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Learning a Continuous Sepsis Severity Score Without Hour-by-Hour Supervision: A Two-Site Retrospective Study
Kevin Zhu, Ryan Zhang, Baraa Abed, Tilendra Choudhary, Malvern Madondo, Mehak Arora, Yixuan Yang, Alasdair Gent, Aditya Nagori, Omer T. Inan, Krista L. Haines, Patrick Georgoff, Suresh M. Agarwal, Vijay Krishnamoorthy, Tetsu Ohnuma, Mihai V. Podgoreanu, Michael R. Pinsky, Gilles Clermont, Craig M. Coopersmith, Craig S. Jabaley, Rishikesan Kamaleswaran
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Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 93%
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Summary
This study developed a continuous, hourly sepsis severity index using Trajectory-ranked Reward Extrapolation (T-REX), an inverse reinforcement learning method. Using data from 29,116 MIMIC-IV patients and 7,691 Emory Healthcare patients, the model learned severity scores based on mortality ranking over 72-hour windows without hour-by-hour supervision. The index successfully separated survivors from non-survivors across baseline severity strata, correlated with physiological changes (lactate, MAP, creatinine), and demonstrated prognostic value comparable to established indices like SOFA-2 and APACHE II, though cross-institutional generalization was moderate.
Entities (11)
Relation Signals (9)
MIMIC-IV → contains → Sepsis Patients
confidence 98% · Data came from two independent ICU cohorts: MIMIC-IV ... A total of 29,116 ... adult patients meeting Sepsis-3 criteria
Emory Healthcare → provideddatafor → Sepsis Severity Index
confidence 95% · and Emory Healthcare (2015–2022) ... We conducted a retrospective two-cohort study
T-REX → usedfor → Sepsis Severity Index
confidence 95% · we present a severity index learned through one such IRL method, Trajectory-ranked Reward Extrapolation (T-REX)
Sepsis Severity Index → comparedto → SOFA-2
confidence 92% · Our index also correlated with established indices ... SOFA-2
Sepsis Severity Index → comparedto → APACHE II
confidence 92% · Our index also correlated with established indices ... APACHE II
Duke University → affiliatedwith → Kevin Zhu
confidence 90% · Kevin Zhu 1,3 ... 1 Department of Biomedical Engineering, Duke University
Sepsis Severity Index → correlateswith → Lactate
confidence 90% · Within-patient change in the index correlated with change in lactate (Spearman rho = 0.39)
Sepsis Severity Index → correlateswith → Mean Arterial Pressure
confidence 85% · Similar, weaker correlations were found for MAP
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Abstract
Abstract:Currently used sepsis severity indices rely on fixed variables and weights established decades ago, which are coarsely discretized and calibrated to a cohort that no longer reflects contemporary critical care. No alternative learned directly from patient trajectories is in routine use. We conducted a retrospective two-cohort study on a total of 29,116 and 7,691 adult patients meeting Sepsis-3 criteria from two hospital systems in Massachusetts and Georgie, respectively. We developed a sepsis index using 43 routinely charted variables over a 72-hour treatment window. Unlike previous studies, we use mortality as a treatment-level ranking signal rather than a per-state target, allowing credit to be redistributed non-uniformly across timesteps. Evaluation was done on a permanent 20% test holdout, using clinical vignettes and Spearman correlation. Uncertainty intervals were obtained by bootstrap resampling of whole patients. Under this ranking scheme, non-survivors scored 1.19-1.64 points higher than survivors on a 0-10 scale within all strata of baseline SOFA-2, with similar results stratifying within lactate, mean arterial pressure (MAP), and creatinine. Within-patient change in the index correlated with change in lactate (Spearman rho = 0.39; n = 1,854). Similar, weaker correlations were found for MAP and creatinine. On a cohort level, cross-institutional agreement measured by Spearman correlation between models trained on different sites, were 70-77% of same-site correlation. External within-patient correlations were 0.54 and 0.59 against ceilings of 0.92 and 0.90. Our index also correlated with established indices, while null controls stayed near zero. Our index demonstrated hourly prognostic information that meaningfully separates patient outcomes and is consistent with clinical expectation, indicating potential as a decision support tool complementing clinical judgement.
