Sepsis Early-Warning CUSUM Detector

Deterioration Scenario

Detector Tuning

Drift rate 1.0 bpm/min

CUSUM slack k 3.0 bpm

CUSUM alarm threshold h 15

Fixed-threshold alarm 115 bpm

Live Status

Heart rate

80.0 bpm

CUSUM S⁺

0.0

Lead time gained

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How it works

Hospitals stream thousands of vital-sign readings per patient per shift. A single elevated heart-rate reading is normal noise; a slow, sustained drift above baseline is an early physiological signature of conditions like sepsis, and it can start hours before any one reading crosses a classic fixed alarm threshold.

A CUSUM (cumulative sum) control chart accumulates small persistent deviations instead of judging each reading alone:

S⁺(n) = max(0, S⁺(n-1) + (x(n) − μ0 − k))
alarm when S⁺(n) > h

x(n)  = heart-rate reading at sample n
μ0    = baseline (resting) heart rate
k     = slack — the per-sample drift you tolerate as noise
h     = decision threshold — how much accumulated evidence triggers an alert

Drift rate — how fast the simulated patient's true heart rate climbs once deterioration starts (bpm per simulated minute).
Slack k — raise it to ignore small fluctuations (fewer false alarms, slower detection); lower it to catch smaller drifts sooner.
Threshold h — how much accumulated evidence is required before CUSUM fires. Lower h reacts faster but tolerates more noise-driven false positives.
Fixed-threshold alarm — the conventional "beep when HR > X bpm" monitor, shown for comparison. It only fires once a single reading actually crosses the line.

Click Trigger Deterioration and watch the cyan CUSUM trace climb and cross its threshold well before the red fixed-threshold line does — the gap between the two alarm times is the early-warning lead time a streaming statistical model buys the clinical team.

Heart rate stream CUSUM S⁺ statistic Fixed-threshold line

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