Question

In a screening test for diabetes mellitus, out of 1000 population, 90 were positive. The gold standard test was then done, in which 100 were positive. Calculate the sensitivity.

• A. 90/100
• B. 100/110
• C. 80/100
• D. 100/100

Hint:

Sensitivity = true positives / all diseased (true positives + false negatives).

Answer 1

The Correct Option is A

Step 1: Sensitivity tells us what proportion of the genuinely diseased people are picked up by the screening test, given by $\frac{a}{a+c}$ with $a$ true positives and $c$ false negatives.

Step 2: The gold standard fixes the total number of true diabetics at 100, so the denominator of all diseased persons is 100.

Step 3: Of these, the screen flagged 90 correctly, leaving $100 - 90 = 10$ diseased individuals it failed to detect.

Step 4: Dividing the correctly detected cases by all true cases gives \[\frac{90}{100},\] which is the sensitivity. \[\boxed{90/100}\]