If a diagnostic test is 100% sensitive and 100% specific, the apparent prevalence equals the true prevalence.

If a diagnostic test is 100% sensitive and 100% specific, the apparent prevalence equals the true prevalence.

• A. Apparent prevalence equals the true prevalence.
• B. Apparent prevalence equals zero.
• C. Apparent prevalence equals one minus true prevalence.
• D. Apparent prevalence cannot be determined.

Answer: (A)

When a diagnostic test is 100% sensitive and 100% specific, there are no misclassified individuals; every diseased person tests positive and every non-diseased person tests negative, so the apparent prevalence matches the true prevalence. This comes from the relation: apparent prevalence = sensitivity × true prevalence + (1 − specificity) × (1 − true prevalence). With Se = 1 and Sp = 1, it becomes apparent prevalence = true prevalence. Therefore the statement is true. The other possibilities would require some misclassification or ambiguity in test results, which cannot occur with a perfect test.

When a diagnostic test is 100% sensitive and 100% specific, there are no misclassified individuals; every diseased person tests positive and every non-diseased person tests negative, so the apparent prevalence matches the true prevalence. This comes from the relation: apparent prevalence = sensitivity × true prevalence + (1 − specificity) × (1 − true prevalence). With Se = 1 and Sp = 1, it becomes apparent prevalence = true prevalence. Therefore the statement is true. The other possibilities would require some misclassification or ambiguity in test results, which cannot occur with a perfect test.