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- Source: https://arxiv.org/abs/2608.27421v1
- Canonical: https://arxiv.org/abs/2608.27421v1
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Learning a Continuous Sepsis Severity Score Without Hour-by-Hour Supervision: A Two- Site Retrospective Study Kevin Zhu 1,3 , Ryan Zhang 2,3 , Baraa Abed 2,3 , Tilendra Choudhary, PhD 3,4 , Malvern Madondo, PhD 3,4 , Mehak Arora 2,3 , Yixuan Yang 2,3 , Alasdair Gent, PhD 3,4 , Aditya Nagori, PhD 3,4 , Omer T Inan, PhD 5,6 , Krista L. Haines, DO 3,7 , Patrick Georgoff, MD 3 , Suresh M. Agarwal, MD 3 , Vijay Krishnamoorthy, MD, PhD 4,7 , Tetsu Ohnuma, MD, PhD, MPH 4 , Mihai V. Podgoreanu, MD 4 , Michael R. Pinsky, MD, CM, Dr hc, FCCP, MCCM 8,9 , Gilles Clermont, MD, MSc 8,9 , Craig M. Coopersmith, MD, FACS, FCCM 10,11 , Craig S. Jabaley, MD, FCCM 10,12 , Rishikesan Kamaleswaran PhD 1,2,3,4 1 Department of Biomedical Engineering, Duke University, Durham, NC. 2 Department of Electrical and Computer Engineering, Duke University, Durham, NC. 3 Department of Surgery, Duke University School of Medicine, Durham, NC. 4 Department of Anesthesiology, Duke University, Durham, NC. 5 School of Electrical and Computer Engineering, Georgia Institute of Technology, GA. 6 Department of Biomedical Engineering, Georgia Institute of Technology, GA. 7 Department of Population Health Sciences, Duke University School of Medicine, Durham, NC, USA. 8 Department of Critical Care Medicine, University of Pittsburgh, PA. 9 School of Medicine, University of Pittsburgh, PA. 10 Emory Critical Care Center, Emory Healthcare, Atlanta, GA. 11 Department of Surgery, Emory University School of Medicine, Atlanta, GA. 12 Department of Anesthesiology, Emory University School of Medicine, Atlanta, GA. Abstract Objective: Currently used sepsis severity indices rely on fixed variables and weights established decades ago, which are coarsely discretized and calibrated to a cohort that no longer reflects contemporary critical care. No alternative learned directly from patient trajectories is in routine use. Design: A retrospective two-cohort study. Setting: Two hospital systems in Massachusetts and Georgia. Patients: A total of 29,116 and 7,691 adult patients meeting Sepsis-3 criteria, excluding outliers from likely data input error. Interventions: None. Measurements and Main Results: We developed an hourly sepsis index using 43 routinely charted variables over a 72-hour treatment window. Unlike previous studies, we use mortality as a treatment-level ranking signal rather than a per-state target, allowing credit to be redistributed non-uniformly across timesteps instead of propagated backward as a constant label. Evaluation was done on a permanent 20% test holdout, using clinical vignettes and Spearman correlation. Uncertainty intervals were obtained by bootstrap resampling of whole patients. Under the mortality ranking, non-survivors scored 1.19–1.64 points higher than survivors on a 0–10 scale within all four strata of baseline SOFA-2, with similar results stratifying within lactate, mean arterial pressure (MAP), and creatinine. Within-patient change in the index correlated with change in lactate (Spearman ρ = 0.39; n = 1854); similar, weaker correlations were found for MAP and creatinine. On a cohort level, cross-institutional agreement, measured by Spearman correlation between models trained on different sites, were 70–77% of same-site correlation. External within-patient correlations were 0.54 and 0.59 against ceilings of 0.92 and 0.90. Our index also correlated with established indices, while null controls stayed near zero. Conclusions: An index learned solely from outcome-ranked trajectories demonstrated hourly prognostic information that meaningfully separates patient outcomes and is consistent with clinical expectation, indicating potential as a decision support tool complementing clinician judgment. Key Points Question: Can a continuous, hourly severity index for sepsis be learned directly from ICU stays ranked only by patient outcome, without consensus-assigned variables, weights, or hourly clinician labels? Findings: In this two-site retrospective study (MIMIC-IV, n = 29,116; Emory Healthcare, n = 7691), an index supervised by the above ordering separated survivors from non-survivors within every stratum of presenting severity, moved with concurrent physiologic change, and lost its signal under label ablation, though cross-institution agreement fell short of the within-institution ceiling. Meaning: A severity index estimated solely from ranking outcomes may warrant use as a prognostic measure, pending local validation and prospective evaluation. Introduction Sepsis is life-threatening organ dysfunction caused by a dysregulated host response to infection [1]. It is among the largest single contributors to global mortality: the Global Burden of Disease 2021 analysis estimated 166 million incident cases and 21.4 million sepsis-related deaths worldwide in 2021, approximately 31.5% of all deaths that year [2], and sepsis is present in more than half of adult hospitalizations ending in death or discharge to hospice, and is the immediate cause of death in two-thirds of those [3]. A common practice in ICUs is the use of severity scores, a numerical value that measures the seriousness, intensity, or critical impact of a condition, injury, or system failure [4]. Some of the most commonly used scores for this method are Sequential Organ Failure Assessment (SOFA) [4], Acute Physiology and Chronic Health Evaluation I (APACHE I) [5], and the Systemic Inflammatory Response Syndrome (SIRS) criteria [6]. These indices remain the operational standard despite being calibrated to a case mix that no longer reflects contemporary critical care [7]. Efforts to modernize them have concentrated on updating their weights: SOFA-2 recalibrates organ-dysfunction thresholds against contemporary outcomes [8], and APACHE IV refits mortality coefficients on a newer cohort [9]. Neither has displaced its predecessor in routine practice due to adoption obstacles [8, 10], but the more consequential point is that both preserve the design their predecessors established. Each assigns points fit to the association between a patient’s state at a single timepoint and subsequent mortality, and each is applied as an independent assessment at each time it is computed. Machine-learned deterioration models produce estimates at a finer temporal resolution, but the prominent examples apply their supervision pointwise. Models such as DeepSOFA [11] and the dynamic mortality model of Thorsen-Meyer et al. [12] issue hourly predictions against a single patient-level outcome, so each hour of an eventual non-survivor’s stay is individually fit toward high risk, including hours in which that patient was not yet deteriorating. Time-to-event formulations [13] weight hours by proximity to the endpoint, but the target remains attached to each timepoint. Our supervision derives from the same outcome but constrains only the accumulated score across a window relative to another window’s, leaving the allocation of that score across hours unconstrained. Sepsis is a disorder defined by its course, and the same physiology carries different meaning in a patient stabilizing than in one deteriorating toward the same state; we therefore ask whether a severity index learned from the relative ordering of whole treatment windows, using methods derived from inverse reinforcement learning (IRL), can represent that course more faithfully than a sequence of independently supervised timepoints. IRL is a branch of reinforcement learning (RL), in which an agent learns some optimal behavior by interacting with its environment [14]. In RL, the reward function defines the specific task the agent is optimizing in the environment. For example, in a navigation task, the reward could be a negative value correlated with the distance from the destination. The closer to the destination the agent gets, the higher the reward. This could also apply to clinical settings: a reward for a sepsis treatment task would be some value correlated with how likely the patient will survive. Under this interpretation, the reward function derived from historical practice could serve as a patient severity score. The goal of IRL is to learn such rewards, given expert trajectories. Thus, we present a severity index learned through one such IRL method, Trajectory-ranked Reward Extrapolation (T-REX) [15] (Fig. 1). Across two independent ICU cohorts, we trained the index under three outcome-based ranking schemes and evaluated it against established severity indices, its own label ablations, and clinical expectations of how severity should respond to physiologic change. The index correlated with SOFA-2, APACHE I, and SIRS, and discriminated in-hospital mortality as well as direct outcome supervision, while both ablations retained no signal. It also carried prognostic information beyond the presenting state, separating survivors from non-survivors within every stratum of baseline severity and moving with concurrent physiologic change over a patient’s own stay. Methods Study Design We conducted a retrospective pilot study to develop and evaluate a severity score for sepsis learned directly from patient trajectories rather than assembled from pre-specified variables and weights. Data came from two independent ICU cohorts: MIMIC-IV (version 3.1, Beth Israel Deaconess Medical Center, 2008–2022) [16] and Emory Healthcare (2015–2022). We included adults 18 years or older who met Sepsis3 criteria during an ICU admission (Supplementary Materials, Data Processing). This study was reviewed and approved by the Duke University Health System Institutional Review Board and was determined to be exempt under IRBPro00114885. Demographics and clinical characteristics of both cohorts are summarized in Table 1. The outcome label is a discharge disposition that counts hospice discharge as death following the endpoint used in US sepsis mortality epidemiology [3], which occurred in 23.7% of Emory patients and 15.1% of MIMIC-IV patients. Within each site, 20% of patients were set aside as a permanent test holdout (1,538 Emory and 5,823 MIMIC-IV admissions), stratified on mortality, and never used for training or model selection. The remaining patients were divided into four mortality-stratified folds (partitions of patients never seen