Question:medium
In a screening test for diabetes mellitus, out of a population of 1000, 90 were positive. The gold standard test was then done, in which 100 were positive. Calculate the sensitivity of the screening test.
In a screening test for diabetes mellitus, out of a population of 1000, 90 were positive. The gold standard test was then done, in which 100 were positive. Calculate the sensitivity of the screening test.
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Sensitivity = TP / all truly diseased = 90 / 100.
Updated On: Jun 23, 2026
- 90/100
- 100/110
- 80/100
- 100/100
Show Solution
The Correct Option is A
Solution and Explanation
Step 1: Anchor on the truth standard. The disease is defined by the gold standard, which labels 100 individuals as truly diabetic. Sensitivity asks: of these 100, how many did the screening test catch?
Step 2: Read off true positives. The screening test flagged 90 positives, all assumed to be among the truly diseased, so true positives $a = 90$.
Step 3: Account for the missed cases. The screening test failed to detect $100 - 90 = 10$ genuinely diseased people; these are the false negatives $c = 10$.
Step 4: Plug into the relation. \[\text{Sensitivity} = \frac{a}{a+c} = \frac{90}{90+10} = \frac{90}{100}\] The denominator is always the total truly diseased (100), confirming option (a) and ruling out the variants that misuse the count.
\[\boxed{90/100}\]
Step 2: Read off true positives. The screening test flagged 90 positives, all assumed to be among the truly diseased, so true positives $a = 90$.
Step 3: Account for the missed cases. The screening test failed to detect $100 - 90 = 10$ genuinely diseased people; these are the false negatives $c = 10$.
Step 4: Plug into the relation. \[\text{Sensitivity} = \frac{a}{a+c} = \frac{90}{90+10} = \frac{90}{100}\] The denominator is always the total truly diseased (100), confirming option (a) and ruling out the variants that misuse the count.
\[\boxed{90/100}\]
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