Spectral clustering of risk score trajectories stratifies sepsis patients by clinical outcome and interventions received

Abstract

Sepsis is not a monolithic disease, but a loose collection of symptoms with diverse outcomes. Thus, stratification and subtyping of sepsis patients is of great importance. We examine the temporal evolution of patient state using our previously-published method for computing risk of transition from sepsis into septic shock. Risk trajectories diverge into four clusters following early prediction of septic shock, stratifying by outcome: the highest-risk and lowest-risk groups have a 76.5% and 10.4% prevalence of septic shock, and 43% and 18% mortality, respectively. These clusters differ also in treatments received and median time to shock onset. Analyses reveal the existence of a rapid (30-60 min) transition in risk at the time of threshold crossing. We hypothesize that this transition occurs as a result of the failure of compensatory biological systems to cope with infection, resulting in a bifurcation of low to high risk. Such a collapse, we believe, represents the true onset of septic shock. Thus, this rapid elevation in risk represents a potential new data-driven definition of septic shock.

Keywords: computational biology; none; sepsis; septic shock; stratification; systems biology.

Figure 1.. Risk score clusters obtained using spectral clustering on the 12 hr following time of early prediction.

Time 0 represents t_d, time of early prediction. Bold solid and dashed lines indicate mean risk within each cluster. Each solid line becomes a dashed line at the cluster median EWT (indicated on figure). Shaded areas indicate one standard deviation from the mean. Black horizontal line indicates risk score threshold for early prediction.

Figure 1—figure supplement 1.. Eigenvalues of Graph Laplacian of post-early prediction risk trajectories.

Figure 1—figure supplement 2.. Receiver operating characteristic curves for early prediction in eICU.

95% confidence intervals, estimated using 100 iterations of bootstrap, are indicated by the shaded area. Using XGBoost, we obtain an average performance of 0.912 AUC, 82.5% sensitivity, 84.1% specificity, a median early warning time of 10.3 hr, and 34.0% positive predictive value. Using GLM, we obtain an average performance of 0.894 AUC, 82.7% sensitivity, 80.8% specificity, a median early warning time of 10.5 hr, and 29.9% positive predictive value.

Figure 1—figure supplement 3.. Risk score clusters obtained using spectral clustering on the 12 hr following time of early prediction in the MIMIC-III database.

Time 0 represents t_d, time of early prediction. Shaded areas indicate one standard deviation from the mean. The red horizontal line indicates risk score threshold for early prediction. Clusters are numbered in descending order of septic shock prevalence.

Figure 2.. Physiological trajectories in (A) Lactate, (B) systolic blood pressure, and (C) heart rate for the 4 clusters of patients illustrated in Figure 1.

Solid lines indicate the mean value of each feature within each cluster. Shaded areas indicate an interval of 1 standard deviation from the mean.

Figure 2—figure supplement 1.. Kullback-Leibler Divergence of Risk Score and physiological variables between the highest-risk and lowest-risk clusters in the window surrounding early prediction.

Figure 2—figure supplement 2.. Physiological trajectories in (A) Lactate, (B) systolic blood pressure, and (C) heart rate for the 3 clusters of patients illustrated in Figure 1—figure supplement 3 in the MIMIC-III database.

Solid lines indicate the mean value of each feature within each cluster. Shaded areas indicate an interval of 1 standard deviation from the mean.

Figure 2—figure supplement 3.. Kullback-Leibler Divergence of Risk Score and physiological variables between the highest-risk and lowest-risk clusters in the window surrounding time of early prediction in the MIMIC-III database.

Figure 3.. Risk trajectory classification accuracy.

The duration of data used consequent to early prediction is specified by the x-axis. 90% confidence intervals, as empirically estimated using bootstrap, are indicated by the shaded area.

Figure 4.. Risk score trajectories following the first instance of intervention.

Threshold for early prediction is indicated by the horizontal line. Bold lines indicate mean risk within each cluster. Shaded areas indicate one standard deviation from the mean. The mean time within each cluster between entry into the pre-shock state and the time of first intervention is indicated on the right-hand side of the figure. A positive number indicates that the time of first intervention is after the time of threshold crossing, whereas a negative number indicates that the first intervention precedes entry into pre-shock.

Figure 4—figure supplement 1.. Eigenvalues of Graph Laplacian of post-intervention risk trajectories.

Figure 5.. Visualization of spectral clustering of risk score trajectories, for a simple example with two clusters.

Risk score trajectories (A) are clustered by using distances between trajectories (B) to project the data into a space in which they are easily separable (C). K-means clustering of the data in this new space yields clusters of risk scores (D).