshow goodness-of-fit test, which compares observed versus expected outcomes across risk deciles [46]. Successful calibration was indicated by low ECE values (<0.05) and non-significant Hosmer-Lemeshow test results (p > 0.05).

Performance metrics.

Model discriminative performance was evaluated using area under the receiver operating characteristic curve (AUROC) and area under the precision-recall curve (AUPRC) on the held-out test set. At the Youden-optimal threshold we additionally reported accuracy, sensitivity, specificity, positive and negative predictive value, and positive and negative likelihood ratios. We assessed performance for ICU mortality prediction across all five time horizons using identical test patients. To quantify the incremental value of the state geometry features, we compared the full STREAM model against a baseline model trained on raw clinical features without geometry features, using out-of-fold predictions on identical patients. The two AUROCs were compared with the DeLong test [47], and we computed the Integrated Discrimination Improvement and the category-free Net Reclassification Improvement [48,49]each with 95% confidence intervals from 2,000 bootstrap resamples [50]

Cross cohort validation and generalization

To assess generalizability, we applied the eICU-trained models to MIMIC-IV without retraining. Cross-dataset application required addressing systematic differences in measurement distributions. We implemented quantile-to-quantile distribution alignment [51]. which maps each MIMIC-IV patient's feature values to equivalent positions in the eICU-CRD reference distribution while preserving patient rankings. This step re-expresses each cohort's measurements in a common reference distribution and removes the need for manual unit conversion when applying the model at a new site; because it preserves each patient's rank within their own cohort, it does not inflate discrimination, as confirmed by the no-alignment sensitivity analysis (S6 Table). Following distribution alignment, MIMIC-IV snapshots were processed through the frozen state detection framework, with each snapshot assigned via Mahalanobis distance to eICU-derived state centroids. Hybrid feature importance scores were calculated identically to eICU-CRD processing. As a sensitivity analysis, we also applied the eICU-trained models to MIMIC-IV after unit conversion and scaling only, without quantile-to-quantile distribution alignment, and recompared discrimination across all horizons.

We evaluated: (1) state-specific mortality rates compared with eICU-CRD patterns, (2) alignment-mortality relationships across ten alignment categories (0–10%, 10–20%, 20–30%, 30–40%, 40–50%, 50–60%, 60–70%, 70–80%, 80–90%, 90–100% time inside state boundaries), (3) predictive performance using AUROC and AUPRC, and (4) feature importance consistency using SHAP values. Detailed validation procedures, alignment quality metrics, and cross-dataset comparison analyses are provided in Section S.M.5 in S1 Text.

Implementation and statistical analysis

All analyses were executed in Python 3.12. Data manipulation was performed using Pandas for tabular operations and NumPy for vectorized numerical computations. Statistical functions were implemented using SciPy, including Wasserstein distance calculations for one-dimensional optimal transport, Mahalanobis distance for state assignment, cosine similarity for geometric comparisons, entropy calculations, chi-squared tests, and signal processing functions for peak detection during threshold optimization. The Python Optimal Transport (POT) library provided implementations of 2-Wasserstein distance for multidimensional population movement detection and Gromov-Wasserstein distance for internal geometric structure analysis within the 3-OT consensus voting system.

Scikit-learn provided preprocessing utilities for the supervised mortality models, including training-only median imputation for continuous variables and mode imputation for categorical variables, K-means clustering for threshold boundary detection, Gaussian Mixture Models for adaptive threshold estimation, and evaluation metrics including receiver operating characteristic curves, precision-recall curves, and calibration assessment tools. XGBoost gradient boosting models were trained using GPU-accelerated histogram-based tree construction. Feature importance was assessed using SHapley Additive exPlanations (SHAP) values calculated through TreeExplainer for gradient boosted models. Permutation-based feature importance with bootstrap resampling provided complementary importance estimates and confidence intervals.

Quantile-to-quantile transformation enabled distribution alignment between MIMIC-IV and eICU-CRD datasets while preserving patient rankings within each cohort. Patient-level train-test splits with outcome stratification ensured that no individual patient appeared in both training and evaluation sets, preventing data leakage. Bootstrap resampling (2,000 iterations) was used to calculate 95% confidence intervals for performance metrics. Publication-quality figures were generated using Matplotlib and Seaborn with consistent styling conforming to journal specifications.

Supporting information

S1 Table. Cohort characteristics of eICU-CRD and MIMIC-IV datasets.

(DOCX)

S2 Table. Feature composition and data availability by prediction time horizon.

