Sepsis and septic shock are the leading causes of in-hospital mortality (Liu et al., 2014), and are the costliest medical conditions in the United States (Torio et al., 2016). Improving outcomes in sepsis patients is therefore of great importance to public health. Kumar et al., 2006 showed that every hour of delayed treatment in septic shock increased mortality by ~8%. More recent studies have corroborated this finding, though delayed treatment remains common in current practice (Kumar et al., 2006; Martin-loeches et al., 2015; Ferrer et al., 2014; Levy et al., 2010; Kalil et al., 2017). Consequently, a number of computational approaches for early prediction of sepsis and septic shock using electronic health record (EHR) data have been developed (Henry et al., 2015; Nemati et al., 2018; Mao et al., 2018; Liu et al., 2019). We recently developed a method for predicting patients with sepsis who are likely to transition to septic shock based on the hypothesis that there exists a detectable physiologically distinct state of sepsis, which we identify as the ‘pre-shock state,’ and that entry into this state presages the impending onset of septic shock (Liu et al., 2019). The pre-shock state was characterized by fitting a regression model to classify data from patients with sepsis who never develop septic shock from those who do. This model was used to calculate a time-evolving risk score that can be updated each time a new measurement becomes available. When a patient’s risk score exceeds a fixed threshold (time of early warning/prediction), we predict that the patient has entered the pre-shock state and is therefore highly likely to develop septic shock. Best performance achieved was 0.93 AUC, 88% sensitivity, 84% specificity, and 52% average positive predictive value, with a median early warning time (EWT) of 7 hr. We also showed that a patient’s risk score at the first observation subsequent to threshold crossing was indicative of the confidence of a positive prediction. For some patients, this ‘patient-specific positive predictive value’ was as high as 91%.

The diverse patterns of sepsis make guideline-driven treatment difficult, as guidelines reflect the needs of the ‘average’ patient. Furthermore, treatments are not without risk. For example, high dosages of vasopressors have been associated with increased mortality (Dünser et al., 2009). Overuse of antibiotics is also a concern. Minderhoud et al., 2017 showed that no evidence of bacterial disease is found in almost 30% of patients with suspected sepsis in the emergency department. A study by Kelm et al., 2015 also showed that 67% of sepsis patients treated with early goal-directed therapy (EGDT) developed signs of fluid overload, which in turn increases risk of complications such as hypertension, pulmonary edema, and respiratory failure. It is likely that no single treatment policy is suitable for all sepsis patients, and thus, there has been interest in subtyping and stratifying sepsis patients in hopes of identifying phenotypes relating to patterns of treatment responsiveness. Individual biomarkers such as serum lactate have been used to stratify sepsis patients by mortality (Mikkelsen et al., 2009). Most recently, Seymour et al., 2019 published a clustering study in which four types of sepsis patients were identified using the most abnormal value of 29 clinical variables observed in the 6 hr following hospital admission; these four types of patients differ in mortality and serum biomarkers of immune response.

In this study, we examine the temporal evolution of patient state as assessed using our previously-published method for computing patient risk of transition into septic shock. Previously we analyzed and interpreted this risk score from the perspective of threshold crossing (i.e. if, when, and/or how steeply a threshold crossing occurs), whereas here the time-evolution of risk in the hours following threshold crossing is hypothesized to yield further insight into patient state. We undertake a novel analysis of time-evolving risk scores to discover the distinct patterns of time-evolving risk that exist across patients. The application of spectral clustering to risk score trajectories reveals that patient risk trajectories diverge into four distinct clusters in the time window following early prediction of septic shock. Patients in these clusters stratify by outcome, as measured by prevalence of septic shock and by mortality. Moreover, these four clusters differ in the treatments received, as well as median time to septic shock onset (i.e. median EWT). In the highest-risk group, by time of early warning, fewer patients had been treated with vasopressors and been adequately fluid resuscitated than in the lowest-risk group. Time to septic shock onset was shorter in the highest-risk group as well. Using k-nearest neighbors to predict cluster membership, we are able to reliably assign patients to these risk categories based on their risk score trajectories.

