Scenario: A hospital system is evaluating a consumer wearable that detects atrial fibrillation (AFib) for remote patient monitoring of 10,000 post-discharge cardiology patients. The device costs $150 per patient and promises to reduce emergency room visits by detecting AFib early.
Given:
- Wearable sensitivity: 92% (detects 92% of actual AFib episodes)
- Wearable specificity: 88% (correctly identifies 88% of non-AFib as normal)
- AFib prevalence in patient population: 12% (1,200 of 10,000 patients have AFib)
- Cost per false positive: $850 (unnecessary cardiology follow-up, ECG, maybe cardioversion)
- Cost per true positive: $200 (planned cardiology visit, medication adjustment)
- Cost per false negative: $12,000 (missed AFib leads to stroke, ER visit, hospitalization)
- Cost per true negative: $0 (no action needed)
Steps:
Step 1: Calculate Expected Outcomes Over 1 Year
Build a confusion matrix for 10,000 patients:
| Device Says AFib |
True Positive (TP) |
False Positive (FP) |
Positive Tests |
| Device Says Normal |
False Negative (FN) |
True Negative (TN) |
Negative Tests |
| Total |
1,200 (12% prevalence) |
8,800 |
10,000 |
Calculate each cell: - TP (Sensitivity x Positive): 0.92 x 1,200 = 1,104 true AFib detections - FN (Missed AFib): 1,200 - 1,104 = 96 missed AFib cases - TN (Specificity x Negative): 0.88 x 8,800 = 7,744 correctly identified as normal - FP (False alarms): 8,800 - 7,744 = 1,056 false AFib alerts
Step 2: Calculate Positive Predictive Value (PPV)
PPV = TP / (TP + FP) = 1,104 / (1,104 + 1,056) = 1,104 / 2,160 = 51.1%
Translation: When the wearable alerts “AFib detected,” only 51% of the time is it actually AFib. The other 49% are false positives.
Step 3: Calculate Financial Impact
Annual costs: - TP cost: 1,104 x $200 = $220,800 (planned interventions) - FP cost: 1,056 x $850 = $897,600 (unnecessary follow-ups) - FN cost: 96 x $12,000 = $1,152,000 (missed strokes) - TN cost: 7,744 x $0 = $0 - Wearable hardware: 10,000 x $150 = $1,500,000
Total annual cost: $3,770,400
Step 4: Compare to Baseline (No Wearable)
Without wearables, assume all AFib is detected only when symptoms occur: - Detected in ER (symptomatic): 40% x 1,200 x $12,000 = $5,760,000 - Undetected (asymptomatic): 60% x 1,200 x $0 (no immediate cost, but future stroke risk)
Baseline cost: ~$5,760,000 (conservative, ignores future complications)
Result: Wearable deployment saves $1,989,600 annually despite 49% false positive rate.
Step 5: Sensitivity Analysis on PPV
What if we could improve specificity from 88% to 95% with better algorithms?
Recalculate with 95% specificity: - FP drops to: (1 - 0.95) x 8,800 = 440 false positives - New PPV: 1,104 / (1,104 + 440) = 71.5%
New FP cost: 440 x $850 = $374,000 (saves $523,600/year)
Key Insights:
1. PPV depends on prevalence, not just sensor accuracy: The same 92% sensitivity / 88% specificity sensor would have: - PPV = 51% at 12% prevalence (this case) - PPV = 22% at 3% prevalence (screening general population) - PPV = 79% at 30% prevalence (high-risk ICU patients)
2. Specificity matters more than sensitivity for rare conditions: Improving specificity from 88% to 95% (7 points) has bigger impact than improving sensitivity from 92% to 99% (7 points) when prevalence is low.
3. False positives have hidden costs: Beyond the $850 direct cost, false alarms cause: - Patient anxiety and loss of trust - Alert fatigue (clinicians ignore future alerts) - Decreased app usage (patients disable notifications)
4. Deployment decision depends on cost ratios: This deployment works because: - False positive cost ($850) << False negative cost ($12,000) - True positive intervention ($200) is cheap compared to ER cost - The 14x cost ratio between FN and FP justifies accepting 49% false positive rate
Decision Rule: Deploy only if:
(FN_cost x FN_count + FP_cost x FP_count) < Baseline_cost
In this case: ($1,152K + $897K + $1,500K) < $5,760K → Deploy
If false positive cost were $2,000 instead of $850: - New FP cost: 1,056 x $2,000 = $2,112,000 - Total: $1,152K + $2,112K + $1,500K = $4,764K → Still worth it
If prevalence were only 3% (general population screening): - TP drops to 276 (sensitivity x 300 actual AFib) - FP jumps to 1,164 (12% of 9,700 non-AFib) - PPV drops to 19% (4 out of 5 alerts are false!) - New FP cost: 1,164 x $850 = $989,400 - Total: $331K (TP) + $989K (FP) + $216K (FN) + $1,500K = $3,036K - Baseline: $1,440K - Do NOT deploy (costs more than benefit)
Key Takeaway: Always calculate PPV for your specific patient population before deploying diagnostic IoT. Sensitivity and specificity alone don’t tell you whether the system is cost-effective. Prevalence, cost ratios, and false positive tolerance determine deployment viability.
