Did the Filter Find More Signal, or Just Remove Noise?
Did the Filter Find More Signal, or Just Remove Noise?
Ada re-derives this chapter’s own numbers step by step, at full precision
ADA · CALCULATION AUDIT
Did the Filter Find More Signal, or Just Remove Noise?
A hospital monitoring system pushes 350 alerts per shift at the nurses’ station, and only 18% deserve action — alert fatigue at the level where clinicians start tuning warnings out. The chapter’s multi-stage filter (patient-specific thresholds, multi-parameter fusion, a prediction model) cuts the flood to 145 alerts with 43% actionable. This audit asks the question those numbers invite: did the filter find more real signal, or just remove noise?
Companion to the chapter Healthcare IoT — every number here comes from that chapter.
Select Calculate for 350 alerts per shift with 18% actionable before applying the filter.
Check compares 63 expected true alerts with 62 retained, showing that the higher actionable percentage mostly removes false alarms.
A filter is safer when false alerts fall while the 63-to-62 true-alert count remains nearly stable; percentage purity alone could hide missed clinical events.
See the relationship before changing it
The figure reads from left to right. The blue input is actionable share after filtering. The middle card names the page’s rule. The green output is actionable alerts. The arrow matters: change the input, apply the rule once, then read the result with its unit.
Derive the baseline in four named moves
- 1
Name the input. The chapter baseline is 43 %.
- 2
Name the relationship. actionable = 145 alerts/shift x share
- 3
Substitute with units. 145 x 43 / 100 = 62.35 alerts/shift
- 4
Read the result. Keep the unit beside the value, then use the result only inside the technical boundary below.
Predict, then change actionable share after filtering
Try Predict how actionable alerts responds when actionable share after filtering moves. Calculate actionable share after filtering; compare actionable alerts with that prediction.
Observe Return to 43 %. Recheck actionable alerts with actionable share after filtering at its chapter value.
Explain The percentage can rise while the count stays nearly flat. Check both.
Check yourself
What should you do before trusting a moved-slider result?
What does this small model leave out?
Technical boundaries
For the alert filter, excluded from this fixed arithmetic are patient-to-patient physiology, motion artefacts, sensor placement error, clinical sensitivity or specificity, or treatment outcomes.
Ada: The alert-fatigue pipeline makes two claims at once: alerts per shift fall from 350 to 145, and the actionable share climbs from 18% to 43%. It is easy to read that second number as “the system now finds more real emergencies.” Let me test that by counting actionable alerts instead of their percentage.
- Actionable before:
0.18 x 350 = 63.0real alerts inside the 350. - Actionable after:
0.43 x 145 = 62.35, about62real alerts inside the 145.
The count of real alerts barely moves — 63 before, 62 after. So the reduction did not come from finding more signal; it came from deleting noise. False alerts fell from 350 - 63 = 287 to 145 - 62 = 83, and of the 350 - 145 = 205 alerts removed, 287 - 83 = 204 were false.
The actionable percentage nearly triples, but not because the numerator grew: 62 / 145 = 0.428. The 43% is the arithmetic of a shrinking denominator over a preserved numerator, not new detection.
Design meaning: a rising “actionable %” is only trustworthy when the real-alert count holds steady — the safety test for a clinical alarm filter is that it strips false alerts without quietly dropping true ones, and 63 -> 62 is exactly the evidence that test demands.
Every number above is taken from the chapter’s own material and re-derived step by step.