Health Economics Metrics

Topic 48 of 76 · HTA frameworks and prevention economics

Screening Economics

Screening economics govern the value of testing asymptomatic populations. The core mathematical fact: at low disease prevalence, even excellent tests generate mostly false positives — and the downstream cost of chasing them can swamp the benefit of the true finds.

Why it matters

Since 1968, WHO's Wilson–Jungner criteria have set the bar for population screening: the condition must be important, the test acceptable and accurate, effective treatment must exist, and the economics must balance. The UK National Screening Committee applies formal cost-effectiveness analysis before approving any national programme — and rejects most proposals. Every "AI will screen everyone for everything" pitch runs into this machinery, and usually loses to the arithmetic below.

The math

Positive predictive value (PPV) — the probability a positive result is real — collapses at low prevalence:

PPV = (sens × prev) / [sens × prev + (1 − spec) × (1 − prev)]

Example: sensitivity 90%, specificity 95%, prevalence 0.5%:
PPV = (0.9 × 0.005) / (0.9 × 0.005 + 0.05 × 0.995)
    = 0.0045 / (0.0045 + 0.04975) ≈ 8.3%

Eleven out of twelve positives are false. Full programme economics:

Cost per true case found = (screening cost + workup cost × all positives) / true positives
Then: is finding a case worth that? (earlier-intervention value per case,
      minus overdiagnosis harm — cases found that would never have mattered)

Worked example

AI retinal screening for a rare condition, 100,000 people, prevalence 0.5%, sens 90%, spec 95%, scan £15, confirmatory workup £400:

True positives:  100,000 × 0.005 × 0.90 = 450
False positives: 100,000 × 0.995 × 0.05 = 4,975
Cost = 100,000 × 15 + (450 + 4,975) × 400 = 1.5M + 2.17M = £3.67M
Cost per true case ≈ £8,156

If early treatment saves £20,000 + 1 QALY per case, the programme clears easily. Raise specificity to 99% (fewer false alarms): workup cost falls to (450 + 995) × 400 = £0.58M, total £2.08M, cost per case ≈ £4,622 — specificity, not sensitivity, is where screening economics are won at low prevalence.

Software engineering connection

Static analysis, security scanning, and anomaly detection are screening programmes over codebases and telemetry, with true-defect prevalence often well under 1% per alert-opportunity. The identical math explains alert fatigue: a 95%-specific scanner on low-prevalence code drowns teams in false positives, and every false positive costs attention and erodes trust until real alerts get ignored (the clinical term is screening harm; the engineering term is pager numbness). The remedies transfer from health: raise specificity before sensitivity, screen higher-prevalence subpopulations (risk-based targeting ↔ changed-code-only scanning), and count triage cost in the tool's economics — see NNT and clinical AI evaluation.

Pitfalls

  • Quoting sensitivity/specificity without prevalence — accuracy without PPV is marketing.
  • Ignoring overdiagnosis: finding indolent "disease" that would never have harmed triggers real treatment costs and harms.
  • Lead-time bias: earlier detection without changed outcomes inflates apparent survival — see earlier intervention.

Sources