Post-test probabilities help determine how likely it is that a test result (positive or negative) correctly reflects the presence or absence of disease. They include Positive Predictive Value (PPV), Negative Predictive Value (NPV), and Accuracy.
Positive Predictive Value (PPV)
PPV is the probability that a person with a positive test result truly has the disease. It reflects how reliable a positive test result is.
Formula:
Interpretation:
- TP (True Positive): Sick people correctly identified as sick.
- FP (False Positive): Healthy people incorrectly identified as sick.
- PPV depends on disease prevalence — higher prevalence → higher PPV.
Negative Predictive Value (NPV)
NPV is the probability that a person with a negative test result truly does not have the disease. It reflects how reliable a negative test result is.
Formula:
Interpretation:
- TN (True Negative): Healthy people correctly identified as healthy.
- FN (False Negative): Sick people are incorrectly identified as healthy.
- NPV increases when disease prevalence decreases.
Accuracy
Definition:
Accuracy measures the overall correctness of a test — the proportion of all results (positive and negative) that are true.
Formula:
Interpretation:
- Reflects how well the test identifies both diseased and healthy individuals correctly.
- Useful for assessing overall test performance, but not sufficient alone.
Summary Table
| Concept | Definition | Formula | Affected by Prevalence |
|---|---|---|---|
| PPV | Probability that a positive test = disease present | TP / (TP + FP) | ✅ Increases with higher prevalence |
| NPV | Probability that a negative test = no disease | TN / (TN + FN) | ⬇️ Decreases with higher prevalence |
| Accuracy | Overall proportion of correct results | (TP + TN) / (TP + TN + FP + FN) | ❌ Not directly affected |
🎯 Learning Objective
By the end of this topic, you should be able to interpret diagnostic test performance by understanding how PPV, NPV, and Accuracy relate to true and false results, and how disease prevalence influences post-test probabilities in real-world clinical decision-making.