together during training), each serving in turn as the validation set while the other three were used for training. The treatment window spanned up to 72 hours, from 24 hours before to 48 hours after sepsis onset, and we collected forty-three physiologic, laboratory, and treatment variables (Supplementary Materials, Table S1). Data Processing Following the methods of Arora et al. [17], patient observations were aggregated hourly and truncated to physiologically plausible ranges. Missing values were imputed by forward fill within each admission, with residual missingness imputed using the corresponding median of the training partition. Score Development We followed the training methodology of T-REX, using a multi-layer perceptron to learn the severity score (Supplementary Materials, Algorithm 1) [15]. T-REX uses a ranking scheme to compare pairs of patient stays; we compared a total of three schemes, which we call mortality, mortality-plus-treatment, and severity-matched. Mortality preferred survivors to non-survivors. Mortality-plus-treatment added treatment intensity as a tiebreaker within the survivor and non- survivor groups. Patient stays with lower cumulative vasopressor dose in the treatment window were preferred to those with higher dosage; if patients had the same survivorship and vasopressor dose, cumulative fluids given in the treatment window was used to break ties. This encodes the clinical principle that lower effective dose is preferred, conditional on survival. Finally, severity- matched preferred survivors to non-survivors; however, a pair of trajectories was only compared if both trajectories fell in the same age, baseline lactate, and baseline modified SOFA-2 bins. This was designed to separate deaths from survivors, but only within strata of comparable baseline severity. Ablation Studies Two ablations were constructed for every ranking scheme and trained identically to the real models. In the shuffled ablation, 50% of preference pairs were inverted at training time. In the random ablation, preference labels were randomized. Because these models share the architecture, the input features, and the data geometry of the real models and differ only in the preference labels, they bound how much of any reported effect can arise without a learnable preference signal. Evaluation Because no ground-truth severity label exists against which a learned index can be scored directly, we evaluated the index indirectly along two axes: the prognostic information content, and the clinical validity of the learned index. Baseline-stratified trajectory analysis (Supplementary Materials, Evaluation Method 1) was used to determine whether the index separates survivors from non-survivors within strata of the presenting state. Within-patient response analysis (Supplementary Materials, Evaluation Method 2) compared the change in the index across each patient’s window with the concurrent change in physiology. Paired cross- institutional scoring (Supplementary Materials, Evaluation Method 3) was applied to every held- out patient to assess the external validity of the score generation method. Additional tests comparing the learned index to established severity scores and robustness of learning (Supplementary Materials, Evaluation Method 4), and performance against a methodological baseline (Supplementary Materials, Evaluation Method 5) were also completed. To evaluate clinical suitability, two goals are emphasized: 1) prognostic information beyond the patient’s presenting state and 2) an hourly reading that remains interpretable at an institution other than the one it was trained at. In addition, a two-part evaluation is proposed: first, ensuring the index’s outcome separation is not a restatement of baseline severity, and second, assessing the alignment between movement in the index and concurrent physiologic change to confirm concordance with clinical expectation. Spearman correlations (labeled as ρ) were averaged in Fisher z space, including within every bootstrap replicate. Uncertainty intervals were obtained by bootstrap resampling of whole patients; all intervals are 95% percentile intervals from a fixed random seed, computed from either 1000 replicates or 200 replicates depending on compute required. Results Model Selection Among the evaluated ranking schemes, the mortality scheme was selected as the final model for evaluation. This model was chosen as all schemes correlated similarly with established severity indices, and the mortality scheme uses the simplest ranking and achieved the highest agreement between replicates across seeds and data folds. Patient Stratification Figure 2 shows the learned score over time from sepsis onset in MIMIC-IV, separately for survivors and non-survivors, within four strata of baseline illness severity defined by each patient’s worst SOFA-2 in the first 24 hours. Bins were ≤ 3 (n = 1045), 4-5 (n = 2016), 6-7 (n = 1475), and ≥ 8 (n = 1287), with in-hospital mortality of 9.3%, 8.9%, 15.0%, and 29.5%, respectively. The score is placed on a frozen 0–10 scale oriented so that higher is sicker, and each curve is the mean across patients of a consensus score formed by averaging the 20 models trained on