# Positive predictive value

Last revised by Stefan Tigges on 6 Jan 2024

Positive predictive value (PPV) is one of the 4 basic diagnostic test metrics in addition to sensitivity, specificity and negative predictive value. Positive predictive value is a measure of how often someone who tests positive for disease actually has disease and is calculated by dividing the number of true positives (TP) by the number of people who tested positive, i.e. true positives and false positives (FP):

• TP/(TP + FP)

The formula shows that a high PPV is achieved by maximizing true positives and minimizing false positives.

Positive predictive value can be expressed as a conditional probability:

• P(Disease positive|Test positive)

Bayes' theorem can be used to calculate PPV if sensitivity, specificity, and the pretest probability (p) are known:

• PPV = [(Sensitivity) x (p)] / [Sensitivity x (p) + (1 - specificity) x (1 - p)]

Unlike sensitivity and specificity, PPV depends to some extent on disease prevalence. When prevalence increases, PPV increases because the proportion of true positives to false positives increases. For example, if the entire population of interest had disease, all of the positives would be true positives, there would be no false positives, resulting in a PPV of 100%. When prevalence decreases, PPV decreases because the proportion of true positives to false positives decreases. For example, if no one in the population of interest had disease, all of the positives would be false positives, there would be no true positives, resulting in a PPV of 0%. Positive predictive value and negative predictive value move in opposite directions as prevalence increases or decreases.