Furthermore, we observe that the transition from sepsis to pre-shock on average occurs on a rapid time scale, with a sharp increase in risk occurring within 30–60 min immediately preceding time of early warning. This rapid change in the risk score is associated with rapid changes in values of systolic and diastolic blood pressure, lactate, and heart rate. Sepsis is defined as dysregulated immune response to infection (Singer et al., 2016). We hypothesize that the rapid transition of risk score results from and is therefore indicative of an abrupt failure of compensatory biological systems to cope with infection, resulting in a change in patient state trajectory that crosses a bifurcation from low to high risk. Such a collapse in compensation, we believe, represents the true onset of septic shock, and thus what we have previously referred to as the pre-shock state represents a potential new data-driven definition of septic shock. Previous studies of dynamical systems models of compensation of inflammatory responses have put forth a similar notion of disease progression in sepsis (Reynolds et al., 2006; Chow et al., 2005; Cameron and Sleigh, 2019; Buchman, 1996). The Infectious Disease Society of America’s recently-published recommended revisions to the National Severe Sepsis and Septic Shock Early Management Bundle (Klompas, 2020) recognizes and acknowledges the ambiguity in determining the time of septic shock onset when applying current definitions, and states that there is a need for a clearer and reproducible definition of septic shock onset.

Using data from the 12 hr time window aligned at the time of early prediction, spectral clustering yielded four clusters. The clusters are labeled in order of descending septic shock prevalence (Figure 1; Figure 1—figure supplement 1; Table 1). Prior to early prediction, the distribution of risk score is homogenous in all four clusters. This is followed by an abrupt increase in risk score within the hour immediately preceding the time of early warning. Following this transition, risk scores diverge into four distinct clusters. Clusters 1 and 4 are of particular interest as they represent the highest and lowest risk patients, respectively, and thus we primarily analyze differences between these two groups of patients. Table 1 shows that these clusters differ by septic shock prevalence (76.5% in the post-prediction high-risk cluster vs. 10.4% in the low-risk cluster) and mortality (43% in the high-risk cluster vs. 18% in the low-risk cluster). Higher risk clusters also have shorter times to septic shock onset (EWTs). In the high-risk cluster, the median elapsed time between the time of early prediction and time of septic shock onset is 9.8 hr, whereas in the low-risk cluster, it is 29.9 hr.

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These four clusters also stratify based on the proportion of patients who have been treated by the time of entry into the pre-shock state (Table 2). Higher risk clusters have a lower proportion of patients who have been treated by the time of early prediction (i.e. higher risk clusters contain more patients with greater delays in treatment). At time of early warning, 7.8% of patients in the high-risk cluster are adequately fluid resuscitated, whereas in the low-risk cluster, 21.3% of patients are adequately fluid resuscitated. Similarly, in the high-risk cluster, 14.3% of patients have been treated with vasopressors by time of early warning, whereas in the low-risk cluster, 50.7% of patients have been treated.

The trajectories of physiological variables associated with patients in each of the risk score clusters evolve in a similar fashion to the risk score (Figure 2). Lactate, which has the greatest contribution to risk score (Supplementary file 1B), has a steep increase preceding time of early prediction (Figure 2A). Systolic blood pressure has a steep decrease preceding time of early prediction (Figure 2B) and slight differences in mean heart rate (HR) are observed between clusters following time of early prediction (Figure 2C). The separation of these trajectories between the post-prediction low-risk and high-risk clusters, as quantified by Kullback-Leibler divergence, is not as great as that of risk score (Figure 2—figure supplement 1). Nevertheless, these rapid and coordinated changes of clinical feature trajectories mimic that seen in the risk score trajectory.

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The results of Table 2 demonstrate that the proportion of patients who have received interventions by time of early prediction varies between the low-risk and high-risk clusters. Early prediction immediately follows an abrupt change in physiological state, as reflected in a steep increase in risk score preceding threshold crossing. A greater proportion of low-risk patients than high-risk patients received intervention prior to this transition, indicating that cluster membership is influenced by intervention. Because, according to the Sepsis-3 criteria, septic shock is a treated state, with adequate fluid resuscitation and the administration of vasopressors as part of the labeling criteria, all septic shock patients receive intervention at some point; however, high-risk patients received one or more interventions at later times relative to the time of early warning as compared to low-risk patients. Moreover, median early warning time is shorter in the high-risk cluster than in the low-risk cluster.

There is not only a temporal difference in initiation of intervention between low-risk and high-risk patients, but also a difference in their physiological states prior to intervention. Table 3 gives the mean values of 20 significantly different features (Wilcoxon rank-sum test, p<0.01, Bonferroni corrected) at 1 hr prior to the first instance of adequate fluid administration, and the eight significantly different features at 1 hr prior to the first instance of vasopressor administration. Not only do patients in the high-risk cluster receive treatment later than low-risk patients (on average), but patients in the high-risk cluster are also in a more severe state 1 hr prior to the first instance of each intervention than those in the low-risk cluster, with higher HR, lower blood pressure, higher lactate, and higher SOFA scores. The data demonstrate that the high-risk and low-risk clusters, the two most distinct in risk trajectory and outcome, differ in patient physiology immediately prior to the first instance of treatment with fluids or vasopressors.

