Turning a 7.8% Sensor Error Into a Safe Alert

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

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Ada ADA · CALCULATION AUDIT

Turning a 7.8% Sensor Error Into a Safe Alert

This chapter pairs a program-economics claim with a safety-critical one, and the safety number is the one that must be exactly right: a continuous glucose monitor carries a 7.8% MARD error, so a reading near the 54 mg/dL danger line can drift several mg/dL above the true value. The chapter’s fix is to alert early — at 62 mg/dL, not 54 — sizing the buffer from the sensor’s own error rather than the clinical cutoff. This audit re-derives that buffer to ask how a 7.8% sensor error becomes a genuinely safe alert.

Companion to the chapter Medication Adherence — every number here comes from that chapter.

Ada: This chapter mixes a program-economics claim with a safety-critical one, and the safety number is the one that must be exactly right. Let me check the adherence return first, then the CGM buffer that decides when an insulin app warns a patient.

  • Adherence savings: 5,000 x (0.72 - 0.52) x 1,200 = 5,000 x 0.20 x 1,200 = 1,200,000 per year; net of a 420,000 program, 1,200,000 - 420,000 = 780,000, paying back in 420,000 / 780,000 x 12 = 6.46, about 6.5 months.
  • CGM low alert: a 15% buffer above the 54 mg/dL danger line is 54 x 1.15 = 62.1, so the app fires at 62 mg/dL, not 54.
  • CGM high alert: a 10% buffer below 250 mg/dL is 250 x 0.90 = 225, firing at 225 mg/dL.
  • Why the buffer is needed: at a true 60 mg/dL, a 7.8% MARD spreads the reading across 60 x 0.078 = 4.68, i.e. about 55-65 mg/dL, so a sensor value sitting comfortably above 54 can still hide a dangerous true glucose.

All consistent. The design meaning is that the safety buffer is not a guess – it is the sensor’s own error spec turned into distance: because the reading can drift several mg/dL above truth near the danger zone, alerting at 62 instead of 54 buys back exactly that uncertainty, which is why a safety-critical IoT design sizes its thresholds from the MARD rather than from the clinical cutoff alone.

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