Two Screening Pathways: Weighing Cost Against Missed Cases
A clinic screens 20,000 adults for a condition affecting 1 in 200 people. The first-line test has 90% sensitivity and 95% specificity. Under Pathway A, everyone who tests positive goes straight to a confirmatory test costing £180. Under Pathway B, everyone who tests positive first takes a triage test costing £40, with 80% sensitivity and 80% specificity; only those positive on both proceed to the £180 confirmatory test. Both pathways use the identical first-line test, and everyone offered testing accepts. Assume the accuracy figures apply exactly to this population.
1. Calculate how many confirmatory tests are performed under each pathway, and how many true cases remain undetected overall.
Read the worked answer
Population split: 100 people have the condition (20,000 ÷ 200); 19,900 do not.
First-line test: sensitivity 90% → 90 true positives, 10 missed. Specificity 95% → 5% of 19,900 = 995 false positives. Total positives = 1,085.
Pathway A: confirmatory tests = 1,085. Undetected cases = 10.
Pathway B: triage is given to all 1,085.
- Of the 90 true positives: 80% = 72 stay positive, 18 become negative and are lost.
- Of the 995 false positives: 20% = 199 stay positive.
- Confirmatory tests = 72 + 199 = 271. Undetected cases = 10 + 18 = 28.
So B roughly quarters the confirmatory workload (271 vs 1,085) but nearly triples the missed cases (28 vs 10).
2. Calculate the total testing cost of each pathway and the cost per true case detected. Present both, then state what the comparison does and does not tell you.
Read the worked answer
Pathway A: 1,085 × £180 = £195,300. Cases detected = 90 → £2,170 per case detected.
Pathway B: triage 1,085 × £40 = £43,400; confirmatory 271 × £180 = £48,780. Total = £92,180. Cases detected = 72 → £1,280 per case detected.
What it tells you: B saves £103,120 (53%) and is cheaper per case found.
What it does not tell you: it does not tell you B is the better programme. Cheaper per case found is not the same as better care - B misses 18 additional real cases, and those people are falsely reassured. Whether that trade is acceptable depends on how much harm a missed diagnosis causes, which the figures do not quantify. The comparison also treats a false positive as free apart from the £180, ignoring anxiety and repeat visits.
3. A commissioner argues: 'Pathway B is clearly superior because it costs half as much and does almost the same job.' Give two reasons a decision-maker should hesitate before accepting this.
Read the worked answer
1. 'Almost the same job' is doing hidden work. B detects 72 of 100 cases against A's 90 - an 18% relative loss of detection, and the 18 missed people are told they are clear. If the condition is one where late diagnosis is serious, a 20% drop in detection is a clinical harm, not a rounding error. The cost saving is certain; the harm is probabilistic and falls on identifiable individuals.
2. The model's assumptions are doing a lot of the work. The arithmetic assumes the published sensitivity and specificity hold exactly in this population and that the triage test behaves independently of the first test. In practice, tests that both miss the same kind of case (for example early or low-burden disease) will miss more than the model predicts, and the true detection loss could exceed 18. A pilot would be needed before committing.
A defensible conclusion: B is worth piloting with audit of interval cancers/diagnoses, not adopting on cost alone.