MIMIC-IV. The mean gap between non-survivors and survivors, averaged over drawn hours, was 1.19, 1.42, 1.36, and 1.64 points across the four strata, so separation was present at every level of presenting severity rather than concentrated in the sickest patients. The same figure stratified on baseline lactate is in the Supplementary Materials (Figure S1) and gave gaps of 1.48, 1.73, and 1.66 points for bins < 2, 2-4, and > 4 mmol/L, with a fourth stratum of patients who had no lactate charted in the first 24 hours separating by 1.33 points. The gap was positive in all eight strata at Emory as well, and MAP and creatinine also showed similar results (Supplementary Materials). Comparison Against Physiology Figure 3 asks whether the learned score moves with a patient’s physiology over that patient’s own stay, which the cross-sectional response shapes cannot establish. For each held-out MIMIC- IV patient, the change in score between the first and last k hours of the treatment window, where , was compared with the change in each of three variables over the same two blocks, with patients contributing only where the variable was measured and not imputed in both blocks. Change in score tracked change in lactate (Spearman ρ = 0.39; n = 1,854) and was strongest among patients whose own baseline lactate was already high, rising from 0.25 to 0.55. Increases in mean arterial pressure (MAP) decreased score and did so most strongly among patients presenting below 65 mmHg and weakest among patients presenting above 85 mmHg. Change in creatinine was correlated with change in score through Spearman correlation only. Compared to lactate, the associations for MAP and creatinine were much weaker. There was also no visual separation between survivors and non-survivors for all panels. Cross-Institutional Performance Figure 4 asks the transfer question at the level of one patient’s time course: when models trained at one institution and models trained at the other score the same held-out patient, do the two series behave similarly? For every held-out patient, the consensus of models trained on MIMIC and models trained on Emory were correlated across that patient’s own hours. The median within-patient Spearman correlation between MIMIC-IV-trained and Emory-trained models was 0.54 (95% CI, 0.53–0.55) over the MIMIC-IV patients and 0.59 (0.56–0.61) over the Emory patients, against within-institution ceilings of 0.92 and 0.90. The two negative controls bound the other end. Agreement was nonetheless widely spread, with an interquartile range of 0.20 to 0.76 in MIMIC-IV and 0.27 to 0.79 at Emory, and 14.2% and 12.7% of patients returned a negative correlation. Both sets of scores are standardized over the same held-out states, which fixes each series’ mean at zero by construction; only rank and within-patient shape are comparable, and no difference in level exists to be interpreted. Comparison of Ranking Schemes Figure 5 shows a sanity check: agreement between the three ranking schemes and four established severity indices in MIMIC-IV. The Emory panel and the full scheme-by-index grid are in the Supplementary Materials. Across the twelve combinations of ranking scheme and index, the mean Spearman correlation between the score and the severity index ran from 0.25 to 0.46 in MIMIC-IV and from 0.18 to 0.59 at Emory. Both ablations sat near zero: across the 24 shuffled-preference and randomized-label conditions at each site, and no mean correlation exceeded 0.08 in absolute value. The ordering of agreement across the four indices was identical in all six combinations of ranking scheme and site: highest against APACHE I with age, then APACHE I without age, then SOFA-2, and lowest against SIRS. Agreement between independently trained replicates of the learned score declined monotonically as the perturbation grew from random seed to cross-validation fold to change of institution. For the mortality scheme, models differing only in random seed agreed at a mean Spearman correlation of 0.79 at Emory and 0.78 in MIMIC-IV. Changing the cross-validation fold cost little, while changing institution cost substantially more, reducing agreement to 0.63 and 0.56, which retained 77% and 70% of the corresponding within-institution agreement. The mortality- plus-treatment and severity-matched schemes follow similar shapes. Adding treatment intensity to the ranking degraded both ends of that ladder: models differing only in random seed agreed at 0.51 at Emory and 0.67 in MIMIC-IV, and models trained at different institutions at 0.44 and 0.38. Severity matching also degraded model performance, but not by as much (Supplementary Materials). Mortality Discrimination Against Controls Discrimination of in-hospital mortality was assessed at the admission time point, over the first 24 hours of the treatment window, against both null ablations and the methodological baseline. Both ablations lost all essentially all signal: across the ranking schemes and both sites, the median per- model AUROC of the shuffled and randomized conditions ran from 0.486 to 0.533, against 0.764 in MIMIC-IV and 0.742 at Emory for the mortality scheme. Taken as a consensus over its 20 models, the mortality score