Question

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.

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

Hint:

Sensitivity = TP / all truly diseased = 90 / 100.

Answer 1

The Correct Option is A

Step 1: Recall the formula. Sensitivity is the ability of a test to correctly identify those who truly have the disease. \[\text{Sensitivity} = \frac{a}{a+c}\] where a = true positives and c = false negatives.
Step 2: Set the gold standard. The gold standard found 100 true diseased people. The screening test detected 90 of these as positive, so true positives a = 90.
Step 3: Find false negatives. The remaining diseased people missed by the screening test are false negatives, c = 100 - 90 = 10.
Step 4: Compute. \[\text{Sensitivity} = \frac{90}{90+10} = \frac{90}{100}\] Hence option (a) is correct. The distractors 80/100 and 100/100 use wrong true-positive counts, and 100/110 mixes total positives incorrectly.