RPM Alarm Threshold: Sensitivity vs Alarm Fatigue

Alarm Threshold

Alarm threshold θ (bpm) 100

Critical prevalence 15%

Signal noise σ (bpm) 6

Critical severity Δμ (bpm) 35

Live Confusion Matrix

Sensitivity (recall)

—

Specificity

—

False alarms / hour

—

Missed criticals

—

Ward Legend

Normal patient (true negative) Critical patient (true positive risk) Alarm currently firing

How it works

Each of the 42 beds streams a noisy heart-rate reading. Normal patients fluctuate around a baseline μ_n = 75 bpm; critical patients run hotter around μ_c = μ_n + Δμ. Both are corrupted by sensor/physiological noise of standard deviation σ, modelled as an Ornstein–Uhlenbeck process:

dv = k(μ − v) dt + σ√dt · N(0,1)
alarm fires when v(t) > θ

Because the two populations' bell curves overlap, no threshold θ is perfect — this is classic signal-detection theory. For two Gaussians of equal σ the analytic detection rates are:

Sensitivity = 1 − Φ((θ − μc) / σ)
Specificity =  Φ((θ − μn) / σ)
Youden's J  = Sensitivity + Specificity − 1, maximised at θ* ≈ (μn + μc) / 2

Push θ low and every critical patient is caught (high sensitivity) but normal patients trigger constantly — the false-alarm rate that causes real-world alarm fatigue and desensitised staff. Push θ high and false alarms vanish but real deteriorations get missed. The "Set optimal θ" button jumps straight to the equal-variance Youden optimum given the current μn, μc and σ; the live confusion matrix is an exponentially-weighted running estimate sampled from the ward every frame, so it settles onto the analytic values within a few seconds.

Active alarms: 0 Simulated time: 0:00

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