matched a consensus ensemble of baseline neural nets trained pointwise against mortality at both sites: 0.791 versus 0.789 in MIMIC-IV (Spearman ρ = 0.74) and 0.765 versus 0.768 at Emory (ρ = 0.43). Individual models trailed the baseline by a small but consistent margin (median difference, –0.017 in MIMIC-IV and –0.022 at Emory). The full grid of ranking schemes, ablations, and comparators is in the Supplementary Materials. Discussion This pilot investigates whether an index built solely from ranked trajectories behaves enough like a severity score to be worth developing into one. Our preliminary findings suggest that preference-based reward learning such as T-REX offers a promising route to a continuous, per- hour severity index for sepsis, learned from the relative ordering of outcome-ranked trajectories rather than from cross-sectional mortality associations, whether these are encoded through expert consensus, as in SOFA, or through regression coefficients rounded to integer points, as in SAPS I and APACHE I. The separation between survivors and non-survivors within every stratum of presenting severity indicates that such a score can carry outcome-relevant information on a finer timescale than indices scored once daily. Directional responses to within-patient change, including movement with rising lactate, suggest that the index tracks the physiology a clinician would watch. Yet agreement between an index trained at one institution and one trained at the other fell well short of the within-institution ceiling, so a score developed elsewhere requires local validation before it can be read at the bedside. Our score differs from established severity indices in how it is learned and from previously reported learned scores in the breadth of its inputs. Conventional indices assign points calibrated to the association between a patient’s state at a single timepoint and subsequent mortality; computing such an index more frequently yields a sequence of independent cross-sectional assessments, each scored without reference to the hours around it. Our index is instead fit to an objective defined over whole treatment windows, ranked by outcome, so that supervision constrains the accumulated score across a window rather than attaching the endpoint label to each state within it. Although the learned reward is evaluated pointwise at inference, this training signal permits an early hour of an eventual non-survivor to score low without penalty, provided the window as a whole orders correctly against a survivor’s. Because it draws on a broad set of partially overlapping physiologic signals rather than a small, fixed panel, no single measurement is required for the score to be produced: it remained computable for the 1,632 of 5,823 MIMIC-IV patients (28.0%) with no lactate value in the first 24 hours of the treatment window, a subgroup for whom lactate-dependent components of conventional indices are undefined. Comparing the beginning and end of each patient’s window, the score moved in directions consistent with clinical expectation, rising with lactate, falling as MAP returned to nominal ranges, and increasing in rank with creatinine (Figure 3). At the cohort level, survivors and non-survivors separated within every stratum of presenting severity at essentially every hour from onset onward (Figure 2), suggesting that the hourly estimate reflects information not fully captured by severity at presentation. A key consideration in interpreting the score is that it is learned from care as delivered and therefore reflects the treatment patterns of the cohorts it was trained on. This is visible in its response to changing creatinine, which strengthened from Spearman ρ = 0.09 among patients whose baseline creatinine was below 1.2 mg/dL to ρ = 0.19 in the 1.2–2.0 mg/dL range, then fell to 0.06 with an interval spanning zero above 2.0 mg/dL. In the stratum where a rising creatinine should carry the most weight, the score largely stopped tracking it; this is contrasted with lactate, which displayed a monotonically increasing correlation as severity increased. Caruana et al. described this pattern in a pneumonia risk model that learned asthma to be protective, because asthmatic patients received more aggressive care and better outcomes followed: a model fit to observed outcomes encodes the response to treatment alongside the illness itself [18]. Our state space offers no way to separate the two, as our 43 inputs do not contain vasopressor, fluid, renal replacement, or mechanical ventilation variables. Thus, our current score has no way to differentiate between patients whose creatinine is high and untreated and those already receiving renal support. Future iterations should add organ-support variables to the state and test whether the sickest strata recover the expected response. The score’s ability to generalize across institutions is bounded, and the bound depends on how the preferences were ranked. Agreement between independently trained models declined monotonically as the perturbation grew from random seed to cross-validation fold to change of institution, and under the mortality scheme it retained most of its within-institution. Adding treatment