Rebuilding the two-by-two table
Sensitivity and specificity are calculated from a two-by-two table that compares the screening test with the reference standard. At the original cut-off, the point-of-care test had 85 true positives, 15 false negatives, 48 false positives, and 352 true negatives, among 100 women with anemia and 400 without. The new cut-off counts more readings as positive. 10 of the 15 false negatives become positive, and 30 of the 352 true negatives become positive, while no positive becomes negative. The new table is: true positives 85 + 10 = 95; false negatives 15 − 10 = 5; false positives 48 + 30 = 78; true negatives 352 − 30 = 322.
Recalculating
Sensitivity is the proportion of people with the disease who test positive: 95 ÷ (95 + 5) × 100 = 95.0%. Specificity is the proportion of people without the disease who test negative: 322 ÷ (78 + 322) × 100 = 322 ÷ 400 × 100 = 80.5%. The column totals, 100 with anemia and 400 without, stay the same because the same 500 women are reclassified, not retested in a different population. Only the split within each column changes when the cut-off moves.
| Cell | Original cut-off | New cut-off |
|---|
| True positives | 85 | 95 |
| False negatives | 15 | 5 |
| False positives | 48 | 78 |
| True negatives | 352 | 322 |
| Sensitivity | 85.0% | 95.0% |
| Specificity | 88.0% | 80.5% |
The trade-off behind the numbers
Sensitivity and specificity do not change with prevalence, but they do change when the cut-off moves. A cut-off that calls more results positive catches more true cases, raising sensitivity, but it also labels more healthy people as positive, lowering specificity. That is exactly the pattern here. The distractors reflect common mistakes: keeping the old sensitivity of 85.0% as if it were fixed; keeping the old specificity of 88.0%; or dividing the new true negatives by the old true negatives (322 ÷ 352 = 91.5%) instead of by all 400 women without anemia. Watch out! The denominator of specificity is always everyone without the disease, never just the old true negatives.
Exam takeaway
Lowering the threshold for a positive test raises sensitivity and lowers specificity; raising it does the reverse. For anemia in pregnancy, a more sensitive cut-off may be preferred so that fewer anemic women are missed, but the RHU must then confirm more false positives with the laboratory test. In calculation items, always rebuild the full two-by-two table first, then apply the formulas column by column.