What 86.6% Sensitivity Actually Buys

What 86.6% Sensitivity Actually Buys

Ada re-derives this chapter’s own numbers step by step, at full precision

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Ada ADA · CALCULATION AUDIT

What 86.6% Sensitivity Actually Buys

In a trial of 1,000 infants over 180 days, a self-powered smart diaper catches 71 of 82 real UTIs — a sensitivity of 86.6% — while raising only 32 false alarms across 180,000 monitoring-days, a specificity of 99.98% that helps prevent 7 kidney infections and turn a $30,000 device into a positive return. This is safety-critical, so the audit rebuilds the confusion matrix and asks what that modest-sounding 86.6% sensitivity actually buys — and whether it, or the specificity, is what makes the device adoptable.

Companion to the chapter Baby Monitoring — every number here comes from that chapter.

See the relationship before changing it

The figure reads from left to right. The blue card is true positives. The middle card applies the page rule. The green card is sensitivity. Walk the arrows once: set the input, apply the rule, then read the result with its unit.

True positives changes sensitivity An input card leads through the rule sensitivity = true positives / 82 x 100 to the sensitivity result. INPUT PAGE INPUT APPLY THE RULE predict calculate check units OUTPUT RESULT
Walk the arrows. More true detections raise sensitivity; specificity is a separate safety gate.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline is 71 of 82 UTIs.

  2. 2

    Name the relationship. sensitivity = true positives / 82 x 100

  3. 3

    Substitute with units. 71 / 82 x 100 = 86.59%

  4. 4

    Read the result. Keep the unit beside the value. Use it only inside the technical boundary on this page.

Predict, then change true positives

Try Predict the direction of sensitivity = true positives / 82 x 100. Test another true positives, then compare sensitivity.

71 of 82 UTIs
Chapter baseline
Sensitivity

Observe More true detections raise sensitivity; specificity is a separate safety gate. Reset true positives to 71 and compare sensitivity.

Explain More true detections raise sensitivity; specificity is a separate safety gate.

Check yourself

What should you do before trusting a moved-control result?
Answer: Predict its direction, apply the shown relationship, keep the units, and reset to the worked baseline.
What does this small model leave out?
Answer: Only true positives moves here. Field effects named in the technical boundary stay fixed.

Honesty note. This teaching model changes only true positives. It is not a field prediction.

TryOpen Check derivation at the displayed false-alarm rate and the chapter's daily event count.
ObserveThe trial records 32 false alarms across 180,000 monitoring-days while 71 of 82 true UTIs appear in the sensitivity count.
ExplainSensitivity is 71 / 82 because missed real infections set that ratio, whereas specificity and caregiver burden depend on false alarms across all non-UTI monitoring-days.

Ada: This is safety-critical, so every digit matters. The smart-diaper trial reports 86.6% sensitivity, 99.98% specificity, and a positive return. Let me rebuild the confusion matrix and the cost case from the raw counts – 82 real UTIs, 71 true positives, 32 false positives, 11 false negatives, over 180,000 monitoring-days.

  • Sensitivity: 71 / (71 + 11) = 71 / 82 = 0.865854, which rounds to 86.6%.
  • Non-UTI days: 180,000 - 82 = 179,918; true negatives: 179,918 - 32 = 179,886.
  • Specificity: 179,886 / 179,918 = 0.999822, which rounds to 99.98% – one false alarm per 179,918 / 32 = 5,622 clean days.
  • Prevented kidney infections: 82 x 0.125 - 82 x 0.04 = 10.25 - 3.28 = 6.97, which rounds to 7 cases.
  • Cost case: 7 x 7,000 = 49,000 in avoided hospitalisation against a 30,000 device cost – a net 49,000 - 30,000 = 19,000.

Every figure reconciles. The design meaning is that the modest-sounding 86.6% sensitivity is not what makes this device adoptable – the 99.98% specificity is, because at a base rate of 82 events in 180,000 days even a small false-positive rate would flood caregivers, and it is that near-zero false-alarm burden, not the detection rate, that keeps the $19,000 net benefit from being erased by lost parental trust.

Technical boundaries
This fixed-rate audit omits changing infant state, correlated sensor errors, alarm suppression, caregiver response, device placement, and clinical validation.

Work the audit first, then check the displayed derivation.

Every number above is taken from the chapter’s own material and re-derived step by step.