intensity to the ranking degraded both ends of that ladder; that scheme is therefore not simply harder to transfer but less reproducible within a single site, before any distribution shift is involved. One potential explanation of this phenomenon is that vasopressor and fluid exposure record how a particular unit responds to deterioration rather than the state of the patient, since dose, timing, and threshold could differ between units. Treatment exposure would need to be expressed in a practice-independent form before it could serve as a transferable ranking signal. Measured within individual patients rather than across pairs of models, the median agreement between MIMIC-IV-trained and Emory-trained scores was much lower than their within- institution ceilings. One notable limitation is that a non-negligible percentage of patients at each institution had the two scores rank their hours in opposite directions. For these patients, a score trained on a different cohort could over- or underestimate their true severity. Prospective evaluation at a third institution, with local recalibration, would establish how far that residual can be reduced. The learned severity index functions as a retrospective analysis tool that assigns an hourly severity value to a patient’s state from routinely charted variables alone, without consensus- assigned weights or manual scoring. Because agreement between institutions fell short of the within-institution ceiling, the next phase of this work will involve retrospective validation at additional health systems with local recalibration, followed by prospective evaluation of safety and usability. Integration as a continuously updating display within existing EHR systems represents a practical pathway toward clinical implementation. Additionally, since the underlying methodology draws from IRL, this score could be used to train reinforcement learning algorithms for future clinical decision support systems, such as those suggesting vasopressor or fluid dosage. Conclusions In this pilot study, we demonstrate that preference-based IRL could be applied to sepsis severity assessment, yielding a continuous hourly index learned from routinely charted data. T-REX and an outcome-based ranking of septic treatment windows were leveraged to learn a severity index that separated survivors from non-survivors within every stratum of presenting severity and moved with each patient’s own physiology over their stay. Compared with established severity indices and with a network trained pointwise on mortality, it discriminated in-hospital mortality at least as well, though agreement between institutions fell short of the within-institution ceiling. Our findings suggest that outcome-ranked trajectory learning can complement expert-derived scoring in sepsis, provided local validation precedes bedside use. Tables and Figures Table 1: Demographic characteristics of the study population Characteristic Emory (n = 7,691) MIMIC (n = 29,116) Age (y), mean (std) 61.7 (16.6) 63.9 (16.3) Sex, n (%) Female 3,556 (46.2) 12,468 (42.8) Male 4,135 (53.8) 16,648 (57.2) Race, n (%) White 3,362 (43.7) 19,439 (66.8) Black or African American 3,601 (46.8) 3,049 (10.5) Hispanic or Latino — 1,111 (3.8) Asian 253 (3.3) 879 (3.0) American Indian or Alaska Native — 61 (0.2) Native Hawaiian or Other Pacific Islander — 41 (0.1) Other — 989 (3.4) Unknown 475 (6.2) 3,547 (12.2) Hospital length of stay (d), median [IQR] 10.6 [6.0, 18.9] 9.2 [5.6, 16.0] In-hospital death or hospice discharge, n (%) 1,824 (23.7) 4,391 (15.1) Fig. 1: Overview of the severity index pipeline. Hourly physiologic and laboratory data extracted from electronic health records (EHR) are input into the model, which applies trajectory-ranked reward extrapolation (T-REX) guided by an outcome ranking of up-to-72-hour sepsis treatment periods rather than by hourly clinician labels. The network learns to give the better-outcome stay the lower summed score over a 24hour segment, shown here for two mortality-discordant patients matched on baseline severity. The result is a continuous hourly severity index learned from contemporary practice rather than derived by consensus. On this scale (from 0 to 10), 5 marks the mean severity across all patient septic ICU hours, and higher values indicate greater severity. MAP = mean arterial pressure, NEE = norepinephrine equivalent, SOFA-2 = Sequential Organ Failure Assessment version 2. Fig. 2: Learned severity score over the 48 hours after sepsis onset in MIMIC-IV, within four strata of baseline severity defined by each patient’s worst SOFA-2 in the first 24 hours. Top row, mean score among survivors (blue) and non-survivors (orange), with 95% percentile intervals from 1,000 bootstrap resamples of whole patients; curves are drawn only over hours where at least 25% of that outcome group contributes a state. Bottom row, one survivor and one non- survivor per stratum, and triangles mark the start of vasopressors. The score is on a frozen 0–10 scale; higher is sicker, from 20 models trained on MIMIC-IV (4 cross-validation folds × 5 random seeds). Fig. 3: Change in the learned severity score against change in three physiologic variables over the same patient’s