How well a test with a given sensitivity and specificity identifies affected and unaffected persons is affected by the prevalence of disease in the population being studied. This approach assumes that the sensitivity and specificity for the test are constant.
total population =
= (TP) + (FP) + (TN) + (FN)
sensitivity =
= (TP) / ((TP) + (FN))
specificity =
= (TN) / ((TN) + (FP))
prevalence =
= ((TP) + (FN)) / (total)
where:
• TP = true positives
• FP = false positives
• TN = true negatives
• FN = false negatives
• sensitivity, specificity and prevalence are expressed as decimal fractions
If the above equations are rearranged:
(TP) + (FN) =
= (prevalence) * (total)
sensitivity =
= (TP) / ((prevalence) * (total))
TP =
= (sensitivity) * (prevalence) * (total)
FN =
= (TP) * (1 – (sensitivity)) / (sensitivity)
(TN) + (FP) =
= (total) * (1 – (prevalence))
TN =
= (specificity) * (total) * (1 – (prevalence))
specificity =
= (TN) / ((total) * (1 – (prevalence)))
FP =
= (TN) * (1 – (specificity)) / (specificity)
If the sensitivity, specificity, prevalence and total population size are given, then the distribution of true and false positives and negatives can be determined.
