Definition
The Positive Predictive Value is defined as
where a "true positive" is the event that the test makes a positive prediction, and the subject has a positive result under the gold standard, and a "false positive" is the event that the test makes a positive prediction, and the subject has a negative result under the gold standard.
The following diagram illustrates how the positive predictive value, negative predictive value, sensitivity, and specificity are related.
| Condition (as determined by "Gold standard") |
||||
| Condition Positive | Condition Negative | |||
| Test Outcome |
Test Outcome Positive |
True Positive | False Positive (Type I error) |
Positive predictive value = Σ True Positive Σ Test Outcome Positive |
| Test Outcome Negative |
False Negative (Type II error) |
True Negative | Negative predictive value = Σ True Negative Σ Test Outcome Negative |
|
| Sensitivity = Σ True Positive Σ Condition Positive |
Specificity = Σ True Negative Σ Condition Negative |
|||
Note that the positive and negative predictive values can only be estimated using data from a cross-sectional study or other population-based study in which valid prevalence estimates may be obtained. In contrast, the sensitivity and specificity can be estimated from case-control studies.
If the prevalence, sensitivity, and specificity are known, the positive predictive value can be obtained from the following identity:
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