stay, among held-out MIMIC-IV patients scored by the mortality-ranked models. Each point is one patient. The left column is the scatter plot for all patients; the columns after are stratified on patient baseline values. The vertical axis is in points of the frozen 0–10 score and is shared across panels. Each panel gives number of patients (n) and the Spearman correlation (ρ), both as a whole cohort and stratified by severity. Blue denotes survivors and orange non-survivors. A similar figure for Emory is presented in the Supplementary Materials. Fig. 4: Agreement between MIMIC-IV-trained and Emory-trained models within individual held-out patients. A: Eight patients, two per institution-by-outcome cell, drawn at random. Each is scored twice, by the 20 Emory-trained models (bluish green) and the 20 MIMIC-IV-trained models (reddish purple). Lines are the consensus across a training site’s models, and bands are the 2.5–97.5 percentile of the individual models. The horizontal axis is hours from sepsis onset, with a dashed line at onset; the vertical axis is the frozen 0–10 score, higher is sicker. B: Cumulative distribution of the within-patient Spearman correlation between the two series at each institution: cross-institution (orange), the within-institution ceiling from 10-against-10 splits of a site’s own models (sky blue), and foreign shuffled (dark gray) and same-site shuffled (light gray) negative controls. Ticks on the x-axis locate the eight patients of A. Fig. 5: Agreement between the learned score and four established severity indices in MIMIC-IV, measured by the Spearman rank correlation between a model’s per-state score and the negated index. Boxes span the interquartile range; the center line is the median, whiskers reach the minimum and maximum, and all 20 models are plotted as points. The white diamond is the mean taken in Fisher z space over the 20 models of each condition. Panels are the four indices, and each ranking scheme within a panel is shown with its two negative controls. Emory results are in the Supplementary Materials. APACHE I APS = APACHE I acute physiology score, implemented without chronic-health points; APACHE I APS + age = the same score with age points. References 1. Singer, M. et al. The third international consensus definitions for sepsis and septic shock (sepsis-3). JAMA 315, 801–810 (2016). 2. Gray, A. P. et al. Global, regional, and national sepsis incidence and mortality, 1990–2021: a systematic analysis. The Lancet Global Health 13, e2013–e2026 (2025). 3. Rhee, C. et al. Prevalence, underlying causes, and preventability of sepsis associated mortality in us acute care hospitals. JAMA Network Open 2, e187571 (2019). 4. Vincent, J.-L. & Moreno, R. Clinical review: scoring systems in the critically ill. Critical Care 14, 207 (2010). 5. Knaus, W. A., Draper, E. A., Wagner, D. P. & Zimmerman, J. E. Apache i: a severity of disease classification system. Critical Care Medicine 13, 818–829 (1985). 6. Bone, R. C. et al. Definitions for sepsis and organ failure and guidelines for the use of innovative therapies in sepsis: The ACCP/SCCM consensus conference committee. Chest 101, 1644–1655 (1992). 7. Soares, M. & Dongelmans, D. A. Why should we not use apache i for performance measurement and benchmarking? Revista Brasileira de terapia intensiva 29, 268–270 (2017). 8. Ranzani, O. T. et al. Development and validation of the sequential organ failure assessment (sofa)-2 score. JAMA 334, 2090–2103 (2025). 9. Zimmerman, J. E., Kramer, A. A., McNair, D. S. & Malila, F. M. Acute physiology and chronic health evaluation (apache) iv: hospital mortality assessment for today’s critically ill patients. Critical Care Medicine 34, 1297–1310 (2006). 10. Quintairos, A., Pilcher, D. & Salluh, J. I. Icu scoring systems. Intensive Care Medicine 49, 223–225 (2023). 11. Shickel, B. et al. Deepsofa: a continuous acuity score for critically ill patients using clinically interpretable deep learning. Scientific reports 9, 1879 (2019). 12. Thorsen-Meyer, H.-C. et al. Dynamic and explainable machine learning prediction of mortality in patients in the intensive care unit: a retrospective study of high-frequency data in electronic patient records. The Lancet Digital Health 2, e179– e191 (2020). 13. Thorsen-Meyer, H.-C. et al. Discrete-time survival analysis in the critically ill: a deep learning approach using heterogeneous data. NPJ digital medicine 5, 142 (2022). 14. Ladosz, P., Weng, L., Kim, M. & Oh, H. Exploration in deep reinforcement learning: A survey. Information Fusion 85, 1–22 (2022). 15. Brown, D., Goo, W., Nagarajan, P. & Niekum, S. Extrapolating beyond suboptimal demonstrations via inverse reinforcement learning from observations, 783–792 (PMLR, 2019). 16. Johnson, A. E. et al. Mimic-iv, a freely accessible electronic health record dataset. Scientific Data 10, 1 (2023). 17. Arora, M. et al. Improving clinical decision support through interpretable machine learning and error handling in electronic health records. Journal of the American Medical Informatics Association 33, 123–132 (2026). 18. Caruana, R. et al. Intelligible models for healthcare: Predicting pneumonia risk and hospital 30-day readmission, 1721–1730 (2015).