Two rules for choosing the test
The infection to be screened is curable, can be passed to the newborn, and is serious if missed. These features call for the most sensitive test available, since every missed case is harmful and treatment is effective. But the program has a hard limit: every positive screen must be confirmed, and the laboratory can confirm no more than 150. The best test is the most sensitive one whose number of positive screens fits within the confirmation capacity.
Calculating positives for each test
With 1,000 women and 5% prevalence, 50 are infected and 950 are not. True positives = sensitivity × 50; false positives = (1 − specificity) × 950. The test at 98%/80% gives 49 + 190 = 239 positives, above capacity. The test at 86%/98% gives 43 + 19 = 62 positives and misses 7. The test at 80%/96% gives 40 + 38 = 78 positives and misses 10. The test at 90%/90% gives 45 + 95 = 140 positives, within the limit, and misses only 5.
| Sensitivity / specificity | True positives | False positives | Total positives | Missed infections |
|---|
| 98% / 80% | 49 | 190 | 239 (over 150) | 1 |
| 86% / 98% | 43 | 19 | 62 | 7 |
| 80% / 96% | 40 | 38 | 78 | 10 |
| 90% / 90% | 45 | 95 | 140 | 5 |
Why the other tests are not best
The 98%/80% test misses only one infection, which makes it attractive, but its 239 positives exceed what the laboratory can confirm, so many women would be left without confirmation. The 86%/98% and 80%/96% tests fit easily within capacity, but they miss 7 and 10 infections, more than the 90%/90% test. Watch out! With low prevalence, false positives come mostly from the large uninfected group, so even a modest drop in specificity adds many positives; always calculate them rather than judging by the percentages.
Exam takeaway
First eliminate tests that exceed the practical limit, then choose the most sensitive of those that remain. This reasoning reflects real program planning, where test accuracy must be balanced against laboratory capacity, cost, and follow-up. Women with a positive screen are confirmed and treated promptly, and the newborn is protected through treatment during pregnancy.