Why can a positive genetic test result have a much lower probability of indicating a condition than the test's accuracy suggests?

A positive genetic test result can have a lower probability of indicating a condition than the test's accuracy suggests because of the influence of the condition's prevalence in the population, a concept explained by Bayes’s theorem.21

While a test may have high sensitivity (correctly identifying those who have the condition) and high specificity (correctly identifying those who do not), the overall probability that a positive result is a "true positive" depends on the ratio of true positives to the total number of positive results, which includes false positives.

If a condition is rare, the number of false positives—even from a highly accurate test—can significantly outnumber the true positives. Mathematically, conditional probability shows that the probability of having the condition given a positive test result is calculated as:2

$$P(A|B)=\frac{P(A)P(B|A)}{P(B|A)P(A)+P(B|\text{not-}A)P(\text{not-}A)}$$

In this formula, $P(A)$ represents the low prevalence of the condition. Because $P(\text{not-}A)$ is very high, even a small false-positive rate ($P(B|\text{not-}A)$) generates a large number of false positives, which lowers the overall predictive value of a positive test result.3