One application of patient stratification via clustering is to predict whether or not any given patient is classified as high-risk. Patients predicted to be in the high-risk cluster are more severely ill than those predicted to be in the low-risk cluster. Classification of risk trajectories was performed using k-nearest neighbors, using between 0 and 12 hr of data following time of early prediction (Figure 3). As the amount of available post-threshold-crossing data increases, so too does the accuracy of classification of patient trajectories. Using a single observation subsequent to time of early prediction, high-risk trajectories can be classified with 76% accuracy. With 10 hr of data (at the current rate of data collection), accuracy exceeds 95%.

Figure 3

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All septic shock patients, as determined by the Sepsis-3 criteria, are treated at some point preceding or at the time of shock onset. Therefore, it is important to distinguish between physiological changes driven by disease progression (which can be observed prior to the first intervention), and changes in physiological state that may reflect response to intervention. We repeated our analysis of risk score trajectories by aligning risk scores about the time of first intervention. First intervention was defined as the earliest time antibiotics were ordered, vasopressors were administered, or adequate fluid resuscitation was achieved. Spectral clustering produced five clusters stratified by septic shock prevalence and mortality (Figure 4; Figure 4—figure supplement 1; Table 4). The highest risk cluster has a 75.9% prevalence of septic shock, and 42.2% mortality, whereas the lowest risk cluster has a 19.2% prevalence of septic shock, and 26.4% mortality. Furthermore, these clusters stratify by the mean time between entry into pre-shock and the time of first intervention (Figure 4). Differences in these times between clusters is statistically significant at the 99% confidence level (Wilcoxon rank-sum test, Bonferroni corrected). In the highest-risk clusters, there is the greatest delay between threshold crossing and the initiation of intervention. In the two lowest-risk clusters, initiation of intervention precedes entry into the pre-shock state on average. Note that risk score trajectories begin to diverge prior to the time of first intervention. For example, in the post-intervention high-risk (red line) cluster 1, the risk score is increasing more than 5 hr before the first intervention is achieved. In the low-risk cluster 5 (magenta line), the risk score is decreasing approximately 3 hr before the first intervention is achieved. In general, the decline of risk scores follows the time of completion of first intervention. However, twelve hours following intervention, patient risk in most clusters is only slightly reduced compared to the value of risk score at the time of first intervention. These results demonstrate that, in the high risk clusters (clusters 1–3), the rate at which risk score growth slows and eventually declines following intervention is relatively slow when compared to rate of risk score growth prior to time of first intervention. Cluster membership, and hence patient risk, is therefore largely determined by patient state at time of first intervention. These results suggest that timely interventions are key to managing patient risk.

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All datasets utilized in this publication are publicly available; the eICU database can be accessed at https://eicu-crd.mit.edu/.

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Author details

1. Ran Liu

   1. Institute for Computational Medicine, The Johns Hopkins University, Baltimore, United States
   2. Department of Biomedical Engineering, The Johns Hopkins University School of Medicine & Whiting School of Engineering, Baltimore, United States

   Contribution

   Conceptualization, Software, Formal analysis, Investigation, Writing - original draft, Writing - review and editing

   For correspondence

   rliu14@jhu.edu

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-0866-9281

2. Joseph L Greenstein

   Institute for Computational Medicine, The Johns Hopkins University, Baltimore, United States

   Contribution

   Methodology, Writing - review and editing

   Competing interests

   No competing interests declared

3. James C Fackler

   1. Department of Anesthesiology and Critical Care Medicine, The Johns Hopkins University School of Medicine, Baltimore, United States
   2. Department of Pediatrics, The Johns Hopkins University School of Medicine, Baltimore, United States

   Contribution

   Conceptualization, Methodology, Writing - review and editing

   Competing interests

   No competing interests declared

4. Melania M Bembea

   1. Department of Anesthesiology and Critical Care Medicine, The Johns Hopkins University School of Medicine, Baltimore, United States
   2. Department of Pediatrics, The Johns Hopkins University School of Medicine, Baltimore, United States

   Contribution

   Conceptualization, Writing - review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0003-4984-520X

5. Raimond L Winslow

   1. Institute for Computational Medicine, The Johns Hopkins University, Baltimore, United States
   2. Department of Biomedical Engineering, The Johns Hopkins University School of Medicine & Whiting School of Engineering, Baltimore, United States

   Contribution

   Conceptualization, Resources, Supervision, Funding acquisition, Methodology, Writing - review and editing

   For correspondence

   rwinslow@jhu.edu

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0003-1719-1651

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