If you know the sensitivity and specificity of a test, true prevalence can be estimated by which formula?

• A. p(D+) = (apparent prevalence + specificity - 1) / (sensitivity + specificity - 1).
• B. p(D+) = apparent prevalence * (sensitivity + specificity - 1).
• C. p(D+) = (apparent prevalence - specificity) / (sensitivity - specificity).
• D. p(D+) = (apparent prevalence + specificity - 1) / (sensitivity + specificity - 1).

Answer: (D)

The main idea is to adjust the observed (apparent) prevalence for misclassification using the test’s sensitivity and specificity. If the true prevalence is P and the test has sensitivity Se and specificity Sp, the observed proportion testing positive (apparent prevalence) is AP = Se·P + (1 − Sp)·(1 − P). This accounts for true positives among those with disease and false positives among those without.

Solving for P gives AP = SeP + (1 − Sp) − (1 − Sp)P = (Se + Sp − 1)P + (1 − Sp). Rearranging: AP − (1 − Sp) = (Se + Sp − 1)P, so P = [AP + Sp − 1] / (Se + Sp − 1).

So true prevalence equals apparent prevalence plus specificity minus one, all divided by sensitivity plus specificity minus one. The denominator is Youden’s index (a measure of overall test accuracy beyond chance). If Se + Sp − 1 is zero, the test provides no information for estimating prevalence.