Estimating true prevalence

If a test with less than 100% sensitivity and specificity is used to estimate prevalence of some characteristic, that estimate will invariably be biased. If the sensitivity and specificity of the test are known, we can estimate the true prevalence with the Rogan-Gladen estimator:

True Prevalence   =   Apparent Prevalence + (Specificity − 1) Specificity + (Sensitivity − 1) where The true prevalence is the proportion of all those who are tested who are actually positive. The apparent prevalence is the proportion of all those who are tested who, rightly or wrongly, test positive.

Note, however, that the apparent prevalence has to be greater than (specificity − 1) for this to be possible. Otherwise you will end up with a negative value for the true prevalence.

In practice this occurs quite frequently since it means (for example) that if the specificity is 0.95, you cannot obtain a corrected prevalence if the apparent prevalence is less than 0.05. In this situation you have to accept that it is simply not possible to accurately assess prevalence with the test available.