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.

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.

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