What is the equation for sensitivity of a test?

• A. a/(a+b)
• B. b/(a+d)
• C. d/(c+d)
• D. (a+c)/(a+b+c+d)

Answer: (A)

Sensitivity is the true positive rate: among those who actually have the disease, what fraction does the test correctly identify? In the standard 2x2 labeling, true positives are a and false negatives are b, so sensitivity equals a/(a+b). This captures the idea of catching disease when it’s present.

The other expressions don’t measure this. Using a+d in the denominator mixes in those without disease and doesn’t reflect the disease group, giving a value that isn’t sensitivity. d/(c+d) is the proportion of true negatives among those without disease, i.e., specificity. The last expression, (a+c)/(a+b+c+d), is overall accuracy, the proportion of correct results across all individuals.