(DOCX)

S3 Table. Baseline model comparison and incremental value of state geometry features (DeLong test, integrated discrimination improvement, and net reclassification improvement).

(DOCX)

S4 Table. Cross-dataset distribution alignment quality.

(DOCX)

S5 Table. Data leakage prevention measures across the STREAM pipeline.

(DOCX)

S6 Table. External validation in MIMIC-IV without quantile-to-quantile distribution alignment.

(DOCX)

S7 Table. Mortality discrimination using optimal-transport versus classical change-point segmentation, with the Gaussian mixture state count for reference.

(DOCX)

S1 Fig. Calibration analysis for the STREAM ICU mortality prediction model.

(A) Reliability diagram comparing predicted probabilities with observed mortality for the original model (red), Platt scaling (green), and isotonic regression (blue); the dashed line indicates perfect calibration. (B) Predicted probability distributions showing concentration of the original model in very low-probability ranges (<0.1) and more appropriate spread after calibration. (C) Expected Calibration Error (ECE) comparison demonstrating substantial reduction in calibration error for both calibrated models relative to the original, confirming that post-hoc calibration successfully corrected probability estimates while maintaining identical discriminative performance (AUROC).

(TIF)

S2 Fig. SHAP Feature Importance Analysis Across All Temporal Horizons for eICU-CRD Mortality Prediction.

(A) 8-hour model, (B) 24-hour model, (C) 48-hour model, (D) 72-hour model, and (E) Full ICU stay model. Violin plots display SHAP value distributions for the top 15 features at each prediction horizon, where values to the right increase predicted mortality and values to the left decrease risk; color indicates underlying feature value (blue = low, pink = high).

(TIF)

S3 Fig. Cross-Dataset SHAP Analysis: eICU-Trained Models Applied to MIMIC-IV Data.

(A) 8-hour model, (B) 24-hour model, (C) 48-hour model, (D) 72-hour model, and (E) Full ICU stay model. Violin plots show SHAP value distributions for frozen eICU-trained XGBoost models applied to MIMIC-IV without retraining, demonstrating feature importance stability across datasets.

(TIF)

S4 Fig. Sensitivity of the five-state structure to the consensus threshold.

The number of detected data-derived physiological states is plotted as the confidence-weighted consensus threshold is varied from 0.25 to 0.60. Five states are produced across the majority-rule band (0.45 to 0.55), within which the published value (0.5) lies, showing the result does not depend on the exact threshold.

(TIF)

S5 Fig. Sensitivity of the outlier-mortality association to the confidence boundary.

ICU mortality for state outliers (0–10% time inside the boundary) and inside-state patients (90–100%) is shown as the boundary is varied from the 90th to the 99th percentile, in eICU-CRD (blue) and MIMIC-IV (red). The large mortality separation is stable across all boundary choices.

(TIF)

S6 Fig. Segmentation-method comparison.

(A) Population-level inter-snapshot Euclidean distance, the signal used by classical change-point detection. (B) Gaussian mixture model selection by Bayesian and Akaike information criteria across candidate state counts. These analyses underlie the comparison of optimal transport against change-point and Gaussian mixture segmentation.

(ZIP)

S1 Text. Supplementary Methods (S.M.1–S.M.5) and Supplementary Results (S.R.1–S.R.6).

(DOCX)

Data Availability

This study used two de-identified, third-party databases not owned by the authors: the eICU Collaborative Research Database (eICU-CRD v2.0) and MIMIC-IV (v3.1). Both databases are available through PhysioNet (MIT Laboratory for Computational Physiology) under credentialed access to any researcher who completes the required human-subjects research training and accepts the PhysioNet Credentialed Health Data Use Agreement. The authors had no special access privileges unavailable to other researchers. eICU-CRD v2.0 is available at https://doi.org/10.13026/C2WM1R (descriptor: Pollard TJ, Johnson AEW, Raffa JD, Celi LA, Mark RG, Badawi O. Sci Data. 2018;5:180178. doi:10.1038/sdata.2018.178). MIMIC-IV v3.1 is available at https://doi.org/10.13026/kpb9-mt58 (descriptor: Johnson AEW, Bulgarelli L, Shen L, et al. Sci Data. 2023;10:1. doi:10.1038/s41597-022-01899-x). The PhysioNet platform is described by Pollard T, et al. Nature Health. 2026. doi:10.1038/s44360-026-00096-z. No new patient-level data were generated in this study.

Funding Statement

The author(s) received no specific funding for this work.