Which of the following options correctly defines how sensitivity and specificity are calculated?

Which of the following options correctly defines how sensitivity and specificity are calculated?

• A. Sensitivity = true positives / (true positives + false negatives); Specificity = true negatives / (true negatives + false positives).
• B. Sensitivity = false positives / (false positives + true negatives); Specificity = false negatives / (false negatives + true positives).
• C. Sensitivity = true positives / (true positives + false negatives); Specificity = true negatives / (true negatives + false positives).
• D. Sensitivity = false negatives / (true positives + false negatives); Specificity = false positives / (true negatives + false positives).

Answer: (C)

Sensitivity and specificity measure how well a test identifies positives and negatives. Sensitivity is the proportion of actual positives that the test correctly identifies, calculated as true positives divided by the sum of true positives and false negatives. This denominator includes everyone who truly has the condition, and the numerator counts how many of them were correctly detected. Specificity is the proportion of actual negatives that the test correctly identifies, calculated as true negatives divided by the sum of true negatives and false positives. Here, the denominator covers all people without the condition, and the numerator counts how many of them were correctly labeled as negative. Think of a 2x2 setup with disease status and test result. True positives are those who have the disease and test positive; false negatives are those who have the disease but test negative; true negatives are those who do not have the disease and test negative; false positives are those who do not have the disease but test positive. Example: in 100 people, 20 have the disease. The test finds 15 of the diseased as positive (true positives) and misses 5 (false negatives). Among the 80 without disease, it correctly marks 70 as negative (true negatives) and incorrectly flags 10 as positive (false positives). Sensitivity = 15 / (15 + 5) = 0.75. Specificity = 70 / (70 + 10) = 0.875. Using false positives in the sensitivity calculation or false negatives in the specificity calculation would not reflect the test’s ability to correctly identify actual positives or actual negatives, respectively; those quantities belong in the other parts of the confusion matrix.

Sensitivity and specificity measure how well a test identifies positives and negatives. Sensitivity is the proportion of actual positives that the test correctly identifies, calculated as true positives divided by the sum of true positives and false negatives. This denominator includes everyone who truly has the condition, and the numerator counts how many of them were correctly detected.

Specificity is the proportion of actual negatives that the test correctly identifies, calculated as true negatives divided by the sum of true negatives and false positives. Here, the denominator covers all people without the condition, and the numerator counts how many of them were correctly labeled as negative.

Think of a 2x2 setup with disease status and test result. True positives are those who have the disease and test positive; false negatives are those who have the disease but test negative; true negatives are those who do not have the disease and test negative; false positives are those who do not have the disease but test positive.

Example: in 100 people, 20 have the disease. The test finds 15 of the diseased as positive (true positives) and misses 5 (false negatives). Among the 80 without disease, it correctly marks 70 as negative (true negatives) and incorrectly flags 10 as positive (false positives). Sensitivity = 15 / (15 + 5) = 0.75. Specificity = 70 / (70 + 10) = 0.875.

Using false positives in the sensitivity calculation or false negatives in the specificity calculation would not reflect the test’s ability to correctly identify actual positives or actual negatives, respectively; those quantities belong in the other parts of the confusion matrix.